David J. Green

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Cohomology of group number 1375 of order 128

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

General information on the group

• The group has 4 minimal generators and exponent 4.
• It is non-abelian.
• It has p-Rank 4.
• Its center has rank 3.
• It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 4.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 3.
• The depth coincides with the Duflot bound.
• The Poincaré series is

  t8  −  t7  +  3·t6  +  t5  +  3·t4  +  5·t3  +  t2  +  2·t  +  1

  (t  +  1)2 · (t  −  1)4 · (t2  +  1)3

• The a-invariants are -∞,-∞,-∞,-5,-4. They were obtained using the filter regular HSOP of the Benson test.

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring generators

The cohomology ring has 19 minimal generators of maximal degree 5:

1. a_1_0, a nilpotent element of degree 1
2. a_1_1, a nilpotent element of degree 1
3. b_1_2, an element of degree 1
4. b_1_3, an element of degree 1
5. a_3_6, a nilpotent element of degree 3
6. a_3_7, a nilpotent element of degree 3
7. a_3_5, a nilpotent element of degree 3
8. b_3_8, an element of degree 3
9. b_3_9, an element of degree 3
10. b_3_10, an element of degree 3
11. b_3_11, an element of degree 3
12. b_3_12, an element of degree 3
13. c_4_21, a Duflot regular element of degree 4
14. c_4_22, a Duflot regular element of degree 4
15. c_4_23, a Duflot regular element of degree 4
16. b_5_33, an element of degree 5
17. b_5_34, an element of degree 5
18. b_5_35, an element of degree 5
19. b_5_36, an element of degree 5

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 103 minimal relations of maximal degree 10:

