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

 0:  0: 1

 1:  0: 1
     1: 1

 2:  0: 1
     2: 1

 3:  1: 1
     3: 1

 4:  0: 1
     1: 1
     2: 1
     4: 1

 5:  2: 1
     5: 1

 6:  3: 1
     6: 1

 7:  5: 1
     7: 1

 8:  1: 1
     3: 1
     4: 1
     8: 1

 9:  2: 1
     4: 1
     5: 1
     9: 1

10:  6: 1
    10: 1

11:  3: 1
     6: 1
     8: 1
    11: 1

12:  5: 1
     7: 1
     9: 1
    12: 1

13:  4: 1
     8: 1
     9: 1
    13: 1

14:  7: 1
    14: 1

15:  6: 1
     8: 1
    10: 1
    11: 1
    13: 1
    15: 1

16:  8: 1
     9: 1
    11: 1
    12: 1
    13: 1
    16: 1

17:  7: 1
     9: 1
    12: 1
    13: 1
    14: 1
    17: 1

18:  6: 1
    10: 1
    11: 1
    18: 1

19:  7: 1
    12: 1
    14: 1
    19: 1

20:  8: 1
    11: 1
    13: 1
    15: 1
    16: 1
    20: 1

21:  9: 1
    12: 1
    13: 1
    16: 1
    17: 1
    21: 1

22: 11: 1
    12: 1
    16: 1
    18: 1
    19: 1
    22: 1

23:  7: 1
    12: 1
    14: 1
    17: 1
    19: 1
    23: 1

24:  6: 1
    10: 1
    11: 1
    15: 1
    18: 1
    24: 1

25:  4: q
     8: q
     9: q
    13: q
    16: 1
    20: 1
    21: 1
    25: 1

26: 11: 1
    15: 1
    16: 1
    18: 1
    20: 1
    22: 1
    24: 1
    26: 1

27:  5: q
     7: q
     9: q
    12: q
    17: 1
    21: 1
    23: 1
    27: 1

28:  3: q
     6: q
     8: q
    11: q
    15: 1
    20: 1
    24: 1
    28: 1

29: 12: 1
    16: 1
    17: 1
    19: 1
    21: 1
    22: 1
    23: 1
    29: 1

30:  2: q^2
     4: q^2
     5: q^2
     9: q^2
    21: 1
    25: 1
    27: 1
    30: 1

31: 16: 1
    20: 1
    21: 1
    22: 1
    25: 1
    26: 1
    29: 1
    31: 1

32:  1: q^2
     3: q^2
     4: q^2
     8: q^2
    20: 1
    25: 1
    28: 1
    32: 1

33: 17: 1
    21: 1
    23: 1
    27: 1
    29: 1
    33: 1

34: 15: 1
    20: 1
    24: 1
    26: 1
    28: 1
    34: 1

35: 13: q
    15: q
    16: q
    17: q
    20: q
    21: q
    26: 1
    29: 1
    31: 1
    33: 1
    34: 1
    35: 1

36: 21: 1
    25: 1
    27: 1
    29: 1
    30: 1
    31: 1
    33: 1
    36: 1

37:  0: q^3
     1: q^3
     2: q^3
     4: q^3
    25: 1
    30: 1
    32: 1
    37: 1

38: 20: 1
    25: 1
    26: 1
    28: 1
    31: 1
    32: 1
    34: 1
    38: 1

39: 29: 1
    31: 1
    33: 1
    35: 1
    36: 1
    39: 1

40: 26: 1
    31: 1
    34: 1
    35: 1
    38: 1
    40: 1

41: 25: 1
    30: 1
    31: 1
    32: 1
    36: 1
    37: 1
    38: 1
    41: 1

42: 22: q
    26: q
    29: q
    31: q
    35: 1
    39: 1
    40: 1
    42: 1

43: 31: 1
    35: 1
    36: 1
    38: 1
    39: 1
    40: 1
    41: 1
    43: 1

44: 35: 1
    39: 1
    40: 1
    42: 1
    43: 1
    44: 1

251 nonzero polynomials, and 570 zero polynomials,
 at 821 Bruhat-comparable pairs.