David J. Green

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Cohomology of group number 1566 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 a unique conjugacy class of maximal elementary abelian subgroups, which is 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

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

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

• The a-invariants are -∞,-∞,-∞,-4,-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 18 minimal generators of maximal degree 8:

1. a_1_0, a nilpotent element of degree 1
2. a_1_1, a nilpotent element of degree 1
3. a_1_2, a nilpotent element of degree 1
4. b_1_3, an element of degree 1
5. a_3_5, a nilpotent element of degree 3
6. a_3_6, a nilpotent element of degree 3
7. a_3_7, a nilpotent element of degree 3
8. a_3_8, a nilpotent element of degree 3
9. b_3_9, an element of degree 3
10. b_3_10, an element of degree 3
11. b_4_16, an element of degree 4
12. c_4_17, a Duflot regular element of degree 4
13. c_4_18, a Duflot regular element of degree 4
14. c_4_19, a Duflot regular element of degree 4
15. a_5_22, a nilpotent element of degree 5
16. b_6_36, an element of degree 6
17. b_6_38, an element of degree 6
18. b_8_67, an element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 95 minimal relations of maximal degree 16:

1. a_1_1·a_1_2 + a_1_0²
2. a_1_1·b_1_3 + a_1_2² + a_1_0·a_1_2
3. a_1_2·b_1_3 + a_1_2² + a_1_1² + a_1_0·a_1_2 + a_1_0·a_1_1 + a_1_0²
4. a_1_1³
5. a_1_0²·a_1_2 + a_1_0²·a_1_1
6. a_1_0·a_1_2² + a_1_0·a_1_1² + a_1_0³
7. a_1_1·a_3_6 + a_1_0·a_3_7 + a_1_0·a_3_5
8. a_1_2·a_3_7 + a_1_2·a_3_5 + a_1_0·a_3_6
9. a_1_1·a_3_8 + a_1_1·a_3_7 + a_1_1·a_3_5 + a_1_0·a_3_6 + a_1_0·a_3_5
10. a_1_2·a_3_6 + a_1_2·a_3_5 + a_1_1·a_3_6 + a_1_0·a_3_8
11. b_1_3·a_3_7 + a_1_1·b_3_9 + a_1_1·a_3_6 + a_1_1·a_3_5
12. b_1_3·a_3_8 + b_1_3·a_3_6 + a_1_0·b_3_9 + a_1_1·a_3_7 + a_1_1·a_3_6 + a_1_1·a_3_5
       + a_1_0·a_3_5
13. b_1_3·a_3_7 + a_1_2·b_3_9 + a_1_2·a_3_6 + a_1_1·a_3_7 + a_1_1·a_3_6 + a_1_0·a_3_6
       + a_1_0·a_3_5
14. a_1_1·b_3_10 + a_1_2·a_3_5 + a_1_1·a_3_7 + a_1_0·a_3_6 + a_1_0·a_3_5
15. b_1_3·a_3_7 + b_1_3·a_3_5 + a_1_0·b_3_10 + a_1_2·a_3_8 + a_1_2·a_3_5 + a_1_1·a_3_6
       + a_1_0·a_3_6 + a_1_0·a_3_5
16. b_1_3·a_3_7 + a_1_2·b_3_10 + a_1_2·a_3_6 + a_1_2·a_3_5 + a_1_0·a_3_6
17. a_1_2²·a_3_5 + a_1_1²·a_3_5 + a_1_0²·a_3_5
18. a_1_1²·a_3_7 + a_1_1²·a_3_5 + a_1_0·a_1_2·a_3_5 + a_1_0²·a_3_8
19. a_1_2²·a_3_8 + a_1_1²·a_3_5 + a_1_0·a_1_2·a_3_8 + a_1_0·a_1_2·a_3_5
       + a_1_0·a_1_1·a_3_7 + a_1_0²·a_3_7
20. b_4_16·a_1_1 + a_1_1²·a_3_7 + a_1_0·a_1_2·a_3_8 + a_1_0·a_1_2·a_3_5 + a_1_0²·a_3_7
       + a_1_0²·a_3_6
21. b_1_3²·a_3_6 + a_1_0·b_1_3·b_3_9 + b_4_16·a_1_0 + a_1_1²·a_3_7 + a_1_1²·a_3_5
       + a_1_0·a_1_2·a_3_5 + a_1_0·a_1_1·a_3_7 + a_1_0²·a_3_5
22. b_4_16·a_1_2 + a_1_1²·a_3_5 + a_1_0·a_1_2·a_3_8 + a_1_0·a_1_2·a_3_5 + a_1_0·a_1_1·a_3_7
       + a_1_0·a_1_1·a_3_5 + a_1_0²·a_3_7
23. a_3_7·a_3_8 + a_3_7² + a_3_6² + a_3_5·a_3_8 + a_3_5·a_3_6 + a_3_5²
24. a_3_7·b_3_10 + a_3_7·b_3_9 + a_3_8² + a_3_7·a_3_8 + a_3_6·a_3_8 + a_3_5·a_3_6
       + a_1_0³·a_3_5 + c_4_18·a_1_1² + c_4_17·a_1_2² + c_4_17·a_1_1²
       + c_4_17·a_1_0·a_1_2
25. a_3_7·b_3_9 + a_3_8² + a_3_7·a_3_8 + a_3_6·a_3_8 + a_1_0³·a_3_5 + c_4_18·a_1_0²
       + c_4_17·a_1_2² + c_4_17·a_1_1² + c_4_17·a_1_0·a_1_2 + c_4_17·a_1_0·a_1_1
26. a_3_8·b_3_10 + a_3_7·b_3_9 + a_3_6·b_3_10 + a_3_5·b_3_9 + a_3_7² + a_3_6·a_3_8
       + a_3_5·a_3_6 + a_3_5² + a_1_0³·a_3_5 + c_4_18·a_1_0·a_1_2 + c_4_18·a_1_0·a_1_1
       + c_4_17·a_1_0²
27. a_3_7·b_3_10 + a_3_8² + a_3_6² + a_3_5·a_3_6 + c_4_18·a_1_2² + c_4_17·a_1_2²
       + c_4_17·a_1_1² + c_4_17·a_1_0·a_1_1
28. b_3_10² + b_1_3³·b_3_9 + a_3_7·b_3_9 + a_3_7·a_3_8 + a_3_6·a_3_8 + a_3_6² + a_3_5²
       + c_4_19·b_1_3² + c_4_17·a_1_1² + c_4_17·a_1_0·a_1_2 + c_4_17·a_1_0·a_1_1
       + c_4_17·a_1_0²
29. a_3_8·b_3_10 + a_3_7·b_3_10 + a_3_6·b_3_10 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_1_0·b_1_3²·b_3_9 + a_3_8² + a_3_7·a_3_8 + a_3_6·a_3_8 + a_3_6·a_3_7 + a_3_5·a_3_7
       + a_3_5·a_3_6 + a_3_5² + c_4_19·a_1_0·b_1_3 + c_4_18·a_1_0·a_1_1 + c_4_17·a_1_2²
       + c_4_17·a_1_1² + c_4_17·a_1_0·a_1_1