1. a_1_1·b_1_2 + a_1_0²
2. a_1_0·b_1_2 + a_1_1² + a_1_0²
3. b_1_2·b_1_3 + a_1_0·a_1_1
4. a_1_0·a_1_1² + a_1_0³
5. a_1_0²·a_1_1
6. a_1_0·a_1_1·b_1_3
7. b_1_2·a_3_5 + b_1_2·a_3_6 + a_1_1·a_3_6 + a_1_0·a_3_7 + a_1_0·a_3_6
8. b_1_2·a_3_7 + b_1_2·a_3_6 + a_1_1·a_3_5 + a_1_0·a_3_7
9. b_1_2·a_3_6 + a_1_1·a_3_7 + a_1_1·a_3_6 + a_1_0·a_3_5
10. b_1_2·b_3_8 + b_1_2·a_3_6 + a_1_0·a_3_6
11. a_1_1·b_3_9 + a_1_1·a_3_6 + a_1_0·a_3_6
12. b_1_2·a_3_6 + a_1_0·b_3_9 + a_1_0·a_3_6
13. b_1_3·b_3_9 + b_1_3·a_3_6 + a_1_0·b_3_8 + a_1_0·a_3_6
14. b_1_2·b_3_10 + b_1_2·b_3_9 + b_1_2·a_3_7 + a_1_1·a_3_6 + a_1_0·a_3_6
15. b_1_3·a_3_6 + a_1_1·b_3_8 + a_1_0·b_3_10 + a_1_0·b_3_8 + a_1_1·a_3_6 + a_1_0·a_3_7
       + a_1_0·a_3_6
16. b_1_2·a_3_7 + a_1_1·b_3_11 + a_1_1·a_3_6 + a_1_0·a_3_7
17. a_1_0·b_3_11 + a_1_1·a_3_7 + a_1_0·a_3_6
18. b_1_3·b_3_11 + b_1_3·a_3_5 + b_1_3·a_3_6 + a_1_1·b_3_10 + a_1_1·b_3_8 + a_1_1·a_3_7
       + a_1_1·a_3_6 + a_1_0·a_3_6
19. a_1_1·b_3_12 + a_1_1·a_3_7 + a_1_1·a_3_6 + a_1_0·a_3_7 + a_1_0·a_3_6
20. b_1_2·a_3_7 + b_1_2·a_3_6 + a_1_0·b_3_12 + a_1_0·a_3_7 + a_1_0·a_3_6
21. b_1_3·b_3_12 + b_1_3·a_3_7 + a_1_1·b_3_8 + a_1_1·a_3_7
22. a_1_0·a_1_1·a_3_7 + a_1_0²·a_3_5
23. a_1_0·a_1_1·b_3_8 + a_1_0·a_1_1·a_3_5 + a_1_0·a_1_1·a_3_7 + a_1_0²·a_3_7
       + a_1_0²·a_3_6
24. a_1_0·a_1_1·b_3_10 + a_1_0·a_1_1·a_3_6 + a_1_0²·a_3_6
25. a_3_5·b_3_9 + a_3_7·b_3_11 + a_3_7·b_3_9 + a_3_7·a_3_5 + a_3_6·a_3_7 + a_3_6²
26. a_3_5·b_3_9 + a_3_6·b_3_11 + a_3_6·a_3_7
27. a_3_5·b_3_11 + a_3_5·b_3_9 + a_3_7·b_3_9 + a_3_6·b_3_9 + a_3_5² + a_3_6²
28. a_3_5·b_3_9 + a_3_7·b_3_12 + a_3_7·b_3_9 + a_3_6·b_3_9 + a_3_5² + a_3_6·a_3_5
       + a_3_6·a_3_7 + a_3_6²
29. a_3_7·b_3_9 + a_3_6·b_3_12 + a_3_6·b_3_9
30. a_3_5·b_3_12 + a_3_7·b_3_9 + a_3_7·a_3_5 + a_3_7² + a_3_6·a_3_7 + a_3_6²
31. b_3_10·b_3_12 + b_3_9·b_3_12 + b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_11 + b_3_8·b_3_9
       + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_7·b_3_10 + a_3_7·b_3_9 + a_3_6·b_3_10 + a_3_6·b_3_9
       + a_3_6·b_3_8 + a_3_5² + a_3_7² + a_3_6·a_3_7 + a_3_6²
32. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_12 + b_3_8·b_3_9 + a_3_5·b_3_9 + a_3_7·b_3_8
       + a_3_6·b_3_10 + a_3_6·a_3_5 + a_3_6²
33. b_3_9² + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_6·a_3_5 + a_3_6·a_3_7
       + c_4_21·b_1_2² + c_4_21·a_1_1² + c_4_21·a_1_0·a_1_1 + c_4_21·a_1_0²
34. b_3_10·b_3_11 + b_3_9·b_3_11 + b_3_9² + b_3_8·b_3_11 + b_1_2³·b_3_12 + b_1_2³·b_3_9
       + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_7·b_3_9 + a_3_6·b_3_10 + a_3_6·b_3_9 + a_3_6·b_3_8
       + a_1_1·b_1_3²·b_3_10 + a_1_1·b_1_3²·b_3_8 + a_3_6² + a_1_0·b_1_3²·a_3_5
       + c_4_21·b_1_2² + c_4_21·a_1_1·b_1_3 + c_4_21·a_1_1²
35. b_3_8·b_3_11 + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_6·b_3_10 + a_3_6·b_3_9
       + a_1_0·b_1_3²·b_3_10 + a_1_0·b_1_3²·b_3_8 + a_3_6·a_3_5 + a_3_6²
       + c_4_21·a_1_0·b_1_3 + c_4_21·a_1_1²
36. b_3_10² + b_3_9² + b_3_8² + b_1_3³·b_3_10 + b_1_3³·b_3_8 + a_3_5·b_3_9
       + b_1_3³·a_3_7 + a_1_1·b_1_3²·b_3_10 + a_1_1·b_1_3²·b_3_8 + a_1_0·b_1_3²·b_3_8
       + a_3_7² + a_3_6·a_3_5 + a_3_6·a_3_7 + a_3_6² + a_1_0·b_1_3²·a_3_5 + c_4_21·b_1_3²
       + c_4_21·a_1_1² + c_4_21·a_1_0·a_1_1
37. b_3_11² + b_1_2³·b_3_11 + a_3_5² + a_3_6² + c_4_22·b_1_2² + c_4_21·a_1_1²
38. b_3_9² + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_6·a_3_5 + a_3_6·a_3_7
       + a_3_6² + c_4_21·b_1_2² + c_4_22·a_1_1² + c_4_21·a_1_0·a_1_1
39. b_3_9² + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_6·b_3_9 + a_3_6·a_3_5
       + a_3_6·a_3_7 + a_3_6² + c_4_21·b_1_2² + c_4_22·a_1_0·a_1_1
40. a_3_5·b_3_9 + a_3_6·a_3_5 + a_3_6·a_3_7 + a_3_6² + c_4_22·a_1_0² + c_4_21·a_1_1²
       + c_4_21·a_1_0·a_1_1
41. b_3_10·b_3_11 + b_3_9·b_3_11 + b_3_9·b_3_10 + b_3_8·b_3_11 + b_3_8·b_3_9 + b_1_2³·b_3_12
       + b_1_2³·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_6·b_3_8
       + a_1_1·b_1_3²·b_3_10 + a_3_6·a_3_5 + a_3_6² + a_1_0·b_1_3²·a_3_5 + c_4_21·b_1_2²
       + c_4_22·a_1_1·b_1_3 + c_4_21·a_1_1² + c_4_21·a_1_0·a_1_1
42. b_3_9² + b_3_8·b_3_11 + b_3_8·b_3_9 + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_8
       + a_3_6·b_3_10 + a_3_6·b_3_8 + a_1_0·b_1_3²·b_3_10 + a_3_6·a_3_7 + c_4_21·b_1_2²
       + c_4_22·a_1_0·b_1_3 + c_4_21·a_1_0·a_1_1
43. b_3_10² + b_3_9² + b_1_3³·b_3_10 + a_3_5·b_3_9 + b_1_3³·a_3_7 + a_1_1·b_1_3²·b_3_8
       + a_1_0·b_1_3²·b_3_8 + a_3_7² + a_3_6·a_3_5 + a_3_6·a_3_7 + c_4_22·b_1_3²
       + c_4_21·a_1_0·a_1_1
44. b_3_12² + b_3_11² + b_3_9² + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_5² + a_3_7²
       + a_3_6·a_3_5 + a_3_6·a_3_7 + c_4_23·b_1_2² + c_4_21·b_1_2² + c_4_21·a_1_0·a_1_1
45. b_3_9² + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5² + c_4_21·b_1_2² + c_4_23·a_1_1²
       + c_4_21·a_1_1²
46. a_3_7·b_3_9 + a_3_7·a_3_5 + a_3_6·a_3_5 + a_3_6·a_3_7 + c_4_23·a_1_0·a_1_1
       + c_4_21·a_1_1²
47. a_3_5·b_3_9 + a_3_7² + a_3_6·a_3_5 + a_3_6·a_3_7 + c_4_23·a_1_0² + c_4_21·a_1_0·a_1_1
48. b_3_9·b_3_11 + b_1_2·b_5_33 + b_1_2³·b_3_11 + a_3_7·b_3_9 + a_3_6·b_3_9 + a_3_5²
       + a_3_7·a_3_5 + a_3_7² + a_3_6² + c_4_21·a_1_0·a_1_1
49. b_3_10·b_3_11 + b_3_9·b_3_11 + b_3_9² + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_10
       + a_3_5·b_3_9 + a_3_6·b_3_10 + a_3_6·b_3_9 + a_1_1·b_5_33 + a_1_1·b_1_3²·b_3_10
       + a_1_1·b_1_3²·b_3_8 + a_3_7·a_3_5 + c_4_21·b_1_2² + c_4_23·a_1_1·b_1_3
       + c_4_21·a_1_0·a_1_1
50. b_3_9·b_3_10 + b_3_8·b_3_11 + b_3_8·b_3_9 + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_9
       + a_3_5·b_3_8 + a_3_7·b_3_9 + a_3_6·b_3_8 + a_1_0·b_5_33 + a_1_0·b_1_3²·b_3_10
       + a_1_0·b_1_3²·b_3_8 + a_3_7² + a_3_6·a_3_5 + a_3_6·a_3_7 + a_3_6² + c_4_21·b_1_2²
       + c_4_23·a_1_0·b_1_3
51. b_3_10² + b_3_9² + b_3_8·b_3_11 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_1_3·b_5_33
       + b_1_3³·b_3_10 + b_1_3³·b_3_8 + a_3_5·b_3_8 + a_3_7·b_3_8 + a_3_6·b_3_8
       + a_1_1·b_1_3²·b_3_8 + a_1_0·b_1_3²·b_3_10 + a_1_0·b_1_3²·b_3_8 + a_3_7²
       + a_1_0·b_1_3²·a_3_5 + c_4_23·b_1_3² + c_4_23·a_1_0·b_1_3 + c_4_21·a_1_0·a_1_1
52. b_3_12² + b_3_11·b_3_12 + b_3_9·b_3_11 + b_1_2·b_5_34 + b_1_2³·b_3_12 + a_3_5·b_3_9
       + a_3_7·a_3_5 + a_3_7² + a_3_6·a_3_5 + a_3_6·a_3_7 + a_3_6² + c_4_21·a_1_1²
       + c_4_21·a_1_0·a_1_1
53. b_3_10·b_3_11 + b_3_9·b_3_11 + b_3_9·b_3_10 + b_3_8·b_3_11 + b_3_8·b_3_9 + b_1_2³·b_3_12
       + b_1_2³·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_7·b_3_9 + a_3_6·b_3_9 + a_3_6·b_3_8
       + a_1_1·b_5_34 + a_3_5² + a_3_7² + a_3_6·a_3_5 + a_3_6² + a_1_0·b_1_3²·a_3_5
       + c_4_21·b_1_2² + c_4_21·a_1_0·a_1_1
54. b_3_9² + b_3_8·b_3_11 + b_3_8·b_3_9 + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_8
       + a_3_6·b_3_10 + a_3_6·b_3_8 + a_1_0·b_5_34 + a_3_5² + a_3_7·a_3_5 + a_3_7²
