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

0: 0: 1

1: 0: 1
   1: 1

2: 1: 1
   2: 1

3: 1: 1
   3: 1

4: 1: 1
   2: 1
   3: 1
   4: 1

5: 3: 1
   5: 1

6: 3: 1
   4: 1
   5: 1
   6: 1

7: 5: 1
   7: 1

8: 0: q
   1: q
   4: 1
   8: 1

23 nonzero polynomials, and 13 zero polynomials,
 at 36 Bruhat-comparable pairs.