30. a_3_7·b_3_10 + a_3_7² + a_3_6² + a_3_5·a_3_6 + c_4_19·a_1_1² + c_4_17·a_1_0·a_1_1
       + c_4_17·a_1_0²
31. a_3_8·b_3_10 + a_3_7·b_3_9 + a_3_6·b_3_10 + a_3_5·b_3_9 + a_3_7·a_3_8 + a_3_6²
       + a_3_5·a_3_7 + a_3_5² + c_4_19·a_1_0·a_1_1 + c_4_17·a_1_0·a_1_2 + c_4_17·a_1_0²
32. a_3_7·b_3_10 + a_3_7·b_3_9 + a_3_8² + a_3_7·a_3_8 + a_3_7² + a_3_6·a_3_8 + a_3_5·a_3_6
       + a_3_5² + a_1_0³·a_3_5 + c_4_19·a_1_0² + c_4_17·a_1_2² + c_4_17·a_1_0·a_1_2
33. a_3_6·a_3_7 + a_3_5·a_3_6 + c_4_19·a_1_0·a_1_2 + c_4_18·a_1_0·a_1_1 + c_4_17·a_1_0·a_1_1
34. a_3_7·b_3_9 + a_3_8² + a_3_7·a_3_8 + a_3_6·a_3_8 + a_3_6² + a_1_0³·a_3_5
       + c_4_19·a_1_2² + c_4_17·a_1_2² + c_4_17·a_1_1² + c_4_17·a_1_0·a_1_2
       + c_4_17·a_1_0·a_1_1 + c_4_17·a_1_0²
35. b_3_9² + b_1_3³·b_3_10 + b_1_3³·b_3_9 + b_4_16·b_1_3² + a_1_0·b_1_3²·b_3_9
       + a_3_6² + c_4_18·b_1_3² + c_4_17·a_1_1²
36. a_3_8·b_3_9 + a_3_7·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_9
       + b_4_16·a_1_0·b_1_3 + a_3_6·a_3_8 + a_3_6² + a_3_5·a_3_6 + c_4_18·a_1_0·b_1_3
       + c_4_18·a_1_0·a_1_1 + c_4_17·a_1_1² + c_4_17·a_1_0·a_1_1 + c_4_17·a_1_0²
37. a_3_8·b_3_10 + a_3_8·b_3_9 + a_3_7·b_3_9 + a_3_6·b_3_10 + a_3_6·b_3_9 + b_1_3·a_5_22
       + a_1_0·b_1_3²·b_3_10 + a_1_0·b_1_3²·b_3_9 + a_3_8² + a_3_7² + a_3_5²
       + a_1_0³·a_3_5 + c_4_17·a_1_2² + c_4_17·a_1_1²
38. a_3_8·b_3_10 + a_3_7·b_3_9 + a_3_6·b_3_10 + a_3_5·b_3_9 + a_3_7·a_3_8 + a_3_7²
       + a_3_6·a_3_7 + a_3_6² + a_3_5·a_3_6 + a_3_5² + a_1_1·a_5_22 + a_1_0³·a_3_5
       + c_4_17·a_1_0·a_1_2 + c_4_17·a_1_0·a_1_1 + c_4_17·a_1_0²
39. a_3_7·b_3_10 + a_3_7·b_3_9 + a_3_8² + a_3_7·a_3_8 + a_3_7² + a_3_6·a_3_8 + a_3_6·a_3_7
       + a_3_6² + a_3_5·a_3_6 + a_3_5² + a_1_0·a_5_22 + a_1_0³·a_3_5 + c_4_17·a_1_2²
       + c_4_17·a_1_0·a_1_2 + c_4_17·a_1_0²
40. a_3_6·a_3_8 + a_3_6² + a_1_2·a_5_22 + c_4_18·a_1_0·a_1_1 + c_4_17·a_1_0·a_1_2
       + c_4_17·a_1_0·a_1_1
41. b_1_3·a_3_6·b_3_9 + a_1_0·b_1_3³·b_3_10 + a_1_0·b_1_3³·b_3_9 + b_4_16·a_3_6
       + a_1_0·b_1_3·a_5_22 + a_1_1²·a_5_22 + c_4_18·a_1_0·b_1_3² + c_4_17·a_1_0·b_1_3²
       + c_4_19·a_1_0²·a_1_1 + c_4_19·a_1_0³ + c_4_18·a_1_0²·a_1_1 + c_4_17·a_1_0²·a_1_1
       + c_4_17·a_1_0³
42. b_1_3·a_3_6·b_3_10 + a_1_0·b_3_9·b_3_10 + b_4_16·a_3_8 + b_4_16·a_3_7 + b_4_16·a_3_5
       + b_4_16·a_1_0·b_1_3² + a_1_0·b_1_3·a_5_22 + a_1_0·a_1_1·a_5_22
       + c_4_17·a_1_0·b_1_3² + c_4_19·a_1_0·a_1_1² + c_4_19·a_1_0²·a_1_1
       + c_4_18·a_1_0·a_1_1² + c_4_18·a_1_0²·a_1_1 + c_4_17·a_1_0·a_1_1²
43. b_1_3·a_3_6·b_3_10 + a_1_0·b_3_9·b_3_10 + b_4_16·a_3_8 + b_4_16·a_3_5
       + b_4_16·a_1_0·b_1_3² + a_1_0·b_1_3·a_5_22 + a_1_0²·a_5_22 + c_4_17·a_1_0·b_1_3²
       + c_4_19·a_1_0²·a_1_1 + c_4_18·a_1_0·a_1_1² + c_4_17·a_1_0·a_1_1²
44. b_4_16·a_3_8 + b_4_16·a_1_0·b_1_3² + a_1_0·a_1_2·a_5_22 + c_4_17·a_1_0·b_1_3²
       + c_4_19·a_1_0·a_1_1² + c_4_19·a_1_0²·a_1_1 + c_4_19·a_1_0³
       + c_4_18·a_1_0·a_1_1² + c_4_18·a_1_0²·a_1_1 + c_4_17·a_1_0·a_1_1²
45. b_1_3·a_3_6·b_3_10 + b_1_3·a_3_6·b_3_9 + a_1_0·b_3_9·b_3_10 + a_1_0·b_1_3³·b_3_10
       + a_1_0·b_1_3³·b_3_9 + b_4_16·a_3_8 + b_4_16·a_3_6 + b_4_16·a_3_5
       + b_4_16·a_1_0·b_1_3² + a_1_2²·a_5_22 + c_4_18·a_1_0·b_1_3² + c_4_19·a_1_0³
       + c_4_18·a_1_0·a_1_1² + c_4_18·a_1_0²·a_1_1 + c_4_17·a_1_0·a_1_1²
       + c_4_17·a_1_0²·a_1_1 + c_4_17·a_1_0³
46. b_1_3·b_3_9·b_3_10 + b_1_3⁴·b_3_10 + b_1_3⁴·b_3_9 + b_6_36·b_1_3 + b_4_16·b_3_10
       + b_4_16·b_1_3³ + b_1_3·a_3_6·b_3_10 + b_4_16·a_3_8 + b_4_16·a_3_7 + b_4_16·a_3_6
       + b_4_16·a_3_5 + c_4_18·b_1_3³ + c_4_19·a_1_0·b_1_3² + c_4_18·a_1_0·b_1_3²
       + c_4_17·a_1_0·b_1_3² + c_4_19·a_1_0·a_1_1² + c_4_18·a_1_0·a_1_1²
       + c_4_18·a_1_0²·a_1_1 + c_4_18·a_1_0³ + c_4_17·a_1_0·a_1_1²
47. b_6_36·a_1_1 + b_4_16·a_3_8 + b_4_16·a_1_0·b_1_3² + c_4_17·a_1_0·b_1_3²
       + c_4_19·a_1_0²·a_1_1 + c_4_18·a_1_0·a_1_1² + c_4_18·a_1_0²·a_1_1
       + c_4_17·a_1_0²·a_1_1
48. b_1_3·a_3_6·b_3_10 + a_1_0·b_1_3³·b_3_10 + a_1_0·b_1_3³·b_3_9 + b_6_36·a_1_0
       + b_4_16·a_3_8 + b_4_16·a_3_7 + a_1_0·b_1_3·a_5_22 + c_4_18·a_1_0·b_1_3²
       + c_4_17·a_1_0·b_1_3² + c_4_19·a_1_0²·a_1_1 + c_4_19·a_1_0³ + c_4_18·a_1_0²·a_1_1
       + c_4_17·a_1_0·a_1_1² + c_4_17·a_1_0²·a_1_1
49. b_1_3·a_3_6·b_3_10 + b_1_3·a_3_6·b_3_9 + a_1_0·b_3_9·b_3_10 + a_1_0·b_1_3³·b_3_10