       + a_1_0·b_1_3²·a_3_5 + c_4_21·b_1_2²
55. b_3_10·b_3_11 + b_3_10² + b_3_9·b_3_11 + b_3_8·b_3_11 + b_1_3·b_5_34 + b_1_2³·b_3_12
       + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_7·b_3_10 + a_3_7·b_3_8 + b_1_3³·a_3_5
       + b_1_3³·a_3_7 + a_1_1·b_1_3²·b_3_10 + a_1_0·b_1_3²·b_3_8 + a_3_6·a_3_7
       + c_4_21·b_1_2² + c_4_23·a_1_1·b_1_3
56. b_3_12² + b_3_11·b_3_12 + b_3_11² + b_3_9·b_3_11 + b_1_2·b_5_35 + b_1_2³·b_3_9
       + a_3_5² + a_3_6·a_3_5 + c_4_21·b_1_2²
57. b_3_10·b_3_11 + b_3_9·b_3_11 + b_3_9² + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_10
       + a_3_6·b_3_10 + a_1_1·b_5_35 + a_3_7² + a_3_6·a_3_7 + a_3_6² + c_4_21·b_1_2²
       + c_4_23·a_1_1·b_1_3
58. b_3_9·b_3_10 + b_3_9² + b_3_8·b_3_11 + b_3_8·b_3_9 + a_3_5·b_3_9 + a_3_5·b_3_8
       + a_3_6·b_3_8 + a_1_0·b_5_35 + a_3_5² + a_3_7² + a_3_6² + c_4_23·a_1_0·b_1_3
       + c_4_21·a_1_1² + c_4_21·a_1_0·a_1_1
59. b_3_10·b_3_11 + b_3_10² + b_3_9·b_3_11 + b_3_8·b_3_11 + b_3_8·b_3_10 + b_3_8·b_3_9
       + b_1_3·b_5_35 + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_7·b_3_8
       + a_1_1·b_1_3²·b_3_8 + a_3_7² + a_3_6·a_3_5 + a_3_6² + a_1_0·b_1_3²·a_3_5
       + c_4_23·b_1_3² + c_4_21·b_1_2² + c_4_21·a_1_0·a_1_1
60. b_3_12² + b_3_11·b_3_12 + b_3_10·b_3_12 + b_3_9·b_3_10 + b_3_8·b_3_11 + b_3_8·b_3_9
       + b_1_2·b_5_36 + b_1_2³·b_3_12 + a_3_5·b_3_8 + a_3_7·b_3_10 + a_3_6·b_3_10 + a_3_6·b_3_9
       + a_3_6·b_3_8 + a_3_5² + a_3_7·a_3_5 + a_3_6·a_3_7 + c_4_21·b_1_2² + c_4_21·a_1_1²
61. b_3_9·b_3_10 + b_3_8·b_3_9 + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_9 + a_3_6·b_3_10
       + a_1_1·b_5_36 + a_1_1·b_1_3²·b_3_10 + a_1_1·b_1_3²·b_3_8 + a_3_5² + a_3_7²
       + a_3_6·a_3_5 + a_1_0·b_1_3²·a_3_5 + c_4_21·b_1_2²
62. b_3_8·b_3_9 + a_3_5·b_3_9 + a_3_7·b_3_9 + a_3_6·b_3_9 + a_3_6·b_3_8 + a_1_0·b_5_36
       + a_1_0·b_1_3²·b_3_10 + a_1_0·b_1_3²·b_3_8 + a_3_5² + a_3_7·a_3_5 + a_3_7²
       + a_3_6·a_3_5 + a_3_6² + c_4_21·a_1_1² + c_4_21·a_1_0·a_1_1
63. b_3_9·b_3_10 + b_3_8·b_3_11 + b_3_8·b_3_9 + b_3_8² + b_1_3·b_5_36 + b_1_3³·b_3_10
       + b_1_3³·b_3_8 + b_1_2³·b_3_12 + b_1_2³·b_3_9 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_7·b_3_8
       + a_3_6·b_3_9 + a_3_6·b_3_8 + b_1_3³·a_3_7 + a_1_1·b_1_3²·b_3_10 + a_1_0·b_1_3²·b_3_10
       + a_1_0·b_1_3²·b_3_8 + a_3_6·a_3_5 + a_3_6² + a_1_0·b_1_3²·a_3_5 + c_4_21·b_1_2²
       + c_4_23·a_1_1·b_1_3 + c_4_21·a_1_1²
64. a_1_0·a_1_1·b_5_33 + a_1_0·a_3_7·a_3_5 + c_4_21·a_1_0³
65. b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_9·b_5_33 + b_1_2³·b_5_33 + a_3_5·b_5_33
       + a_3_7·b_5_33 + b_1_3²·a_3_7·b_3_10 + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_8
       + c_4_23·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_2·b_3_9
       + c_4_22·b_1_2⁴ + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8 + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_8
       + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_1_3³ + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_0·b_3_10 + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_6
       + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
66. b_3_11·b_5_33 + b_1_2³·b_5_33 + a_3_5·b_5_33 + a_3_6·b_5_33 + a_1_1·b_1_3²·b_5_33
       + a_1_0·b_1_3·a_3_5·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_8 + a_1_0·b_1_3⁴·a_3_5
       + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴ + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8
       + c_4_23·a_1_1·b_1_3³ + c_4_21·a_1_1·b_3_10 + c_4_21·a_1_1·b_1_3³
       + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_7
       + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_6
67. b_3_11·b_5_33 + b_1_2³·b_5_33 + a_3_5·b_5_33 + a_1_0·b_1_3²·b_5_33
       + a_1_0·b_1_3·a_3_5·b_3_10 + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴ + c_4_23·a_1_1·b_3_10
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8 + c_4_23·a_1_0·b_1_3³
       + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_1·b_3_8 + c_4_21·a_1_0·b_3_10
       + c_4_21·a_1_0·b_1_3³ + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_7
       + c_4_21·a_1_0·a_3_6
68. b_3_11·b_5_33 + b_3_8·b_5_33 + b_1_3³·b_5_33 + b_1_2³·b_5_33 + a_3_5·b_5_33
       + b_1_3²·a_3_7·b_3_8 + b_1_3⁵·a_3_7 + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3⁴·b_3_8
       + a_1_0·b_1_3·a_3_5·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_8 + a_1_0·b_1_3⁴·a_3_5
       + c_4_23·b_1_3·b_3_8 + c_4_23·b_1_3⁴ + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_8
       + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴ + c_4_21·b_1_3·b_3_10 + c_4_21·b_1_3⁴
       + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_1_3³
       + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_8 + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_1_3³ + c_4_21·b_1_3·a_3_7 + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_0·b_1_3³ + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6
       + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_6
69. b_3_10·b_5_33 + b_1_2³·b_5_34 + b_1_2³·b_5_33 + a_3_7·b_5_33 + a_3_6·b_5_33
       + b_1_3²·a_3_7·b_3_10 + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_10
       + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_23·b_1_3·b_3_10 + c_4_23·b_1_2⁴ + c_4_22·b_1_3·b_3_10
       + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_2⁴ + c_4_21·b_1_2·b_3_11 + c_4_23·b_1_3·a_3_7
       + c_4_23·a_1_1·b_3_8 + c_4_23·a_1_0·b_3_8 + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_10
       + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_3³ + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_0·b_3_10 + c_4_23·a_1_1·a_3_6 + c_4_22·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_6
70. b_3_12·b_5_34 + b_3_12·b_5_33 + b_3_10·b_5_33 + b_1_2⁵·b_3_11 + a_3_6·b_5_33
       + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_8
       + c_4_23·b_1_3·b_3_10 + c_4_23·b_1_2·b_3_12 + c_4_23·b_1_2·b_3_11 + c_4_22·b_1_3·b_3_10
       + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_2·b_3_12 + c_4_22·b_1_2·b_3_11 + c_4_22·b_1_2⁴
       + c_4_21·b_1_2·b_3_11 + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_1_3³
       + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_3³ + c_4_21·a_1_1·b_1_3³
       + c_4_21·a_1_0·b_3_10 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_7
       + c_4_22·a_1_1·a_3_6 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_7
       + c_4_21·a_1_0·a_3_6
71. b_3_12·b_5_33 + b_3_10·b_5_34 + b_1_3⁵·b_3_10 + a_3_6·b_5_33 + b_1_3²·a_3_7·b_3_10
       + b_1_3²·a_3_7·b_3_8 + b_1_3⁵·a_3_7 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3·a_3_5·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_23·b_1_2·b_3_9
       + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3⁴ + c_4_22·b_1_2·b_3_9 + c_4_21·b_1_2·b_3_11
       + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8
       + c_4_22·b_1_3·a_3_5 + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_1·b_3_8 + c_4_21·a_1_0·b_1_3³
       + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_5
       + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_7
72. b_3_11·b_5_34 + b_3_11·b_5_33 + b_3_10·b_5_33 + a_3_5·b_5_33 + a_3_7·b_5_33 + a_3_6·b_5_33
       + b_1_3²·a_3_5·b_3_10 + b_1_3²·a_3_7·b_3_10 + a_1_1·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·a_3_5 + c_4_23·b_1_3·b_3_10 + c_4_23·b_1_2·b_3_11
       + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_2·b_3_12 + c_4_22·b_1_2·b_3_11
       + c_4_21·b_1_2·b_3_11 + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8
       + c_4_23·a_1_0·b_3_10 + c_4_22·b_1_3·a_3_5 + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_10
       + c_4_22·a_1_1·b_3_8 + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_1_3³ + c_4_21·a_1_1·b_3_10 + c_4_21·a_1_0·b_1_3³
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7
       + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_0·a_3_7
       + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_6
73. a_3_7·b_5_34 + b_1_3²·a_3_7·b_3_10 + c_4_22·b_1_3·a_3_7 + c_4_23·a_1_1·a_3_5
       + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6
       + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_7 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_7
       + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
74. a_3_6·b_5_34 + a_3_6·b_5_33 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + c_4_23·a_1_1·b_3_8 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8
       + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_3_8 + c_4_21·a_1_1·b_3_10 + c_4_21·a_1_1·b_1_3³
       + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_1_3³ + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6
       + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_6
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_1·a_3_6
       + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_6
75. a_3_5·b_5_34 + b_1_3²·a_3_5·b_3_10 + c_4_22·b_1_3·a_3_5 + c_4_23·a_1_1·a_3_5
       + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_7
       + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_6
76. b_3_12·b_5_33 + b_3_9·b_5_34 + a_3_7·b_5_33 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + c_4_23·b_1_2·b_3_9 + c_4_22·b_1_2·b_3_9 + c_4_21·b_1_2·b_3_11 + c_4_23·a_1_1·b_3_8
       + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_1_3³ + c_4_21·a_1_1·b_3_10 + c_4_21·a_1_1·b_1_3³
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_7
       + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_6
77. b_3_11·b_5_33 + b_3_8·b_5_34 + b_3_8·b_5_33 + b_1_3⁵·b_3_8 + b_1_2³·b_5_33
       + a_3_7·b_5_33 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_23·b_1_3·b_3_8
       + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3⁴ + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴
       + c_4_21·b_1_3·b_3_10 + c_4_21·b_1_3⁴ + c_4_23·b_1_3·a_3_5 + c_4_23·b_1_3·a_3_7
       + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8 + c_4_23·a_1_0·b_3_10 + c_4_22·b_1_3·a_3_5
       + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_0·b_3_10
       + c_4_21·a_1_1·b_1_3³ + c_4_21·a_1_0·b_3_8 + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6
       + c_4_23·a_1_0·a_3_5 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5
       + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_5
78. b_3_12·b_5_35 + b_3_10·b_5_35 + b_3_8·b_5_33 + b_1_3⁵·b_3_10 + b_1_3⁵·b_3_8
       + b_1_2³·b_5_33 + b_1_2⁵·b_3_11 + b_1_2⁵·b_3_9 + a_3_5·b_5_33 + a_3_6·b_5_33
       + b_1_3²·a_3_5·b_3_10 + b_1_3²·a_3_5·b_3_8 + b_1_3²·a_3_7·b_3_8 + b_1_3⁵·a_3_7
       + a_1_1·b_1_3⁴·b_3_10 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_8 + a_1_0·b_1_3⁴·a_3_5
       + c_4_23·b_1_3·b_3_10 + c_4_23·b_1_3·b_3_8 + c_4_23·b_1_2·b_3_12 + c_4_23·b_1_2·b_3_11
       + c_4_23·b_1_2·b_3_9 + c_4_23·b_1_2⁴ + c_4_22·b_1_2·b_3_11 + c_4_21·b_1_3·b_3_10
       + c_4_21·b_1_3⁴ + c_4_21·b_1_2·b_3_12 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_9
       + c_4_21·b_1_2⁴ + c_4_23·b_1_3·a_3_5 + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_0·b_3_10
       + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_1·b_3_8 + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_8
       + c_4_22·a_1_0·b_1_3³ + c_4_21·b_1_3·a_3_7 + c_4_21·a_1_0·b_3_10 + c_4_23·a_1_1·a_3_5
       + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5
       + c_4_21·a_1_1·a_3_6
79. b_3_11·b_5_35 + a_3_5·b_5_33 + a_3_6·b_5_33 + b_1_3²·a_3_5·b_3_10 + b_1_3²·a_3_5·b_3_8
       + a_1_1·b_1_3⁴·b_3_10 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_10 + a_1_0·b_1_3⁴·a_3_5
       + c_4_23·b_1_2·b_3_11 + c_4_22·b_1_2·b_3_12 + c_4_22·b_1_2·b_3_9 + c_4_21·b_1_2·b_3_11
       + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8 + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_1·b_1_3³ + c_4_21·a_1_0·b_1_3³ + c_4_22·a_1_0·a_3_7
       + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5
80. a_3_7·b_5_35 + a_3_7·b_5_33 + b_1_3²·a_3_7·b_3_10 + b_1_3²·a_3_7·b_3_8
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_6 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_0·a_3_5
       + c_4_22·a_1_0·a_3_7 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_6
81. b_3_11·b_5_33 + b_1_2³·b_5_33 + a_3_5·b_5_33 + a_3_6·b_5_35 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴
       + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8 + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_0·b_1_3³ + c_4_23·a_1_1·a_3_7 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_1·a_3_6
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_7 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_5
82. a_3_5·b_5_35 + a_3_5·b_5_33 + b_1_3²·a_3_5·b_3_10 + b_1_3²·a_3_5·b_3_8
       + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6
       + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5
       + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_7
       + c_4_21·a_1_0·a_3_6
83. b_3_12·b_5_35 + b_3_11·b_5_33 + b_3_9·b_5_35 + b_1_2⁵·b_3_11 + b_1_2⁵·b_3_9
       + a_3_5·b_5_33 + a_3_7·b_5_33 + b_1_3²·a_3_7·b_3_10 + b_1_3²·a_3_7·b_3_8
       + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_10
       + c_4_23·b_1_2·b_3_12 + c_4_23·b_1_2·b_3_11 + c_4_23·b_1_2·b_3_9 + c_4_23·b_1_2⁴
       + c_4_22·b_1_2·b_3_11 + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴ + c_4_21·b_1_2·b_3_12
       + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_9 + c_4_21·b_1_2⁴ + c_4_23·a_1_1·b_3_10
       + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_1·b_3_8 + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_1_3³ + c_4_22·a_1_0·a_3_5
       + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_5
84. b_3_8·b_5_35 + a_3_5·b_5_33 + a_1_1·b_1_3⁴·b_3_10 + a_1_1·b_1_3⁴·b_3_8
       + a_1_0·b_1_3⁴·a_3_5 + c_4_23·b_1_3·b_3_8 + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_8
       + c_4_21·b_1_3·b_3_10 + c_4_23·b_1_3·a_3_5 + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_10
       + c_4_22·a_1_0·b_3_10 + c_4_21·b_1_3·a_3_5 + c_4_21·b_1_3·a_3_7 + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_1·b_3_8 + c_4_21·a_1_1·b_1_3³ + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8
       + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_6
       + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
85. b_3_12·b_5_35 + b_3_12·b_5_33 + b_3_11·b_5_33 + b_3_10·b_5_33 + b_1_2³·b_5_36
       + b_1_2³·b_5_33 + b_1_2⁵·b_3_11 + b_1_2⁵·b_3_9 + a_3_5·b_5_33 + a_3_7·b_5_33
       + b_1_3²·a_3_7·b_3_8 + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_10
       + c_4_23·b_1_3·b_3_10 + c_4_23·b_1_2·b_3_12 + c_4_23·b_1_2·b_3_11 + c_4_22·b_1_3·b_3_10
       + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_2·b_3_11 + c_4_22·b_1_2·b_3_9 + c_4_21·b_1_2·b_3_12
       + c_4_21·b_1_2·b_3_11 + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_0·b_3_8
       + c_4_22·b_1_3·a_3_7 + c_4_22·a_1_1·b_3_10 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_3³
       + c_4_21·a_1_0·b_3_10 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6
       + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_0·a_3_7
       + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_7
86. b_3_12·b_5_36 + b_3_11·b_5_33 + b_1_2⁵·b_3_12 + b_1_2⁵·b_3_11 + a_3_5·b_5_33
       + a_3_6·b_5_33 + b_1_3²·a_3_7·b_3_10 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_10
       + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_23·b_1_2·b_3_12 + c_4_23·b_1_2·b_3_11
       + c_4_23·b_1_2·b_3_9 + c_4_23·b_1_2⁴ + c_4_22·b_1_2·b_3_12 + c_4_22·b_1_2·b_3_11
       + c_4_22·b_1_2⁴ + c_4_23·a_1_1·b_3_10 + c_4_23·a_1_1·b_3_8 + c_4_22·b_1_3·a_3_7
       + c_4_22·a_1_1·b_3_8 + c_4_22·a_1_1·b_1_3³ + c_4_21·b_1_3·a_3_7 + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_1·b_3_8 + c_4_21·a_1_1·b_1_3³ + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_6
       + c_4_22·a_1_1·a_3_6 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
87. b_3_12·b_5_33 + b_3_11·b_5_33 + b_3_10·b_5_36 + b_3_10·b_5_33 + b_1_3⁵·b_3_10
       + b_1_2⁵·b_3_9 + a_3_7·b_5_33 + b_1_3²·a_3_5·b_3_10 + b_1_3²·a_3_5·b_3_8
       + b_1_3²·a_3_7·b_3_8 + b_1_3⁵·a_3_7 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_10 + c_4_23·b_1_3·b_3_10
       + c_4_23·b_1_2·b_3_9 + c_4_23·b_1_2⁴ + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_3⁴
       + c_4_21·b_1_3·b_3_10 + c_4_21·b_1_2·b_3_12 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2⁴
       + c_4_23·b_1_3·a_3_5 + c_4_23·a_1_1·b_3_8 + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_3_8
       + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_1_3³ + c_4_21·a_1_1·b_3_10
       + c_4_21·a_1_0·b_3_10 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7
       + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5
       + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_6
88. b_3_12·b_5_33 + b_3_11·b_5_36 + b_3_10·b_5_33 + b_1_2³·b_5_33 + b_1_3²·a_3_5·b_3_10
       + b_1_3²·a_3_7·b_3_10 + a_1_1·b_1_3⁴·b_3_10 + a_1_0·b_1_3⁴·b_3_8
       + a_1_0·b_1_3·a_3_5·b_3_10 + a_1_0·b_1_3⁴·a_3_5 + c_4_23·b_1_3·b_3_10
       + c_4_23·b_1_2·b_3_11 + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_8 + c_4_22·b_1_2·b_3_12
       + c_4_22·b_1_2·b_3_11 + c_4_22·b_1_2⁴ + c_4_21·b_1_2·b_3_11 + c_4_23·b_1_3·a_3_7
       + c_4_23·a_1_1·b_3_8 + c_4_23·a_1_0·b_3_10 + c_4_22·b_1_3·a_3_5 + c_4_22·b_1_3·a_3_7
       + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_1_3³
       + c_4_21·b_1_3·a_3_5 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_1_3³
       + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_7
       + c_4_22·a_1_0·a_3_7 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_6
89. a_3_7·b_5_36 + b_1_3²·a_3_7·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_10
       + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_22·b_1_3·a_3_7 + c_4_21·b_1_3·a_3_7
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_5
       + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_6
       + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_7
90. a_3_6·b_5_36 + a_3_6·b_5_33 + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3⁴·b_3_10
       + a_1_0·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_8
       + c_4_23·a_1_1·b_3_8 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_3_10
       + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_8
       + c_4_21·a_1_1·b_3_10 + c_4_21·a_1_1·b_3_8 + c_4_21·a_1_1·b_1_3³ + c_4_21·a_1_0·b_3_8
       + c_4_21·a_1_0·b_1_3³ + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_5
       + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_5
       + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_1·a_3_7 + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
91. a_3_5·b_5_36 + b_1_3²·a_3_5·b_3_10 + a_1_0·b_1_3·a_3_5·b_3_10
       + a_1_0·b_1_3·a_3_5·b_3_8 + c_4_22·b_1_3·a_3_5 + c_4_21·b_1_3·a_3_5
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_6 + c_4_23·a_1_0·a_3_7 + c_4_22·a_1_1·a_3_6
       + c_4_22·a_1_0·a_3_7 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_0·a_3_5
92. b_3_12·b_5_33 + b_3_10·b_5_33 + b_3_9·b_5_36 + b_1_2³·b_5_33 + b_1_2⁵·b_3_9
       + a_3_6·b_5_33 + b_1_3²·a_3_7·b_3_10 + a_1_1·b_1_3⁴·b_3_8 + c_4_23·b_1_3·b_3_10
       + c_4_23·b_1_2·b_3_9 + c_4_23·b_1_2⁴ + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3·b_3_8
       + c_4_22·b_1_2·b_3_9 + c_4_22·b_1_2⁴ + c_4_21·b_1_2·b_3_12 + c_4_21·b_1_2·b_3_11
       + c_4_21·b_1_2⁴ + c_4_23·b_1_3·a_3_7 + c_4_23·a_1_0·b_3_8 + c_4_22·b_1_3·a_3_7
       + c_4_22·a_1_1·b_1_3³ + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_8 + c_4_21·a_1_1·b_3_8
       + c_4_21·a_1_1·b_1_3³ + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_0·a_3_7
       + c_4_22·a_1_1·a_3_7 + c_4_22·a_1_0·a_3_7 + c_4_21·a_1_1·a_3_6 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
93. b_3_8·b_5_36 + b_3_8·b_5_33 + b_1_3⁵·b_3_8 + a_3_5·b_5_33 + a_3_6·b_5_33
       + a_1_1·b_1_3⁴·b_3_8 + a_1_0·b_1_3·a_3_5·b_3_10 + c_4_23·b_1_3·b_3_8
       + c_4_22·b_1_3·b_3_10 + c_4_22·b_1_3⁴ + c_4_21·b_1_3·b_3_10 + c_4_21·b_1_3·b_3_8
       + c_4_21·b_1_3⁴ + c_4_23·b_1_3·a_3_5 + c_4_23·a_1_0·b_3_10 + c_4_22·a_1_1·b_3_8
       + c_4_22·a_1_0·b_3_8 + c_4_21·b_1_3·a_3_5 + c_4_21·a_1_1·b_1_3³ + c_4_21·a_1_0·b_3_10
       + c_4_23·a_1_1·a_3_7 + c_4_23·a_1_0·a_3_7 + c_4_23·a_1_0·a_3_6 + c_4_22·a_1_1·a_3_7
