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

 0:  0: 1

 1:  1: 1

 2:  2: 1

 3:  3: 1

 4:  0: 1
     1: 1
     4: 1

 5:  0: 1
     2: 1
     5: 1

 6:  0: 1
     1: 1
     6: 1

 7:  2: 1
     3: 1
     7: 1

 8:  0: 1
     1: 1
     4: 1
     6: 1
     8: 1

 9:  0: 1
     1: 1
     4: 1
     6: 1
     9: 1

10:  0: 1
     1: 1
     2: 1
     4: 1
     5: 1
    10: 1

11:  0: 1
     1: 1
     2: 1
     5: 1
     6: 1
    11: 1

12:  0: 1
     2: 1
     3: 1
     5: 1
     7: 1
    12: 1

13:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1
     6: 1
     7: 1
    13: 1

14:  0: 1
     1: q+1
     2: 1
     4: 1
     5: 1
     6: 1
     8: 1
    10: 1
    11: 1
    14: 1

15:  0: 1
     1: q+1
     2: 1
     4: 1
     5: 1
     6: 1
     9: 1
    10: 1
    11: 1
    15: 1

16:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1
     6: 1
     7: 1
    11: 1
    12: 1
    13: 1
    16: 1

17:  1: q
     3: q
    13: 1
    17: 1

18:  0: 2
     1: 2
     2: q+1
     4: 2
     5: 1
     6: 2
     8: 1
     9: 1
    10: 1
    11: 1
    18: 1

19:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     7: 1
    10: 1
    12: 1
    19: 1

20:  0: 2
     1: 2
     2: 1
     3: 1
     4: 2
     5: 1
     6: 2
     7: 1
     8: 1
     9: 1
    10: 1
    13: 1
    20: 1

21:  0: 1
     1: 1
     2: 1
     4: 1
     5: 1
     6: 1
     8: 1
    10: 1
    11: 1
    14: 1
    18: 1
    21: 1

22:  0: 1
     1: 1
     2: 1
     4: 1
     5: 1
     6: 1
     9: 1
    10: 1
    11: 1
    15: 1
    18: 1
    22: 1

23:  0: 2
     1: 2
     2: q+1
     3: q+1
     4: 2
     5: 1
     6: 2
     7: q+1
     8: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    16: 1
    18: 1
    19: 1
    20: 1
    23: 1

24:  0: q
     1: q
     3: q
     4: q
    13: 1
    17: 1
    20: 1
    24: 1

25:  0: q+1
     1: q+1
     2: 1
     3: 1
     4: 1
     5: 1
     6: q+1
     7: 1
     8: 1
    10: 1
    11: 1
    12: 1
    13: 1
    14: 1
    16: 1
    20: 1
    25: 1

26:  0: q+1
     1: q+1
     2: 1
     3: 1
     4: 1
     5: 1
     6: q+1
     7: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    15: 1
    16: 1
    20: 1
    26: 1

27:  0: 2
     1: q+2
     2: 2
     3: q+1
     4: 2
     5: 2
     6: 2
     7: 1
     8: 1
     9: 1
    10: 2
    11: 2
    12: 1
    13: 2
    14: 1
    15: 1
    16: 1
    17: 1
    20: 1
    27: 1

28:  0: 2
     1: 2
     2: 2
     3: q^2+1
     4: 2
     5: 2
     6: 2
     7: 1
     8: 1
     9: 1
    10: 2
    11: 2
    12: 1
    13: 1
    14: 1
    15: 1
    16: 1
    18: 2
    19: 1
    20: 1
    21: 1
    22: 1
    23: 1
    27: 1
    28: 1

29:  0: q
     1: q
     2: q
     3: q
     4: q
     5: q
    10: q
    13: 1
    17: 1
    20: 1
    24: 1
    27: 1
    29: 1

30:  0: q+1
     1: q+1
     2: 1
     3: 1
     4: q+1
     5: 1
     6: q+1
     7: 1
     8: q+1
    10: 1
    11: 1
    12: 1
    13: 1
    14: 1
    16: 1
    18: 1
    19: 1
    20: 1
    21: 1
    23: 1
    25: 1
    30: 1

31:  0: q+1
     1: q+1
     2: 1
     3: 1
     4: q+1
     5: 1
     6: q+1
     7: 1
     9: q+1
    10: 1
    11: 1
    12: 1
    13: 1
    15: 1
    16: 1
    18: 1
    19: 1
    20: 1
    22: 1
    23: 1
    26: 1
    31: 1

32:  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
    16: 1
    20: 1
    25: 1
    27: 1
    32: 1

33:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    15: 1
    16: 1
    20: 1
    26: 1
    27: 1
    33: 1

34:  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
    16: 1
    18: 1
    19: 1
    20: 1
    21: 1
    23: 1
    25: 1
    27: 1
    28: 1
    30: 1
    32: 1
    34: 1

35:  0: q
     1: q
     2: q
     3: q
     4: q
     5: q
     6: q
     7: q
     8: q
    10: q
    13: q
    20: q
    27: 1
    29: 1
    32: 1
    35: 1

36:  0: q
     1: q^2+q
     2: q
     3: q
     4: q
     5: q
     6: q
     7: q
     8: q
    10: q
    11: q
    12: q
    13: q
    14: q
    16: q
    19: q
    30: 1
    36: 1

37:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    15: 1
    16: 1
    18: 1
    19: 1
    20: 1
    22: 1
    23: 1
    26: 1
    27: 1
    28: 1
    31: 1
    33: 1
    37: 1

38:  0: q
     1: q
     2: q
     3: q
     4: q
     5: q
     6: q
     7: q
     9: q
    10: q
    13: q
    20: q
    27: 1
    29: 1
    33: 1
    38: 1

39:  0: q
     1: q^2+q
     2: q
     3: q
     4: q
     5: q
     6: q
     7: q
     9: q
    10: q
    11: q
    12: q
    13: q
    15: q
    16: q
    19: q
    31: 1
    39: 1

466 nonzero polynomials, and 72 zero polynomials,
 at 538 Bruhat-comparable pairs.