       + a_1_0·b_1_3³·b_3_9 + b_6_36·a_1_2 + b_4_16·a_3_7 + b_4_16·a_3_6 + b_4_16·a_3_5
       + c_4_18·a_1_0·b_1_3² + c_4_17·a_1_0·b_1_3² + c_4_18·a_1_0·a_1_1²
       + c_4_18·a_1_0²·a_1_1 + c_4_17·a_1_0²·a_1_1
50. b_6_38·b_1_3 + b_4_16·b_3_9 + b_4_16·b_1_3³ + a_1_0·b_1_3³·b_3_9 + b_4_16·a_3_8
       + b_4_16·a_3_7 + b_4_16·a_3_6 + b_4_16·a_3_5 + a_1_0·b_1_3·a_5_22 + c_4_18·b_1_3³
       + c_4_19·a_1_0·a_1_1² + c_4_19·a_1_0²·a_1_1 + c_4_19·a_1_0³ + c_4_18·a_1_0²·a_1_1
       + c_4_18·a_1_0³ + c_4_17·a_1_0·a_1_1² + c_4_17·a_1_0²·a_1_1
51. b_6_38·a_1_1 + c_4_19·a_1_0·a_1_1² + c_4_19·a_1_0²·a_1_1 + c_4_18·a_1_0²·a_1_1
       + c_4_17·a_1_0·a_1_1² + c_4_17·a_1_0²·a_1_1 + c_4_17·a_1_0³
52. b_1_3·a_3_6·b_3_10 + b_1_3·a_3_6·b_3_9 + a_1_0·b_3_9·b_3_10 + a_1_0·b_1_3³·b_3_10
       + a_1_0·b_1_3³·b_3_9 + b_6_38·a_1_0 + b_4_16·a_3_7 + b_4_16·a_3_5 + a_1_0·b_1_3·a_5_22
       + c_4_19·a_1_0²·a_1_1 + c_4_18·a_1_0·a_1_1² + c_4_18·a_1_0²·a_1_1 + c_4_18·a_1_0³
       + c_4_17·a_1_0·a_1_1² + c_4_17·a_1_0²·a_1_1 + c_4_17·a_1_0³
53. b_6_38·a_1_2 + b_4_16·a_3_8 + b_4_16·a_3_7 + b_4_16·a_1_0·b_1_3² + a_1_0·b_1_3·a_5_22
       + c_4_17·a_1_0·b_1_3² + c_4_19·a_1_0²·a_1_1 + c_4_17·a_1_0·a_1_1²
54. b_4_16·b_1_3⁴ + b_4_16² + a_1_0·b_1_3⁴·b_3_10 + b_4_16·a_1_0·b_1_3³
       + c_4_17·b_1_3⁴
55. b_3_10·a_5_22 + a_1_0·b_1_3⁴·b_3_10 + a_1_0·b_1_3⁴·b_3_9 + b_4_16·a_1_0·b_3_10
       + b_4_16·a_1_0·b_1_3³ + c_4_19·a_1_0·b_3_9 + c_4_18·a_1_0·b_3_10
       + c_4_18·a_1_0·b_1_3³ + c_4_19·a_1_2·a_3_8 + c_4_19·a_1_2·a_3_5 + c_4_19·a_1_0·a_3_7
       + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_1·a_3_7 + c_4_18·a_1_1·a_3_5 + c_4_18·a_1_0·a_3_6
       + c_4_18·a_1_0·a_3_5 + c_4_17·a_1_0·a_3_7
56. a_3_7·a_5_22 + a_1_0·a_1_1²·a_5_22 + c_4_19·a_1_2·a_3_8 + c_4_19·a_1_2·a_3_5
       + c_4_19·a_1_1·a_3_7 + c_4_19·a_1_1·a_3_5 + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_6
       + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_1·a_3_7 + c_4_18·a_1_1·a_3_5 + c_4_18·a_1_0·a_3_7
57. a_3_8·a_5_22 + a_3_6·a_5_22 + a_1_0·a_1_1²·a_5_22 + c_4_18·a_1_2·a_3_5
       + c_4_18·a_1_1·a_3_7 + c_4_18·a_1_0·a_3_8 + c_4_18·a_1_0·a_3_7 + c_4_18·a_1_0·a_3_5
       + c_4_17·a_1_2·a_3_5 + c_4_17·a_1_1·a_3_7 + c_4_17·a_1_0·a_3_6
58. a_3_8·a_5_22 + a_3_5·a_5_22 + a_1_0·a_1_1²·a_5_22 + c_4_19·a_1_1·a_3_7
       + c_4_19·a_1_1·a_3_5 + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_7 + c_4_18·a_1_2·a_3_5
       + c_4_18·a_1_1·a_3_7 + c_4_18·a_1_1·a_3_5 + c_4_18·a_1_0·a_3_8 + c_4_18·a_1_0·a_3_6
       + c_4_17·a_1_2·a_3_5 + c_4_17·a_1_0·a_3_7 + c_4_17·a_1_0·a_3_6
59. a_3_8·a_5_22 + a_1_0³·a_5_22 + c_4_19·a_1_2·a_3_8 + c_4_19·a_1_2·a_3_5
       + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_7 + c_4_19·a_1_0·a_3_5 + c_4_18·a_1_2·a_3_5
       + c_4_18·a_1_1·a_3_7 + c_4_18·a_1_0·a_3_8 + c_4_18·a_1_0·a_3_6 + c_4_18·a_1_0·a_3_5
       + c_4_17·a_1_2·a_3_5 + c_4_17·a_1_1·a_3_7 + c_4_17·a_1_0·a_3_7 + c_4_17·a_1_0·a_3_6
60. b_3_9·a_5_22 + a_1_0·b_1_3⁴·b_3_10 + b_6_36·a_1_0·b_1_3 + b_4_16·a_1_0·b_3_9
       + b_4_16·a_1_0·b_1_3³ + a_1_0·a_1_1²·a_5_22 + c_4_19·a_1_0·b_1_3³
       + c_4_18·a_1_0·b_3_10 + c_4_18·a_1_0·b_3_9 + c_4_18·a_1_0·b_1_3³ + c_4_19·a_1_2·a_3_8
       + c_4_19·a_1_2·a_3_5 + c_4_19·a_1_0·a_3_8 + c_4_19·a_1_0·a_3_7 + c_4_19·a_1_0·a_3_5
       + c_4_18·a_1_2·a_3_8 + c_4_18·a_1_2·a_3_5 + c_4_18·a_1_1·a_3_5 + c_4_18·a_1_0·a_3_6
       + c_4_17·a_1_1·a_3_7 + c_4_17·a_1_0·a_3_7
61. b_6_36·a_3_8 + b_4_16·a_5_22 + b_4_16·a_1_0·b_1_3·b_3_9 + c_4_17·a_1_0·b_1_3·b_3_10
       + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_2·a_3_8 + c_4_19·a_1_0²·a_3_8
       + c_4_19·a_1_0²·a_3_7 + c_4_19·a_1_0²·a_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0·a_1_1·a_3_5 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_1²·a_3_5 + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_5
62. a_3_6·b_3_9·b_3_10 + a_1_0·b_1_3⁵·b_3_10 + b_6_36·a_1_0·b_1_3² + b_4_16·a_5_22
       + c_4_19·a_1_0·b_1_3⁴ + c_4_18·a_1_0·b_1_3·b_3_10 + c_4_18·a_1_0·b_1_3⁴
       + c_4_17·a_1_0·b_1_3⁴ + b_4_16·c_4_18·a_1_0 + c_4_19·a_1_0·a_1_2·a_3_8
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_0²·a_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0·a_1_2·a_3_8 + c_4_18·a_1_0·a_1_1·a_3_5 + c_4_18·a_1_0²·a_3_8