       + c_4_22·a_1_1·a_3_6 + c_4_22·a_1_0·a_3_7 + c_4_22·a_1_0·a_3_6 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_7 + c_4_21·a_1_0·a_3_6
94. b_5_33² + b_1_3⁵·b_5_33 + b_1_2⁵·b_5_34 + b_1_3⁷·a_3_7 + a_1_1·b_1_3⁴·b_5_33
       + a_1_0·b_1_3⁴·b_5_33 + a_1_0·b_1_3⁶·b_3_10 + c_4_23·b_1_3⁶ + c_4_23·b_1_2⁶
       + c_4_22·b_1_3³·b_3_10 + c_4_22·b_1_3³·b_3_8 + c_4_22·b_1_2³·b_3_12
       + c_4_22·b_1_2³·b_3_9 + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_3⁶
       + c_4_21·b_1_2³·b_3_11 + c_4_23·a_1_1·b_1_3⁵ + c_4_22·b_1_3³·a_3_7
       + c_4_22·a_1_1·b_1_3²·b_3_10 + c_4_22·a_1_1·b_1_3²·b_3_8 + c_4_22·a_1_1·b_1_3⁵
       + c_4_22·a_1_0·b_1_3²·b_3_8 + c_4_21·b_1_3³·a_3_7 + c_4_21·a_1_1·b_1_3²·b_3_8
       + c_4_21·a_1_1·b_1_3⁵ + c_4_21·a_1_0·b_1_3²·b_3_8 + c_4_21·a_1_0·b_1_3⁵
       + c_4_22·a_1_0·b_1_3²·a_3_5 + c_4_23²·b_1_3² + c_4_21·c_4_22·b_1_3²
       + c_4_21·c_4_22·b_1_2² + c_4_23²·a_1_0² + c_4_22²·a_1_0²
       + c_4_21·c_4_22·a_1_0² + c_4_21²·a_1_1² + c_4_21²·a_1_0²
95. b_5_34² + b_1_3⁷·b_3_10 + b_1_2⁵·b_5_33 + b_1_2⁷·b_3_11 + b_1_3⁷·a_3_7
       + a_1_1·b_1_3⁶·b_3_8 + a_1_0·b_1_3⁶·b_3_8 + c_4_23·b_1_2³·b_3_11 + c_4_22·b_1_3⁶
       + c_4_22·b_1_2³·b_3_9 + c_4_21·b_1_2³·b_3_11 + c_4_23²·b_1_2²
       + c_4_22·c_4_23·b_1_2² + c_4_22²·b_1_3² + c_4_21·c_4_22·b_1_2²
       + c_4_23²·a_1_1² + c_4_22·c_4_23·a_1_1² + c_4_22²·a_1_1² + c_4_22²·a_1_0²
       + c_4_21·c_4_23·a_1_0² + c_4_21·c_4_22·a_1_0²
96. b_5_33·b_5_35 + b_5_33·b_5_34 + b_5_33² + b_1_3⁵·b_5_33 + b_1_2²·b_3_9·b_5_34
       + b_1_3²·a_3_7·b_5_33 + b_1_3⁴·a_3_7·b_3_8 + b_1_3⁷·a_3_7 + a_1_0·b_1_3⁶·b_3_10
       + a_1_0·b_1_3⁶·b_3_8 + a_1_0·b_1_3·a_3_5·b_5_33 + a_1_0·b_1_3³·a_3_5·b_3_10
       + a_1_0·b_1_3⁶·a_3_5 + c_4_23·b_1_3³·b_3_8 + c_4_23·b_1_3⁶ + c_4_23·b_1_2³·b_3_9
       + c_4_22·b_1_3·b_5_33 + c_4_22·b_1_3³·b_3_10 + c_4_22·b_1_3³·b_3_8
       + c_4_22·b_1_2·b_5_33 + c_4_22·b_1_2³·b_3_12 + c_4_22·b_1_2³·b_3_9
       + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_3⁶ + c_4_21·b_1_2·b_5_33 + c_4_21·b_1_2³·b_3_11
       + c_4_23·a_3_5·b_3_8 + c_4_23·a_3_7·b_3_10 + c_4_23·a_3_7·b_3_8 + c_4_23·b_1_3³·a_3_5
       + c_4_23·b_1_3³·a_3_7 + c_4_23·a_1_1·b_1_3²·b_3_10 + c_4_23·a_1_1·b_1_3²·b_3_8
       + c_4_23·a_1_0·b_5_33 + c_4_23·a_1_0·b_1_3²·b_3_10 + c_4_23·a_1_0·b_1_3⁵
       + c_4_22·a_3_5·b_3_10 + c_4_22·a_3_5·b_3_8 + c_4_22·b_1_3³·a_3_7
       + c_4_22·a_1_1·b_1_3²·b_3_8 + c_4_22·a_1_1·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·b_3_10
       + c_4_22·a_1_0·b_1_3⁵ + c_4_21·a_3_5·b_3_10 + c_4_21·a_3_7·b_3_10
       + c_4_21·b_1_3³·a_3_5 + c_4_21·a_1_1·b_5_33 + c_4_21·a_1_1·b_1_3²·b_3_10
       + c_4_21·a_1_0·b_1_3⁵ + c_4_23·a_3_6·a_3_5 + c_4_23·a_1_0·b_1_3²·a_3_5
       + c_4_22·a_3_7·a_3_5 + c_4_22·a_3_6·a_3_5 + c_4_22·a_3_6·a_3_7 + c_4_21·a_3_6·a_3_5
       + c_4_21·a_1_0·b_1_3²·a_3_5 + c_4_21·c_4_22·b_1_2² + c_4_23²·a_1_1·b_1_3
       + c_4_21·c_4_22·a_1_1·b_1_3 + c_4_23²·a_1_0·a_1_1 + c_4_23²·a_1_0²
       + c_4_22·c_4_23·a_1_0·a_1_1 + c_4_22²·a_1_1² + c_4_22²·a_1_0²
       + c_4_21·c_4_23·a_1_0·a_1_1 + c_4_21·c_4_22·a_1_1² + c_4_21·c_4_22·a_1_0²
       + c_4_21²·a_1_1²
97. b_5_34·b_5_35 + b_1_3⁵·b_5_33 + b_1_3⁷·b_3_10 + b_1_3⁷·b_3_8 + b_1_3²·a_3_5·b_5_33
       + b_1_3⁴·a_3_5·b_3_10 + b_1_3⁴·a_3_5·b_3_8 + a_1_1·b_1_3⁴·b_5_33
       + a_1_1·b_1_3⁶·b_3_10 + a_1_1·b_1_3⁶·b_3_8 + a_1_0·b_1_3⁴·b_5_33
       + a_1_0·b_1_3⁶·b_3_10 + a_1_0·b_1_3⁶·b_3_8 + a_1_0·b_1_3·a_3_5·b_5_33
       + a_1_0·b_1_3³·a_3_5·b_3_8 + a_1_0·b_1_3⁶·a_3_5 + c_4_23·b_1_3³·b_3_10
       + c_4_23·b_1_3⁶ + c_4_23·b_1_2³·b_3_12 + c_4_23·b_1_2³·b_3_11
       + c_4_23·b_1_2³·b_3_9 + c_4_22·b_1_3·b_5_33 + c_4_22·b_1_2·b_5_34
       + c_4_22·b_1_2³·b_3_9 + c_4_21·b_1_2·b_5_34 + c_4_23·a_3_5·b_3_10
       + c_4_23·a_3_7·b_3_10 + c_4_23·a_3_7·b_3_8 + c_4_23·a_1_1·b_1_3²·b_3_10
       + c_4_23·a_1_1·b_1_3²·b_3_8 + c_4_23·a_1_1·b_1_3⁵ + c_4_23·a_1_0·b_1_3²·b_3_10
       + c_4_23·a_1_0·b_1_3²·b_3_8 + c_4_22·b_1_3³·a_3_7 + c_4_22·a_1_1·b_1_3²·b_3_8
       + c_4_22·a_1_1·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·b_3_8 + c_4_21·a_3_7·b_3_10
       + c_4_21·a_1_1·b_1_3²·b_3_10 + c_4_21·a_1_1·b_1_3⁵ + c_4_21·a_1_0·b_5_33
       + c_4_21·a_1_0·b_1_3²·b_3_10 + c_4_21·a_1_0·b_1_3²·b_3_8 + c_4_21·a_1_0·b_1_3⁵
       + c_4_23·a_3_7·a_3_5 + c_4_22·a_3_7·a_3_5 + c_4_22·a_3_6·a_3_5
       + c_4_22·a_1_0·b_1_3²·a_3_5 + c_4_21·a_3_6·a_3_5 + c_4_21·a_1_0·b_1_3²·a_3_5
       + c_4_23²·b_1_2² + c_4_22·c_4_23·b_1_2² + c_4_21·c_4_22·b_1_2²
       + c_4_23²·a_1_1·b_1_3 + c_4_22·c_4_23·a_1_0·b_1_3 + c_4_21·c_4_22·a_1_0·b_1_3
       + c_4_23²·a_1_0·a_1_1 + c_4_22·c_4_23·a_1_0² + c_4_21·c_4_23·a_1_1²
       + c_4_21·c_4_22·a_1_1² + c_4_21·c_4_22·a_1_0·a_1_1 + c_4_21²·a_1_1²
98. b_5_35² + b_1_3⁵·b_5_33 + b_1_3⁷·b_3_10 + b_1_3⁷·b_3_8 + b_1_2⁵·b_5_33
       + b_1_2⁷·b_3_11 + b_1_2⁷·b_3_9 + a_1_1·b_1_3⁴·b_5_33 + a_1_1·b_1_3⁶·b_3_10
       + a_1_1·b_1_3⁶·b_3_8 + a_1_0·b_1_3⁴·b_5_33 + a_1_0·b_1_3⁶·b_3_10
       + a_1_0·b_1_3⁶·b_3_8 + a_1_0·b_1_3⁶·a_3_5 + c_4_23·b_1_3⁶ + c_4_23·b_1_2³·b_3_11
       + c_4_23·b_1_2⁶ + c_4_22·b_1_3³·b_3_10 + c_4_22·b_1_3³·b_3_8 + c_4_22·b_1_2³·b_3_9
       + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_2³·b_3_11 + c_4_21·b_1_2⁶
       + c_4_23·a_1_1·b_1_3⁵ + c_4_22·b_1_3³·a_3_7 + c_4_22·a_1_1·b_1_3²·b_3_10
       + c_4_22·a_1_1·b_1_3²·b_3_8 + c_4_22·a_1_1·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·b_3_8
       + c_4_21·b_1_3³·a_3_7 + c_4_21·a_1_1·b_1_3²·b_3_8 + c_4_21·a_1_1·b_1_3⁵
       + c_4_21·a_1_0·b_1_3²·b_3_8 + c_4_21·a_1_0·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·a_3_5
       + c_4_23²·b_1_3² + c_4_23²·b_1_2² + c_4_22·c_4_23·b_1_2² + c_4_22²·b_1_2²
       + c_4_21·c_4_22·b_1_3² + c_4_21·c_4_22·b_1_2² + c_4_21²·b_1_2²
       + c_4_22²·a_1_0² + c_4_21·c_4_23·a_1_1² + c_4_21·c_4_22·a_1_1²
99. b_5_33·b_5_36 + b_5_33·b_5_34 + b_5_33² + b_1_3⁵·b_5_33 + b_1_2²·b_3_9·b_5_34
       + b_1_2⁵·b_5_33 + b_1_2⁷·b_3_11 + b_1_3²·a_3_7·b_5_33 + b_1_3⁷·a_3_7
       + a_1_0·b_1_3⁴·b_5_33 + a_1_0·b_1_3⁶·b_3_10 + a_1_0·b_1_3⁶·a_3_5 + c_4_23·b_1_3⁶
       + c_4_23·b_1_2³·b_3_11 + c_4_23·b_1_2³·b_3_9 + c_4_22·b_1_3³·b_3_10
       + c_4_22·b_1_3³·b_3_8 + c_4_22·b_1_2³·b_3_11 + c_4_21·b_1_3·b_5_33
       + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_3⁶ + c_4_21·b_1_2·b_5_34 + c_4_21·b_1_2·b_5_33
       + c_4_23·a_3_5·b_3_8 + c_4_23·a_3_7·b_3_10 + c_4_23·b_1_3³·a_3_5 + c_4_23·a_1_1·b_5_33
       + c_4_23·a_1_0·b_5_33 + c_4_23·a_1_0·b_1_3²·b_3_10 + c_4_23·a_1_0·b_1_3²·b_3_8
       + c_4_22·a_3_5·b_3_10 + c_4_22·a_3_5·b_3_8 + c_4_22·a_3_7·b_3_10 + c_4_22·a_3_7·b_3_8
       + c_4_22·b_1_3³·a_3_7 + c_4_22·a_1_1·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·b_3_10
       + c_4_21·a_3_5·b_3_10 + c_4_21·b_1_3³·a_3_5 + c_4_21·b_1_3³·a_3_7
