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

 0:  0: 1

 1:  1: 1

 2:  0: 1
     1: 1
     2: 1

 3:  0: 1
     3: 1

 4:  1: 1
     4: 1

 5:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1

 6:  3: 1
     6: 1

 7:  4: 1
     7: 1

 8:  0: 1
     1: 1
     2: 1
     3: 1
     8: 1

 9:  0: 1
     1: 1
     2: 1
     4: 1
     9: 1

10:  3: 1
     4: 1
     5: 1
     6: 1
     7: 1
    10: 1

11:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     8: 1
     9: 1
    11: 1

12:  3: 1
     6: 1
     8: 1
    12: 1

13:  4: 1
     7: 1
     9: 1
    13: 1

14:  6: 1
    14: 1

15:  7: 1
    15: 1

16:  3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     8: 1
     9: 1
    10: 1
    11: 1
    12: 1
    13: 1
    16: 1

17:  6: 1
     7: 1
    10: 1
    14: 1
    15: 1
    17: 1

18:  6: 1
     7: 1
    10: 1
    14: 1
    15: 1
    18: 1

19:  0: q
     3: q
     8: 1
     9: 1
    11: 1
    12: 1
    19: 1

20:  1: q
     4: q
     8: 1
     9: 1
    11: 1
    13: 1
    20: 1

21:  6: 1
    12: 1
    14: 1
    21: 1

22:  7: 1
    13: 1
    15: 1
    22: 1

23:  8: 1
     9: 1
    11: 1
    12: 1
    13: 1
    16: 1
    19: 1
    20: 1
    23: 1

24:  6: 1
     7: 1
    10: 1
    12: 1
    13: 1
    14: 1
    15: 1
    16: 1
    17: 1
    21: 1
    22: 1
    24: 1

25:  6: 1
     7: 1
    10: 1
    12: 1
    13: 1
    14: 1
    15: 1
    16: 1
    18: 1
    21: 1
    22: 1
    25: 1

26:  6: 1
     7: 1
    10: 1
    14: 1
    15: 1
    17: 1
    18: 1
    26: 1

27: 12: 1
    19: 1
    21: 1
    27: 1

28: 13: 1
    20: 1
    22: 1
    28: 1

29: 12: 1
    13: 1
    16: 1
    19: 1
    20: 1
    21: 1
    22: 1
    23: 1
    24: 1
    27: 1
    28: 1
    29: 1

30: 12: 1
    13: 1
    16: 1
    19: 1
    20: 1
    21: 1
    22: 1
    23: 1
    25: 1
    27: 1
    28: 1
    30: 1

31:  6: 1
     7: 1
    10: 1
    12: 1
    13: 1
    14: 1
    15: 1
    16: 1
    17: 1
    18: 1
    21: 1
    22: 1
    24: 1
    25: 1
    26: 1
    31: 1

32:  3: q
     4: q
     5: q
     6: q
     7: q
    10: q
    26: 1
    32: 1

33:  8: q
    12: q
    19: 1
    20: 1
    23: 1
    27: 1
    33: 1

34:  9: q
    13: q
    19: 1
    20: 1
    23: 1
    28: 1
    34: 1

35: 19: 1
    20: 1
    23: 1
    27: 1
    28: 1
    29: 1
    33: 1
    34: 1
    35: 1

36: 19: 1
    20: 1
    23: 1
    27: 1
    28: 1
    30: 1
    33: 1
    34: 1
    36: 1

37: 12: 1
    13: 1
    16: 1
    19: 1
    20: 1
    21: 1
    22: 1
    23: 1
    24: 1
    25: 1
    27: 1
    28: 1
    29: 1
    30: 1
    31: 1
    37: 1

38:  3: q
     4: q
     5: q
     6: q
     7: q
     8: q
     9: q
    10: q
    11: q
    12: q
    13: q
    16: q
    26: 1
    31: 1
    32: 1
    38: 1

39:  0: q^2
     1: q^2
     2: q^2
     3: q^2
     4: q^2
     5: q^2
    32: 1
    39: 1

40: 19: 1
    20: 1
    23: 1
    27: 1
    28: 1
    29: 1
    30: 1
    33: 1
    34: 1
    35: 1
    36: 1
    37: 1
    40: 1

41:  8: q
     9: q
    11: q
    12: q
    13: q
    16: q
    19: q
    20: q
    23: q
    31: 1
    37: 1
    38: 1
    41: 1

42: 19: q
    20: q
    27: q
    28: q
    33: 1
    34: 1
    35: 1
    36: 1
    42: 1

43:  0: q^2
     1: q^2
     2: q^2
     3: q^2
     4: q^2
     5: q^2
     8: q^2
     9: q^2
    11: q^2
    32: 1
    38: 1
    39: 1
    43: 1

44:  0: q^3
     1: q^3
     2: q^3
    39: 1
    44: 1

324 nonzero polynomials, and 361 zero polynomials,
 at 685 Bruhat-comparable pairs.