       + c_4_18·a_1_0²·a_3_7 + c_4_18·a_1_0²·a_3_6 + c_4_17·a_1_1²·a_3_5
       + c_4_17·a_1_0·a_1_1·a_3_7 + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_5
63. b_1_3⁶·b_3_9 + b_6_36·b_3_10 + b_6_36·b_1_3³ + b_4_16·b_1_3²·b_3_9
       + a_3_6·b_3_9·b_3_10 + a_1_0·b_1_3⁵·b_3_10 + a_1_0·b_1_3⁵·b_3_9
       + b_4_16·a_1_0·b_1_3·b_3_10 + b_4_16·a_1_0·b_1_3·b_3_9 + b_4_16²·a_1_0
       + c_4_19·b_1_3²·b_3_9 + c_4_19·b_1_3⁵ + c_4_18·b_1_3²·b_3_10 + b_4_16·c_4_19·b_1_3
       + c_4_19·a_1_0·b_1_3·b_3_10 + c_4_19·a_1_0·b_1_3·b_3_9 + c_4_17·a_1_0·b_1_3·b_3_10
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_0²·a_3_7 + c_4_19·a_1_0²·a_3_6
       + c_4_18·a_1_0·a_1_1·a_3_5 + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_1²·a_3_5 + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_5
64. b_6_36·a_3_7 + c_4_19·a_1_0·a_1_2·a_3_8 + c_4_19·a_1_0²·a_3_8 + c_4_18·a_1_1²·a_3_5
       + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_7
       + c_4_18·a_1_0²·a_3_6 + c_4_17·a_1_1²·a_3_5 + c_4_17·a_1_0·a_1_2·a_3_5
       + c_4_17·a_1_0·a_1_1·a_3_7 + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_7
65. a_1_0·b_1_3⁵·b_3_10 + b_6_36·a_3_6 + b_4_16·a_1_0·b_1_3·b_3_10
       + c_4_19·a_1_0·b_1_3⁴ + c_4_18·a_1_0·b_1_3·b_3_10 + c_4_18·a_1_0·b_1_3·b_3_9
       + c_4_18·a_1_0·b_1_3⁴ + c_4_17·a_1_0·b_1_3·b_3_10 + c_4_17·a_1_0·b_1_3⁴
       + b_4_16·c_4_18·a_1_0 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_5
       + c_4_19·a_1_0²·a_3_7 + c_4_19·a_1_0²·a_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_1²·a_3_5 + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0·a_1_1·a_3_7
       + c_4_18·a_1_0²·a_3_7 + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_7
66. a_3_6·b_3_9·b_3_10 + a_1_0·b_1_3⁵·b_3_10 + a_1_0·b_1_3⁵·b_3_9 + b_6_36·a_3_5
       + b_4_16·a_5_22 + b_4_16·a_1_0·b_1_3·b_3_9 + c_4_19·a_1_0·b_1_3·b_3_9
       + c_4_18·a_1_0·b_1_3⁴ + c_4_17·a_1_0·b_1_3⁴ + b_4_16·c_4_19·a_1_0
       + b_4_16·c_4_18·a_1_0 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_7
       + c_4_19·a_1_0²·a_3_8 + c_4_19·a_1_0²·a_3_6 + c_4_18·a_1_1²·a_3_5
       + c_4_18·a_1_0·a_1_2·a_3_8 + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0·a_1_1·a_3_7
       + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_5 + c_4_17·a_1_0·a_1_2·a_3_5
       + c_4_17·a_1_0·a_1_1·a_3_7 + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_8
       + c_4_17·a_1_0²·a_3_6
67. b_6_38·a_3_8 + b_4_16·a_1_0·b_1_3·b_3_9 + b_4_16²·a_1_0 + c_4_17·a_1_0·b_1_3·b_3_9
       + b_4_16·c_4_18·a_1_0 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_2·a_3_5
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_0·a_1_1·a_3_5 + c_4_19·a_1_0²·a_3_6
       + c_4_19·a_1_0²·a_3_5 + c_4_18·a_1_1²·a_3_5 + c_4_18·a_1_0·a_1_1·a_3_5
       + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_7 + c_4_18·a_1_0²·a_3_6
       + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_2·a_3_5 + c_4_17·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_5
68. b_1_3⁶·b_3_10 + b_6_38·b_3_10 + b_6_36·b_3_9 + b_4_16·b_1_3²·b_3_9 + b_4_16²·b_1_3
       + a_3_6·b_3_9·b_3_10 + a_1_0·b_1_3⁵·b_3_10 + a_1_0·b_1_3⁵·b_3_9
       + b_4_16·a_1_0·b_1_3·b_3_10 + c_4_19·b_1_3⁵ + c_4_18·b_1_3²·b_3_9 + c_4_18·b_1_3⁵
       + c_4_17·b_1_3⁵ + c_4_19·a_1_0·b_1_3·b_3_9 + c_4_18·a_1_0·b_1_3·b_3_9
       + c_4_17·a_1_0·b_1_3·b_3_9 + c_4_17·a_1_0·b_1_3⁴ + b_4_16·c_4_19·a_1_0
       + b_4_16·c_4_18·a_1_0 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_2·a_3_8
       + c_4_19·a_1_0²·a_3_8 + c_4_19·a_1_0²·a_3_7 + c_4_18·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0·a_1_1·a_3_7 + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_7
       + c_4_17·a_1_0²·a_3_6
69. b_6_38·a_3_7 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_2·a_3_8
       + c_4_19·a_1_0·a_1_2·a_3_5 + c_4_19·a_1_0²·a_3_8 + c_4_18·a_1_1²·a_3_5
       + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_7
       + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_2·a_3_5 + c_4_17·a_1_0·a_1_1·a_3_5
       + c_4_17·a_1_0²·a_3_7 + c_4_17·a_1_0²·a_3_6 + c_4_17·a_1_0²·a_3_5
70. b_6_38·a_3_6 + b_4_16·a_1_0·b_1_3·b_3_10 + b_4_16·a_1_0·b_1_3·b_3_9