       + c_4_21·a_1_1·b_1_3²·b_3_10 + c_4_21·a_1_1·b_1_3²·b_3_8 + c_4_21·a_1_0·b_5_33
       + c_4_21·a_1_0·b_1_3²·b_3_8 + c_4_21·a_1_0·b_1_3⁵ + c_4_23·a_3_7·a_3_5
       + c_4_23·a_3_6·a_3_7 + c_4_23·a_1_0·b_1_3²·a_3_5 + c_4_22·a_1_0·b_1_3²·a_3_5
       + c_4_21·a_3_7·a_3_5 + c_4_23²·b_1_3² + c_4_21·c_4_23·b_1_2²
       + c_4_21·c_4_22·b_1_3² + c_4_21·c_4_22·b_1_2² + c_4_23²·a_1_1·b_1_3
       + c_4_23²·a_1_0·b_1_3 + c_4_21·c_4_22·a_1_1·b_1_3 + c_4_21·c_4_22·a_1_0·b_1_3
       + c_4_23²·a_1_0² + c_4_22²·a_1_0² + c_4_21·c_4_23·a_1_1²
       + c_4_21·c_4_23·a_1_0·a_1_1 + c_4_21·c_4_23·a_1_0² + c_4_21²·a_1_0²
100. b_5_35·b_5_36 + b_5_34·b_5_36 + b_5_33·b_5_34 + b_5_33² + b_1_3⁷·b_3_8
        + b_1_2²·b_3_9·b_5_34 + b_1_2⁵·b_5_33 + b_1_2⁷·b_3_12 + b_1_2⁷·b_3_11 + b_1_2⁷·b_3_9
        + b_1_3⁴·a_3_5·b_3_10 + b_1_3⁴·a_3_5·b_3_8 + b_1_3⁴·a_3_7·b_3_10
        + a_1_1·b_1_3⁶·b_3_10 + a_1_0·b_1_3⁶·b_3_10 + a_1_0·b_1_3³·a_3_5·b_3_8
        + a_1_0·b_1_3⁶·a_3_5 + c_4_23·b_1_2·b_5_33 + c_4_23·b_1_2³·b_3_12
        + c_4_23·b_1_2³·b_3_9 + c_4_22·b_1_3⁶ + c_4_22·b_1_2·b_5_34 + c_4_22·b_1_2³·b_3_11
        + c_4_21·b_1_3·b_5_33 + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_3³·b_3_8 + c_4_21·b_1_3⁶
        + c_4_21·b_1_2·b_5_36 + c_4_21·b_1_2³·b_3_12 + c_4_21·b_1_2³·b_3_11 + c_4_21·b_1_2⁶
        + c_4_23·a_3_5·b_3_8 + c_4_23·a_3_7·b_3_10 + c_4_23·b_1_3³·a_3_5
        + c_4_23·b_1_3³·a_3_7 + c_4_23·a_1_1·b_5_33 + c_4_23·a_1_1·b_1_3²·b_3_10
        + c_4_23·a_1_1·b_1_3²·b_3_8 + c_4_23·a_1_0·b_5_33 + c_4_23·a_1_0·b_1_3²·b_3_8
        + c_4_22·a_3_5·b_3_8 + c_4_22·a_3_7·b_3_8 + c_4_22·b_1_3³·a_3_7 + c_4_22·a_1_1·b_5_33
        + c_4_22·a_1_0·b_5_33 + c_4_22·a_1_0·b_1_3²·b_3_10 + c_4_22·a_1_0·b_1_3⁵
        + c_4_21·a_3_5·b_3_10 + c_4_21·a_3_5·b_3_8 + c_4_21·a_3_7·b_3_10 + c_4_21·a_3_7·b_3_8
        + c_4_21·b_1_3³·a_3_5 + c_4_21·a_1_1·b_5_33 + c_4_21·a_1_1·b_1_3²·b_3_10
        + c_4_21·a_1_0·b_5_33 + c_4_23·a_3_7·a_3_5 + c_4_22·a_3_6·a_3_7
        + c_4_22·a_1_0·b_1_3²·a_3_5 + c_4_23²·b_1_3² + c_4_22²·b_1_3²
        + c_4_23²·a_1_1·b_1_3 + c_4_23²·a_1_0·b_1_3 + c_4_22·c_4_23·a_1_1·b_1_3
        + c_4_21·c_4_23·a_1_0·b_1_3 + c_4_21·c_4_22·a_1_0·b_1_3 + c_4_21²·a_1_1·b_1_3
        + c_4_23²·a_1_1² + c_4_22·c_4_23·a_1_1² + c_4_22·c_4_23·a_1_0²
        + c_4_22²·a_1_0² + c_4_21·c_4_23·a_1_1² + c_4_21·c_4_23·a_1_0·a_1_1
        + c_4_21·c_4_23·a_1_0² + c_4_21²·a_1_1² + c_4_21²·a_1_0·a_1_1
101. b_5_36² + b_5_33² + b_1_3⁵·b_5_33 + b_1_3⁷·b_3_10 + b_1_2⁵·b_5_36
        + a_1_1·b_1_3⁴·b_5_33 + a_1_1·b_1_3⁶·b_3_8 + a_1_0·b_1_3⁴·b_5_33
        + a_1_0·b_1_3⁶·b_3_10 + a_1_0·b_1_3⁶·b_3_8 + c_4_23·b_1_3⁶ + c_4_23·b_1_2³·b_3_12
        + c_4_23·b_1_2³·b_3_11 + c_4_23·b_1_2³·b_3_9 + c_4_23·b_1_2⁶
        + c_4_22·b_1_3³·b_3_10 + c_4_22·b_1_3³·b_3_8 + c_4_22·b_1_3⁶
        + c_4_22·b_1_2³·b_3_12 + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_3⁶
        + c_4_21·b_1_2³·b_3_12 + c_4_21·b_1_2⁶ + c_4_23·a_1_1·b_1_3⁵
        + c_4_22·b_1_3³·a_3_7 + c_4_22·a_1_1·b_1_3²·b_3_10 + c_4_22·a_1_1·b_1_3²·b_3_8
        + c_4_22·a_1_1·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·b_3_8 + c_4_21·b_1_3³·a_3_7
        + c_4_21·a_1_1·b_1_3²·b_3_8 + c_4_21·a_1_1·b_1_3⁵ + c_4_21·a_1_0·b_1_3²·b_3_8
        + c_4_21·a_1_0·b_1_3⁵ + c_4_22·a_1_0·b_1_3²·a_3_5 + c_4_23²·b_1_3²
        + c_4_23²·b_1_2² + c_4_22·c_4_23·b_1_2² + c_4_22²·b_1_3²
        + c_4_21·c_4_23·b_1_2² + c_4_21·c_4_22·b_1_3² + c_4_21²·b_1_3²
        + c_4_23²·a_1_1² + c_4_23²·a_1_0² + c_4_22·c_4_23·a_1_0² + c_4_22²·a_1_1²
        + c_4_21·c_4_23·a_1_1² + c_4_21·c_4_23·a_1_0² + c_4_21·c_4_22·a_1_0²
        + c_4_21²·a_1_1²
102. b_5_34·b_5_36 + b_5_33² + b_1_3⁵·b_5_33 + b_1_3⁷·b_3_10 + b_1_2⁵·b_5_33
        + b_1_3²·a_3_5·b_5_33 + b_1_3⁴·a_3_5·b_3_10 + b_1_3⁴·a_3_5·b_3_8
        + a_1_1·b_1_3⁴·b_5_33 + a_1_1·b_1_3⁶·b_3_8 + a_1_0·b_1_3·a_3_5·b_5_33
        + c_4_23·b_1_3⁶ + c_4_23·b_1_2·b_5_36 + c_4_23·b_1_2·b_5_34 + c_4_23·b_1_2·b_5_33
        + c_4_22·b_1_3³·b_3_10 + c_4_22·b_1_3³·b_3_8 + c_4_22·b_1_3⁶
        + c_4_22·b_1_2³·b_3_12 + c_4_22·b_1_2⁶ + c_4_21·b_1_3⁶ + c_4_21·b_1_2·b_5_34
        + c_4_21·b_1_2·b_5_33 + c_4_23·b_1_3³·a_3_5 + c_4_23·a_1_1·b_1_3⁵
        + c_4_23·a_1_0·b_1_3⁵ + c_4_22·a_3_5·b_3_8 + c_4_22·a_3_7·b_3_10
        + c_4_22·b_1_3³·a_3_7 + c_4_22·a_1_1·b_5_33 + c_4_22·a_1_1·b_1_3⁵
        + c_4_22·a_1_0·b_5_33 + c_4_22·a_1_0·b_1_3²·b_3_8 + c_4_21·a_3_5·b_3_10
        + c_4_21·a_3_7·b_3_10 + c_4_21·a_3_7·b_3_8 + c_4_21·b_1_3³·a_3_5
        + c_4_21·b_1_3³·a_3_7 + c_4_21·a_1_1·b_5_33 + c_4_21·a_1_1·b_1_3²·b_3_8
        + c_4_21·a_1_1·b_1_3⁵ + c_4_21·a_1_0·b_1_3⁵ + c_4_23·a_3_6·a_3_5
        + c_4_23·a_3_6·a_3_7 + c_4_23·a_1_0·b_1_3²·a_3_5 + c_4_22·a_3_7·a_3_5
        + c_4_22·a_3_6·a_3_5 + c_4_22·a_1_0·b_1_3²·a_3_5 + c_4_21·a_3_6·a_3_5
        + c_4_21·a_1_0·b_1_3²·a_3_5 + c_4_23²·b_1_3² + c_4_23²·b_1_2²
        + c_4_22·c_4_23·b_1_2² + c_4_22²·b_1_3² + c_4_21·c_4_23·b_1_2²
        + c_4_22·c_4_23·a_1_1·b_1_3 + c_4_22·c_4_23·a_1_0·b_1_3 + c_4_21·c_4_22·a_1_0·b_1_3
        + c_4_21²·a_1_0·b_1_3 + c_4_23²·a_1_0·a_1_1 + c_4_22·c_4_23·a_1_0·a_1_1
        + c_4_22·c_4_23·a_1_0² + c_4_22²·a_1_1² + c_4_22²·a_1_0·a_1_1 + c_4_22²·a_1_0²
        + c_4_21·c_4_23·a_1_1² + c_4_21·c_4_22·a_1_1² + c_4_21²·a_1_0²
103. b_5_33·b_5_34 + b_5_33² + b_1_3⁵·b_5_33 + b_1_2²·b_3_9·b_5_34 + b_1_3²·a_3_5·b_5_33
        + b_1_3⁴·a_3_7·b_3_10 + b_1_3⁷·a_3_7 + a_1_1·b_1_3⁴·b_5_33 + a_1_0·b_1_3⁴·b_5_33
        + a_1_0·b_1_3·a_3_5·b_5_33 + a_1_0·b_1_3³·a_3_5·b_3_10 + a_1_0·b_1_3³·a_3_5·b_3_8
        + c_4_23·b_1_3³·b_3_10 + c_4_23·b_1_3⁶ + c_4_23·b_1_2·b_5_33 + c_4_23·b_1_2³·b_3_9
        + c_4_22·b_1_3·b_5_33 + c_4_22·b_1_2·b_5_36 + c_4_22·b_1_2·b_5_34
        + c_4_22·b_1_2³·b_3_11 + c_4_21·b_1_3³·b_3_10 + c_4_21·b_1_3⁶
        + c_4_21·b_1_2³·b_3_11 + c_4_23·a_3_5·b_3_10 + c_4_23·a_3_7·b_3_10
        + c_4_23·a_3_7·b_3_8 + c_4_23·a_1_1·b_1_3⁵ + c_4_23·a_1_0·b_1_3²·b_3_8
        + c_4_22·a_3_5·b_3_10 + c_4_22·a_3_5·b_3_8 + c_4_22·a_1_1·b_1_3²·b_3_8
        + c_4_22·a_1_1·b_1_3⁵ + c_4_22·a_1_0·b_1_3⁵ + c_4_21·a_3_7·b_3_10
        + c_4_21·a_1_1·b_1_3²·b_3_10 + c_4_21·a_1_1·b_1_3²·b_3_8 + c_4_21·a_1_1·b_1_3⁵
        + c_4_21·a_1_0·b_5_33 + c_4_21·a_1_0·b_1_3²·b_3_10 + c_4_21·a_1_0·b_1_3²·b_3_8
        + c_4_21·a_1_0·b_1_3⁵ + c_4_23·a_3_6·a_3_7 + c_4_23·a_1_0·b_1_3²·a_3_5
        + c_4_22·a_3_6·a_3_7 + c_4_21·a_3_6·a_3_5 + c_4_21·a_3_6·a_3_7
        + c_4_21·a_1_0·b_1_3²·a_3_5 + c_4_23²·b_1_3² + c_4_21·c_4_22·b_1_3²
        + c_4_23²·a_1_1·b_1_3 + c_4_21·c_4_22·a_1_1·b_1_3 + c_4_22·c_4_23·a_1_0·a_1_1
        + c_4_22·c_4_23·a_1_0² + c_4_22²·a_1_1² + c_4_22²·a_1_0·a_1_1 + c_4_22²·a_1_0²
        + c_4_21·c_4_23·a_1_0·a_1_1 + c_4_21·c_4_23·a_1_0² + c_4_21·c_4_22·a_1_1²
        + c_4_21·c_4_22·a_1_0·a_1_1 + c_4_21·c_4_22·a_1_0² + c_4_21²·a_1_0·a_1_1

