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

 0:  0: 1

 1:  0: 1
     1: 1

 2:  0: 1
     2: 1

 3:  0: 1
     3: 1

 4:  0: 1
     1: 1
     3: 1
     4: 1

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

 6:  3: 1
     6: 1

 7:  0: 2
     1: 1
     2: 1
     3: 1
     7: 1

 8:  3: 1
     4: 1
     6: 1
     8: 1

 9:  3: 1
     5: 1
     6: 1
     9: 1

10:  3: 1
     4: 1
     6: 1
    10: 1

11:  3: 1
     5: 1
     6: 1
    11: 1

12:  0: 1
     1: 1
     3: 1
     4: 1
     7: 1
    12: 1

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

14:  3: 1
     6: 1
     7: 1
    14: 1

15:  3: 1
     4: 1
     6: 1
     8: 1
    10: 1
    15: 1

16:  3: 1
     5: 1
     6: 1
     9: 1
    11: 1
    16: 1

17:  3: 1
     4: 1
     6: 1
     7: 1
     8: 1
    12: 1
    14: 1
    17: 1

18:  3: 1
     5: 1
     6: 1
     7: 1
     9: 1
    13: 1
    14: 1
    18: 1

19:  3: 1
     4: 1
     6: 1
     7: 1
    10: 1
    12: 1
    14: 1
    19: 1

20:  3: 1
     5: 1
     6: 1
     7: 1
    11: 1
    13: 1
    14: 1
    20: 1

21:  0: q
     3: q
     7: 2
    12: 1
    13: 1
    14: 1
    21: 1

22:  0: q
     1: q
     3: q
     4: q
    15: 1
    22: 1

23:  0: q
     2: q
     3: q
     5: q
    16: 1
    23: 1

24:  7: 1
    12: 1
    14: 1
    17: 1
    21: 1
    24: 1

25:  7: 1
    13: 1
    14: 1
    18: 1
    21: 1
    25: 1

26:  3: 1
     4: 1
     6: 1
     7: 1
     8: 1
    10: 1
    12: 1
    14: 1
    15: 1
    17: 1
    19: 1
    26: 1

27:  3: 1
     5: 1
     6: 1
     7: 1
     9: 1
    11: 1
    13: 1
    14: 1
    16: 1
    18: 1
    20: 1
    27: 1

28:  7: 1
    12: 1
    14: 1
    19: 1
    21: 1
    28: 1

29:  7: 1
    13: 1
    14: 1
    20: 1
    21: 1
    29: 1

30:  7: 1
    12: 1
    14: 1
    17: 1
    19: 1
    21: 1
    24: 1
    26: 1
    28: 1
    30: 1

31:  0: q
     1: q
     3: q
     4: q
     7: q
    12: q
    15: 1
    22: 1
    26: 1
    31: 1

32:  7: q
    14: q
    21: 1
    24: 1
    29: 1
    32: 1

33:  7: q
    14: q
    21: 1
    25: 1
    28: 1
    33: 1

34:  0: q^2
     1: q^2
    22: 1
    34: 1

35:  7: 1
    13: 1
    14: 1
    18: 1
    20: 1
    21: 1
    25: 1
    27: 1
    29: 1
    35: 1

36:  0: q
     2: q
     3: q
     5: q
     7: q
    13: q
    16: 1
    23: 1
    27: 1
    36: 1

37:  0: q^2
     2: q^2
    23: 1
    37: 1

225 nonzero polynomials, and 157 zero polynomials,
 at 382 Bruhat-comparable pairs.