       + c_4_18·a_1_0·b_1_3·b_3_9 + c_4_17·a_1_0·b_1_3·b_3_9 + c_4_19·a_1_1²·a_3_5
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_0²·a_3_6 + c_4_18·a_1_0·a_1_1·a_3_5
       + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_7 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_7
       + c_4_17·a_1_0²·a_3_5
71. b_6_38·a_3_5 + b_4_16·a_5_22 + b_4_16·a_1_0·b_1_3·b_3_10 + b_4_16²·a_1_0
       + c_4_18·a_1_0·b_1_3·b_3_10 + b_4_16·c_4_18·a_1_0 + c_4_19·a_1_1²·a_3_5
       + c_4_19·a_1_0·a_1_2·a_3_8 + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_0·a_1_1·a_3_5
       + c_4_19·a_1_0²·a_3_8 + c_4_19·a_1_0²·a_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0·a_1_2·a_3_8 + c_4_18·a_1_0·a_1_1·a_3_7 + c_4_17·a_1_1²·a_3_5
       + c_4_17·a_1_0·a_1_1·a_3_7 + c_4_17·a_1_0·a_1_1·a_3_5 + c_4_17·a_1_0²·a_3_8
       + c_4_17·a_1_0²·a_3_7 + c_4_17·a_1_0²·a_3_5
72. b_6_38·b_3_9 + b_4_16·b_1_3²·b_3_10 + b_4_16²·b_1_3 + a_1_0·b_1_3⁵·b_3_10
       + a_1_0·b_1_3⁵·b_3_9 + b_4_16·a_5_22 + b_4_16·a_1_0·b_1_3·b_3_10 + b_4_16²·a_1_0
       + c_4_18·b_1_3²·b_3_9 + b_4_16·c_4_18·b_1_3 + c_4_18·a_1_0·b_1_3⁴
       + c_4_17·a_1_0·b_1_3⁴ + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_2·a_3_5
       + c_4_19·a_1_0²·a_3_8 + c_4_19·a_1_0²·a_3_6 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_7 + c_4_18·a_1_0²·a_3_5
       + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_7 + c_4_17·a_1_0²·a_3_6
       + c_4_17·a_1_0²·a_3_5
73. b_1_3⁶·b_3_10 + b_1_3⁶·b_3_9 + b_8_67·b_1_3 + b_6_36·b_3_9 + b_4_16·b_1_3²·b_3_9
       + a_3_6·b_3_9·b_3_10 + a_1_0·b_1_3⁵·b_3_9 + b_4_16·a_5_22 + b_4_16·a_1_0·b_1_3·b_3_10
       + c_4_19·b_1_3²·b_3_10 + c_4_19·b_1_3⁵ + c_4_18·b_1_3²·b_3_10
       + c_4_18·b_1_3²·b_3_9 + c_4_18·b_1_3⁵ + b_4_16·c_4_19·b_1_3 + b_4_16·c_4_18·b_1_3
       + b_4_16·c_4_17·b_1_3 + c_4_19·a_1_0·b_1_3·b_3_10 + c_4_18·a_1_0·b_1_3·b_3_10
       + c_4_17·a_1_0·b_1_3·b_3_10 + c_4_17·a_1_0·b_1_3·b_3_9 + c_4_17·a_1_0·b_1_3⁴
       + b_4_16·c_4_18·a_1_0 + b_4_16·c_4_17·a_1_0 + c_4_19·a_1_0·a_1_1·a_3_5
       + c_4_19·a_1_0²·a_3_8 + c_4_19·a_1_0²·a_3_7 + c_4_18·a_1_0·a_1_2·a_3_8
       + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0·a_1_1·a_3_7 + c_4_18·a_1_0·a_1_1·a_3_5
       + c_4_18·a_1_0²·a_3_7 + c_4_17·a_1_1²·a_3_5 + c_4_17·a_1_0²·a_3_8
74. b_8_67·a_1_1 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0²·a_3_8 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_0·a_1_1·a_3_7 + c_4_18·a_1_0²·a_3_8 + c_4_18·a_1_0²·a_3_7
       + c_4_17·a_1_0·a_1_1·a_3_5
75. a_1_0·b_1_3⁵·b_3_9 + b_8_67·a_1_0 + b_4_16·a_5_22 + b_4_16·a_1_0·b_1_3·b_3_10
       + c_4_19·a_1_0·b_1_3·b_3_10 + c_4_17·a_1_0·b_1_3⁴ + b_4_16·c_4_19·a_1_0
       + b_4_16·c_4_17·a_1_0 + c_4_19·a_1_1²·a_3_5 + c_4_19·a_1_0·a_1_1·a_3_5
       + c_4_19·a_1_0²·a_3_6 + c_4_18·a_1_1²·a_3_5 + c_4_18·a_1_0·a_1_2·a_3_8
       + c_4_18·a_1_0·a_1_2·a_3_5 + c_4_18·a_1_0·a_1_1·a_3_5 + c_4_18·a_1_0²·a_3_6
       + c_4_18·a_1_0²·a_3_5 + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0²·a_3_7 + c_4_17·a_1_0²·a_3_6 + c_4_17·a_1_0²·a_3_5
76. b_8_67·a_1_2 + c_4_19·a_1_0·a_1_2·a_3_8 + c_4_19·a_1_0·a_1_2·a_3_5
       + c_4_19·a_1_0·a_1_1·a_3_7 + c_4_19·a_1_0·a_1_1·a_3_5 + c_4_19·a_1_0²·a_3_5
       + c_4_18·a_1_1²·a_3_5 + c_4_18·a_1_0²·a_3_7 + c_4_18·a_1_0²·a_3_6
       + c_4_17·a_1_1²·a_3_5 + c_4_17·a_1_0·a_1_2·a_3_8 + c_4_17·a_1_0·a_1_1·a_3_7
       + c_4_17·a_1_0²·a_3_8 + c_4_17·a_1_0²·a_3_7
77. a_5_22² + c_4_18·c_4_19·a_1_2² + c_4_18·c_4_19·a_1_1² + c_4_18·c_4_19·a_1_0²
       + c_4_18²·a_1_1² + c_4_18²·a_1_0² + c_4_17·c_4_19·a_1_2²
       + c_4_17·c_4_19·a_1_1² + c_4_17·c_4_18·a_1_1²
78. b_4_16·b_3_9·b_3_10 + b_4_16·b_1_3³·b_3_9 + b_4_16·b_6_36 + b_4_16²·b_1_3²
       + b_6_36·a_1_0·b_3_10 + b_6_36·a_1_0·b_1_3³ + b_4_16·b_1_3·a_5_22
       + b_4_16·a_1_0·b_1_3²·b_3_10 + b_4_16²·a_1_0·b_1_3 + c_4_17·b_1_3³·b_3_10
       + b_4_16·c_4_18·b_1_3² + c_4_19·a_1_0·b_1_3²·b_3_9 + c_4_18·a_1_0·b_1_3²·b_3_10
       + c_4_17·a_1_0·b_1_3²·b_3_9 + b_4_16·c_4_17·a_1_0·b_1_3 + c_4_19·a_1_0³·a_3_5
       + c_4_17·a_1_0³·a_3_5
79. b_4_16·b_1_3³·b_3_9 + b_4_16·b_6_38 + b_4_16²·b_1_3² + b_6_36·a_1_0·b_3_10
       + b_6_36·a_1_0·b_3_9 + b_4_16·b_1_3·a_5_22 + b_4_16·a_1_0·b_1_3²·b_3_10