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Data used for Benson′s test

• Benson′s completion test succeeded in degree 10.
• The completion test was perfect: It applied in the last degree in which a generator or relation was found.
• The following is a filter regular homogeneous system of parameters:
  1. c_4_21, a Duflot regular element of degree 4
  2. c_4_22, a Duflot regular element of degree 4
  3. c_4_23, a Duflot regular element of degree 4
  4. b_1_3² + b_1_2², an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 7, 10].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 3

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. b_1_2 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_6 → 0, an element of degree 3
6. a_3_7 → 0, an element of degree 3
7. a_3_5 → 0, an element of degree 3
8. b_3_8 → 0, an element of degree 3
9. b_3_9 → 0, an element of degree 3
10. b_3_10 → 0, an element of degree 3
11. b_3_11 → 0, an element of degree 3
12. b_3_12 → 0, an element of degree 3
13. c_4_21 → c_1_2⁴ + c_1_1⁴, an element of degree 4
14. c_4_22 → c_1_1⁴, an element of degree 4
15. c_4_23 → c_1_2⁴ + c_1_0⁴, an element of degree 4
16. b_5_33 → 0, an element of degree 5
17. b_5_34 → 0, an element of degree 5
18. b_5_35 → 0, an element of degree 5
19. b_5_36 → 0, an element of degree 5

Restriction map to a maximal el. ab. subgp. of rank 4

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. b_1_2 → c_1_3, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_6 → 0, an element of degree 3
6. a_3_7 → 0, an element of degree 3
7. a_3_5 → 0, an element of degree 3
8. b_3_8 → 0, an element of degree 3
9. b_3_9 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
10. b_3_10 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
11. b_3_11 → c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
12. b_3_12 → c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_1·c_1_3² + c_1_1²·c_1_3 + c_1_0·c_1_3²
       + c_1_0²·c_1_3, an element of degree 3
13. c_4_21 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴ + c_1_0·c_1_3³
       + c_1_0²·c_1_3², an element of degree 4
14. c_4_22 → c_1_1·c_1_3³ + c_1_1⁴, an element of degree 4
15. c_4_23 → c_1_2·c_1_3³ + c_1_2⁴ + c_1_1·c_1_3³ + c_1_1²·c_1_3² + c_1_0·c_1_3³ + c_1_0⁴, an element of degree 4
16. b_5_33 → c_1_1·c_1_3⁴ + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3 + c_1_1⁴·c_1_3, an element of degree 5
17. b_5_34 → c_1_2·c_1_3⁴ + c_1_2⁴·c_1_3 + c_1_1·c_1_3⁴ + c_1_1⁴·c_1_3 + c_1_0·c_1_3⁴
       + c_1_0·c_1_1·c_1_3³ + c_1_0·c_1_1²·c_1_3² + c_1_0²·c_1_1·c_1_3²
       + c_1_0²·c_1_1²·c_1_3 + c_1_0⁴·c_1_3, an element of degree 5
18. b_5_35 → c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_1·c_1_3⁴ + c_1_1⁴·c_1_3 + c_1_0·c_1_3⁴
       + c_1_0·c_1_1·c_1_3³ + c_1_0·c_1_1²·c_1_3² + c_1_0²·c_1_1·c_1_3²
       + c_1_0²·c_1_1²·c_1_3 + c_1_0⁴·c_1_3, an element of degree 5
19. b_5_36 → c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_1·c_1_3⁴ + c_1_1·c_1_2·c_1_3³
       + c_1_1·c_1_2²·c_1_3² + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3
       + c_1_1⁴·c_1_3 + c_1_0·c_1_2·c_1_3³ + c_1_0·c_1_2²·c_1_3² + c_1_0²·c_1_3³
       + c_1_0²·c_1_2·c_1_3² + c_1_0²·c_1_2²·c_1_3 + c_1_0⁴·c_1_3, an element of degree 5

Restriction map to a maximal el. ab. subgp. of rank 4

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. b_1_2 → 0, an element of degree 1
4. b_1_3 → c_1_3, an element of degree 1
5. a_3_6 → 0, an element of degree 3
6. a_3_7 → 0, an element of degree 3
7. a_3_5 → 0, an element of degree 3
8. b_3_8 → c_1_2²·c_1_3, an element of degree 3
9. b_3_9 → 0, an element of degree 3
10. b_3_10 → c_1_1²·c_1_3, an element of degree 3
11. b_3_11 → 0, an element of degree 3
12. b_3_12 → 0, an element of degree 3
13. c_4_21 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1²·c_1_3² + c_1_1⁴, an element of degree 4
14. c_4_22 → c_1_1²·c_1_3² + c_1_1⁴, an element of degree 4
15. c_4_23 → c_1_2²·c_1_3² + c_1_2⁴ + c_1_1²·c_1_3² + c_1_0²·c_1_3² + c_1_0⁴, an element of degree 4
16. b_5_33 → c_1_2⁴·c_1_3 + c_1_1²·c_1_2²·c_1_3 + c_1_1⁴·c_1_3 + c_1_0²·c_1_3³ + c_1_0⁴·c_1_3, an element of degree 5
17. b_5_34 → c_1_1⁴·c_1_3, an element of degree 5
18. b_5_35 → c_1_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1²·c_1_3³ + c_1_1²·c_1_2²·c_1_3
       + c_1_1⁴·c_1_3 + c_1_0²·c_1_3³ + c_1_0⁴·c_1_3, an element of degree 5
19. b_5_36 → c_1_2²·c_1_3³ + c_1_2⁴·c_1_3 + c_1_1²·c_1_3³, an element of degree 5

About the group

Ring generators

Ring relations

Completion information

Restriction maps

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