       + b_4_16·a_1_0·b_1_3²·b_3_9 + b_4_16²·a_1_0·b_1_3 + c_4_17·b_1_3³·b_3_9
       + b_4_16·c_4_18·b_1_3² + c_4_19·a_1_0·b_1_3²·b_3_9 + c_4_18·a_1_0·b_1_3²·b_3_9
       + c_4_17·a_1_0·b_1_3²·b_3_10 + c_4_17·a_1_0·b_1_3²·b_3_9
       + b_4_16·c_4_19·a_1_0·b_1_3 + b_4_16·c_4_18·a_1_0·b_1_3 + c_4_19·a_1_0³·a_3_5
80. b_6_36·a_5_22 + b_6_36·a_1_0·b_1_3·b_3_10 + b_6_36·a_1_0·b_1_3⁴
       + c_4_19·a_1_0·b_1_3³·b_3_10 + c_4_19·a_1_0·b_1_3³·b_3_9
       + c_4_18·a_1_0·b_1_3³·b_3_10 + c_4_17·a_1_0·b_1_3³·b_3_10 + b_4_16·c_4_19·a_3_6
       + b_4_16·c_4_19·a_1_0·b_1_3² + b_4_16·c_4_18·a_3_5 + b_4_16·c_4_18·a_1_0·b_1_3²
       + c_4_19·a_1_0·b_1_3·a_5_22 + c_4_18·a_1_0·a_1_2·a_5_22 + c_4_18·a_1_0·a_1_1·a_5_22
       + c_4_18·a_1_0²·a_5_22 + c_4_17·a_1_1²·a_5_22 + c_4_17·a_1_0·a_1_1·a_5_22
       + c_4_17·a_1_0²·a_5_22 + c_4_18·c_4_19·a_1_0·b_1_3² + c_4_18²·a_1_0·b_1_3²
       + c_4_17·c_4_19·a_1_0·b_1_3² + c_4_19²·a_1_0·a_1_1² + c_4_19²·a_1_0²·a_1_1
       + c_4_19²·a_1_0³ + c_4_18·c_4_19·a_1_0·a_1_1² + c_4_18·c_4_19·a_1_0³
       + c_4_17·c_4_19·a_1_0·a_1_1² + c_4_17·c_4_19·a_1_0²·a_1_1
       + c_4_17·c_4_18·a_1_0·a_1_1² + c_4_17·c_4_18·a_1_0²·a_1_1 + c_4_17·c_4_18·a_1_0³
81. b_6_38·a_5_22 + b_4_16²·a_3_5 + b_4_16²·a_1_0·b_1_3² + c_4_18·a_1_0·b_1_3³·b_3_10
       + c_4_18·a_1_0·b_1_3³·b_3_9 + c_4_18·b_6_36·a_1_0 + c_4_17·a_1_0·b_1_3³·b_3_9
       + b_4_16·c_4_19·a_1_0·b_1_3² + b_4_16·c_4_18·a_3_6 + c_4_17·a_1_0·b_1_3·a_5_22
       + c_4_19·a_1_1²·a_5_22 + c_4_19·a_1_0·a_1_1·a_5_22 + c_4_19·a_1_0²·a_5_22
       + c_4_18·a_1_0²·a_5_22 + c_4_17·c_4_18·a_1_0·b_1_3² + c_4_18·c_4_19·a_1_0·a_1_1²
       + c_4_18·c_4_19·a_1_0³ + c_4_18²·a_1_0²·a_1_1 + c_4_17·c_4_19·a_1_0·a_1_1²
       + c_4_17·c_4_19·a_1_0²·a_1_1 + c_4_17·c_4_18·a_1_0·a_1_1²
       + c_4_17·c_4_18·a_1_0²·a_1_1
82. b_8_67·a_3_8 + b_4_16·b_6_36·a_1_0 + b_4_16²·a_3_5 + c_4_17·a_1_0·b_1_3³·b_3_9
       + c_4_17·b_6_36·a_1_0 + b_4_16·c_4_19·a_3_5 + b_4_16·c_4_19·a_1_0·b_1_3²
       + b_4_16·c_4_17·a_3_5 + c_4_19·a_1_0·a_1_2·a_5_22 + c_4_19·a_1_0·a_1_1·a_5_22
       + c_4_18·a_1_1²·a_5_22 + c_4_18·a_1_0·a_1_1·a_5_22 + c_4_18·a_1_0²·a_5_22
       + c_4_17·a_1_1²·a_5_22 + c_4_17·c_4_19·a_1_0·b_1_3² + c_4_17²·a_1_0·b_1_3²
       + c_4_19²·a_1_0·a_1_1² + c_4_19²·a_1_0²·a_1_1 + c_4_19²·a_1_0³
       + c_4_18·c_4_19·a_1_0³ + c_4_18²·a_1_0·a_1_1² + c_4_17·c_4_19·a_1_0·a_1_1²
       + c_4_17·c_4_19·a_1_0²·a_1_1 + c_4_17·c_4_18·a_1_0²·a_1_1 + c_4_17·c_4_18·a_1_0³
       + c_4_17²·a_1_0·a_1_1² + c_4_17²·a_1_0²·a_1_1
83. b_8_67·b_3_10 + b_6_36·b_1_3²·b_3_10 + b_6_36·b_1_3²·b_3_9 + b_4_16·b_6_36·b_1_3
       + b_4_16²·b_3_9 + b_6_36·a_5_22 + b_6_36·a_1_0·b_1_3·b_3_9 + b_6_36·a_1_0·b_1_3⁴
       + b_4_16²·a_3_5 + b_4_16²·a_1_0·b_1_3² + c_4_18·b_1_3⁴·b_3_9
       + c_4_17·b_1_3⁴·b_3_10 + c_4_17·b_1_3⁴·b_3_9 + b_4_16·c_4_19·b_3_10
       + b_4_16·c_4_19·b_3_9 + b_4_16·c_4_18·b_3_10 + b_4_16·c_4_17·b_3_10
       + c_4_19·a_1_0·b_1_3³·b_3_10 + c_4_19·a_1_0·b_1_3³·b_3_9 + c_4_19·b_6_36·a_1_0
       + c_4_18·b_6_36·a_1_0 + c_4_17·a_1_0·b_1_3³·b_3_9 + b_4_16·c_4_19·a_3_6
       + b_4_16·c_4_19·a_3_5 + b_4_16·c_4_18·a_3_5 + b_4_16·c_4_17·a_3_5
       + b_4_16·c_4_17·a_1_0·b_1_3² + c_4_19·a_1_0·b_1_3·a_5_22
       + c_4_18·a_1_0·b_1_3·a_5_22 + c_4_19·a_1_0·a_1_1·a_5_22 + c_4_18·a_1_1²·a_5_22
       + c_4_18·a_1_0·a_1_2·a_5_22 + c_4_18·a_1_0·a_1_1·a_5_22 + c_4_17·a_1_0²·a_5_22
       + c_4_19²·b_1_3³ + c_4_19²·a_1_0·b_1_3² + c_4_18·c_4_19·a_1_0·b_1_3²
       + c_4_19²·a_1_0·a_1_1² + c_4_17·c_4_19·a_1_0·a_1_1²
       + c_4_17·c_4_19·a_1_0²·a_1_1 + c_4_17·c_4_18·a_1_0·a_1_1² + c_4_17²·a_1_0²·a_1_1
       + c_4_17²·a_1_0³
84. b_8_67·a_3_7 + c_4_19·a_1_0·b_1_3·a_5_22 + c_4_18·a_1_0·b_1_3·a_5_22
       + c_4_17·a_1_0·b_1_3·a_5_22 + c_4_19·a_1_0·a_1_1·a_5_22 + c_4_18·a_1_1²·a_5_22
       + c_4_18·a_1_0·a_1_1·a_5_22 + c_4_18·a_1_0²·a_5_22 + c_4_17·a_1_0·a_1_2·a_5_22
       + c_4_17·a_1_0²·a_5_22 + c_4_19²·a_1_0·a_1_1² + c_4_19²·a_1_0³
       + c_4_18·c_4_19·a_1_0·a_1_1² + c_4_18·c_4_19·a_1_0²·a_1_1 + c_4_18·c_4_19·a_1_0³
       + c_4_18²·a_1_0·a_1_1² + c_4_18²·a_1_0³ + c_4_17·c_4_19·a_1_0²·a_1_1
       + c_4_17·c_4_19·a_1_0³ + c_4_17·c_4_18·a_1_0²·a_1_1
85. b_8_67·a_3_6 + b_6_36·a_5_22 + b_6_36·a_1_0·b_1_3·b_3_9 + b_4_16²·a_3_6
       + b_4_16²·a_3_5 + c_4_19·a_1_0·b_1_3³·b_3_9 + c_4_19·b_6_36·a_1_0
       + c_4_18·a_1_0·b_1_3³·b_3_10 + c_4_18·a_1_0·b_1_3³·b_3_9
       + c_4_17·a_1_0·b_1_3³·b_3_10 + c_4_17·b_6_36·a_1_0 + b_4_16·c_4_18·a_3_6
       + b_4_16·c_4_18·a_1_0·b_1_3² + b_4_16·c_4_17·a_3_6 + b_4_16·c_4_17·a_3_5
       + c_4_18·a_1_0·b_1_3·a_5_22 + c_4_18·a_1_1²·a_5_22 + c_4_18·a_1_0·a_1_1·a_5_22
       + c_4_17·a_1_1²·a_5_22 + c_4_17·a_1_0·a_1_2·a_5_22 + c_4_17·a_1_0²·a_5_22
       + c_4_18²·a_1_0·b_1_3² + c_4_17·c_4_19·a_1_0·b_1_3²
       + c_4_17·c_4_18·a_1_0·b_1_3² + c_4_19²·a_1_0·a_1_1²
       + c_4_18·c_4_19·a_1_0·a_1_1² + c_4_18·c_4_19·a_1_0²·a_1_1 + c_4_18·c_4_19·a_1_0³
       + c_4_18²·a_1_0·a_1_1² + c_4_17·c_4_19·a_1_0·a_1_1² + c_4_17·c_4_19·a_1_0³
       + c_4_17·c_4_18·a_1_0·a_1_1² + c_4_17·c_4_18·a_1_0³ + c_4_17²·a_1_0·a_1_1²
86. b_8_67·a_3_5 + b_6_36·a_5_22 + b_6_36·a_1_0·b_1_3·b_3_9 + b_6_36·a_1_0·b_1_3⁴
       + b_4_16·b_6_36·a_1_0 + b_4_16²·a_3_6 + b_4_16²·a_1_0·b_1_3²
       + c_4_19·a_1_0·b_1_3³·b_3_10 + c_4_19·a_1_0·b_1_3³·b_3_9
       + c_4_18·a_1_0·b_1_3³·b_3_10 + c_4_18·a_1_0·b_1_3³·b_3_9
       + c_4_17·a_1_0·b_1_3³·b_3_9 + b_4_16·c_4_19·a_3_5 + b_4_16·c_4_18·a_1_0·b_1_3²
       + b_4_16·c_4_17·a_3_5 + b_4_16·c_4_17·a_1_0·b_1_3² + c_4_18·a_1_0·b_1_3·a_5_22
       + c_4_17·a_1_0·b_1_3·a_5_22 + c_4_19·a_1_1²·a_5_22 + c_4_19·a_1_0²·a_5_22
       + c_4_18·a_1_1²·a_5_22 + c_4_18·a_1_0·a_1_2·a_5_22 + c_4_17·a_1_1²·a_5_22
       + c_4_17·a_1_0·a_1_1·a_5_22 + c_4_17·a_1_0²·a_5_22 + c_4_19²·a_1_0·b_1_3²
       + c_4_18·c_4_19·a_1_0·b_1_3² + c_4_18²·a_1_0·b_1_3² + c_4_18²·a_1_0²·a_1_1
       + c_4_18²·a_1_0³ + c_4_17·c_4_19·a_1_0²·a_1_1 + c_4_17·c_4_19·a_1_0³
       + c_4_17·c_4_18·a_1_0²·a_1_1 + c_4_17²·a_1_0²·a_1_1
87. b_8_67·b_3_9 + b_6_36·b_1_3²·b_3_10 + b_6_36·b_1_3²·b_3_9 + b_6_36·b_1_3⁵
       + b_4_16·b_6_36·b_1_3 + b_4_16²·b_3_9 + b_4_16²·b_1_3³ + b_6_36·a_5_22
       + b_6_36·a_1_0·b_1_3⁴ + b_4_16·b_6_36·a_1_0 + b_4_16²·a_3_6 + b_4_16²·a_3_5
       + c_4_19·b_1_3⁴·b_3_10 + c_4_19·b_6_36·b_1_3 + c_4_18·b_1_3⁴·b_3_9
       + c_4_17·b_1_3⁴·b_3_9 + b_4_16·c_4_19·b_3_10 + b_4_16·c_4_19·b_3_9
       + b_4_16·c_4_19·b_1_3³ + b_4_16·c_4_18·b_3_10 + b_4_16·c_4_18·b_3_9
       + b_4_16·c_4_18·b_1_3³ + b_4_16·c_4_17·b_3_9 + c_4_19·a_1_0·b_1_3³·b_3_10
       + c_4_19·a_1_0·b_1_3³·b_3_9 + c_4_18·a_1_0·b_1_3³·b_3_10
       + c_4_18·a_1_0·b_1_3³·b_3_9 + c_4_18·a_1_0·b_1_3⁶ + c_4_18·b_6_36·a_1_0
       + c_4_17·a_1_0·b_1_3³·b_3_10 + c_4_17·a_1_0·b_1_3³·b_3_9 + c_4_17·a_1_0·b_1_3⁶
       + c_4_17·b_6_36·a_1_0 + b_4_16·c_4_19·a_1_0·b_1_3² + b_4_16·c_4_18·a_3_6
       + b_4_16·c_4_17·a_3_6 + b_4_16·c_4_17·a_3_5 + c_4_19·a_1_0·b_1_3·a_5_22
       + c_4_18·a_1_0·b_1_3·a_5_22 + c_4_17·a_1_0·b_1_3·a_5_22 + c_4_19·a_1_1²·a_5_22
       + c_4_19·a_1_0·a_1_2·a_5_22 + c_4_19·a_1_0²·a_5_22 + c_4_18·a_1_1²·a_5_22
       + c_4_17·a_1_0·a_1_1·a_5_22 + c_4_17·a_1_0²·a_5_22 + c_4_18·c_4_19·b_1_3³
       + c_4_19²·a_1_0·b_1_3² + c_4_18·c_4_19·a_1_0·b_1_3² + c_4_18²·a_1_0·b_1_3²
       + c_4_17·c_4_19·a_1_0·b_1_3² + c_4_17²·a_1_0·b_1_3²
       + c_4_18·c_4_19·a_1_0²·a_1_1 + c_4_18²·a_1_0²·a_1_1 + c_4_17·c_4_19·a_1_0³
       + c_4_17·c_4_18·a_1_0·a_1_1² + c_4_17·c_4_18·a_1_0³ + c_4_17²·a_1_0·a_1_1²
       + c_4_17²·a_1_0²·a_1_1 + c_4_17²·a_1_0³
88. b_6_36·b_1_3³·b_3_9 + b_6_36·b_1_3⁶ + b_6_36² + b_4_16·b_6_36·b_1_3²
       + b_6_36·a_1_0·b_1_3²·b_3_9 + b_4_16²·a_1_0·b_3_9 + b_4_16²·a_1_0·b_1_3³
       + c_4_19·b_1_3⁵·b_3_10 + c_4_19·b_1_3⁵·b_3_9 + c_4_18·b_1_3⁵·b_3_10
       + c_4_17·b_1_3⁵·b_3_10 + c_4_17·b_1_3⁵·b_3_9 + b_4_16²·c_4_18
       + c_4_19·a_1_0·b_1_3⁴·b_3_10 + c_4_18·a_1_0·b_1_3⁴·b_3_10 + c_4_18·a_1_0·b_1_3⁷
       + c_4_17·a_1_0·b_1_3⁴·b_3_9 + c_4_17·a_1_0·b_1_3⁷ + b_4_16·c_4_18·a_1_0·b_1_3³
       + b_4_16·c_4_17·a_1_0·b_1_3³ + c_4_18·c_4_19·b_1_3⁴ + c_4_18²·b_1_3⁴
       + c_4_17·c_4_19·b_1_3⁴ + c_4_17·c_4_18·b_1_3⁴
89. b_6_36·b_1_3³·b_3_9 + b_6_36·b_1_3⁶ + b_6_36·b_6_38 + b_6_36²
       + b_4_16·b_6_36·b_1_3² + b_6_36·a_1_0·b_1_3⁵ + b_4_16²·a_1_0·b_3_10
       + c_4_19·b_1_3⁵·b_3_10 + c_4_19·b_1_3⁵·b_3_9 + c_4_18·b_1_3⁵·b_3_10
       + c_4_18·b_6_36·b_1_3² + c_4_17·b_1_3⁵·b_3_9 + c_4_17·b_6_36·b_1_3²
       + b_4_16·c_4_18·b_1_3·b_3_10 + b_4_16·c_4_18·b_1_3·b_3_9 + b_4_16·c_4_17·b_1_3·b_3_10
       + b_4_16²·c_4_19 + b_4_16²·c_4_18 + b_4_16²·c_4_17 + c_4_19·a_1_0·b_1_3⁴·b_3_9
       + c_4_18·a_1_0·b_1_3⁴·b_3_10 + c_4_18·a_1_0·b_1_3⁷ + c_4_17·a_1_0·b_1_3⁷
       + b_4_16·c_4_18·a_1_0·b_3_10 + b_4_16·c_4_18·a_1_0·b_1_3³ + c_4_19·a_1_0³·a_5_22
       + c_4_18·a_1_0·a_1_1²·a_5_22 + c_4_17·a_1_0·a_1_1²·a_5_22 + c_4_18·c_4_19·b_1_3⁴
       + c_4_18²·b_1_3⁴ + c_4_17²·b_1_3⁴ + c_4_17²·a_1_0·b_1_3³
90. b_6_38² + b_4_16²·b_1_3·b_3_10 + b_4_16²·b_1_3·b_3_9 + b_4_16²·a_1_0·b_3_10
       + b_4_16²·a_1_0·b_3_9 + b_4_16²·a_1_0·b_1_3³ + b_4_16²·c_4_18 + b_4_16²·c_4_17
       + b_4_16·c_4_17·a_1_0·b_1_3³ + c_4_18²·b_1_3⁴ + c_4_17²·b_1_3⁴
91. b_6_36·b_1_3³·b_3_9 + b_6_36·b_1_3⁶ + b_6_36² + b_4_16·b_8_67
       + b_4_16²·b_1_3·b_3_10 + b_4_16²·a_1_0·b_1_3³ + c_4_19·b_1_3⁵·b_3_10
       + c_4_19·b_1_3⁵·b_3_9 + c_4_18·b_1_3⁵·b_3_10 + c_4_17·b_1_3⁵·b_3_10
       + c_4_17·b_6_36·b_1_3² + b_4_16·c_4_19·b_1_3·b_3_10 + b_4_16·c_4_17·b_1_3·b_3_10
       + b_4_16²·c_4_19 + b_4_16²·c_4_18 + c_4_19·a_1_0·b_1_3⁴·b_3_10
       + c_4_19·a_1_0·b_1_3⁴·b_3_9 + c_4_18·a_1_0·b_1_3⁴·b_3_10
       + c_4_18·a_1_0·b_1_3⁴·b_3_9 + c_4_18·a_1_0·b_1_3⁷ + c_4_17·a_1_0·b_1_3⁴·b_3_9
       + c_4_17·a_1_0·b_1_3⁷ + c_4_17·b_6_36·a_1_0·b_1_3 + b_4_16·c_4_19·a_1_0·b_3_10
       + b_4_16·c_4_19·a_1_0·b_3_9 + b_4_16·c_4_19·a_1_0·b_1_3³
       + b_4_16·c_4_18·a_1_0·b_3_10 + b_4_16·c_4_18·a_1_0·b_3_9 + b_4_16·c_4_17·a_1_0·b_3_9
       + c_4_19·a_1_0·a_1_1²·a_5_22 + c_4_19·a_1_0³·a_5_22 + c_4_18·a_1_0·a_1_1²·a_5_22
       + c_4_18·a_1_0³·a_5_22 + c_4_17·a_1_0³·a_5_22 + c_4_18·c_4_19·b_1_3⁴
       + c_4_18²·b_1_3⁴ + c_4_17·c_4_19·b_1_3⁴ + c_4_17·c_4_18·b_1_3⁴
       + c_4_17²·b_1_3⁴ + c_4_17·c_4_19·a_1_0·b_1_3³ + c_4_17·c_4_18·a_1_0·b_1_3³
92. b_8_67·a_5_22 + b_6_36²·a_1_0 + b_4_16²·a_5_22 + b_4_16³·a_1_0 + c_4_18·b_6_36·a_3_6
       + c_4_17·b_6_36·a_3_6 + b_4_16·c_4_19·a_5_22 + b_4_16·c_4_18·a_1_0·b_1_3·b_3_9
       + b_4_16·c_4_17·a_5_22 + b_4_16·c_4_17·a_1_0·b_1_3·b_3_10 + b_4_16²·c_4_18·a_1_0
       + c_4_19²·a_1_0·b_1_3·b_3_9 + c_4_18·c_4_19·a_1_0·b_1_3·b_3_10
       + c_4_18·c_4_19·a_1_0·b_1_3⁴ + c_4_18²·a_1_0·b_1_3·b_3_10
       + c_4_18²·a_1_0·b_1_3·b_3_9 + c_4_17·c_4_19·a_1_0·b_1_3⁴
       + c_4_17·c_4_18·a_1_0·b_1_3·b_3_9 + c_4_17·c_4_18·a_1_0·b_1_3⁴
       + c_4_17²·a_1_0·b_1_3·b_3_10 + c_4_17²·a_1_0·b_1_3⁴ + b_4_16·c_4_18·c_4_19·a_1_0
       + b_4_16·c_4_17·c_4_18·a_1_0 + c_4_19²·a_1_0·a_1_2·a_3_8
       + c_4_19²·a_1_0·a_1_1·a_3_5 + c_4_19²·a_1_0²·a_3_6
       + c_4_18·c_4_19·a_1_0·a_1_2·a_3_8 + c_4_18·c_4_19·a_1_0·a_1_2·a_3_5
       + c_4_18·c_4_19·a_1_0²·a_3_6 + c_4_18·c_4_19·a_1_0²·a_3_5 + c_4_18²·a_1_1²·a_3_5
       + c_4_18²·a_1_0·a_1_1·a_3_5 + c_4_18²·a_1_0²·a_3_8 + c_4_18²·a_1_0²·a_3_7
       + c_4_18²·a_1_0²·a_3_5 + c_4_17·c_4_19·a_1_1²·a_3_5
       + c_4_17·c_4_19·a_1_0·a_1_2·a_3_8 + c_4_17·c_4_19·a_1_0·a_1_1·a_3_5
       + c_4_17·c_4_19·a_1_0²·a_3_8 + c_4_17·c_4_19·a_1_0²·a_3_7
       + c_4_17·c_4_19·a_1_0²·a_3_6 + c_4_17·c_4_19·a_1_0²·a_3_5
       + c_4_17·c_4_18·a_1_0·a_1_2·a_3_5 + c_4_17·c_4_18·a_1_0·a_1_1·a_3_7
       + c_4_17·c_4_18·a_1_0²·a_3_8 + c_4_17·c_4_18·a_1_0²·a_3_7
       + c_4_17·c_4_18·a_1_0²·a_3_6 + c_4_17·c_4_18·a_1_0²·a_3_5 + c_4_17²·a_1_0²·a_3_5
93. b_6_36·b_1_3⁸ + b_6_36·b_8_67 + b_6_36²·b_1_3² + b_6_36²·a_1_0·b_1_3
       + b_4_16²·a_1_0·b_1_3²·b_3_10 + b_4_16²·a_1_0·b_1_3²·b_3_9
       + c_4_19·b_6_36·b_1_3·b_3_9 + c_4_19·b_6_36·b_1_3⁴ + c_4_18·b_6_36·b_1_3·b_3_9
       + c_4_17·b_6_36·b_1_3·b_3_10 + c_4_17·b_6_36·b_1_3·b_3_9 + b_4_16·c_4_19·b_6_38
       + b_4_16·c_4_18·b_1_3³·b_3_10 + b_4_16·c_4_18·b_6_36 + b_4_16·c_4_17·b_6_38
       + b_4_16²·c_4_19·b_1_3² + b_4_16²·c_4_17·b_1_3² + c_4_19·b_6_36·a_1_0·b_3_10
       + c_4_19·b_6_36·a_1_0·b_3_9 + c_4_19·b_6_36·a_1_0·b_1_3³ + c_4_18·a_1_0·b_1_3⁹
       + c_4_18·b_6_36·a_1_0·b_3_10 + c_4_18·b_6_36·a_1_0·b_3_9
       + c_4_18·b_6_36·a_1_0·b_1_3³ + c_4_17·a_1_0·b_1_3⁹ + c_4_17·b_6_36·a_1_0·b_3_9
       + b_4_16·c_4_19·b_1_3·a_5_22 + b_4_16·c_4_19·a_1_0·b_1_3²·b_3_10
       + b_4_16·c_4_19·a_1_0·b_1_3²·b_3_9 + b_4_16·c_4_17·b_1_3·a_5_22
       + b_4_16·c_4_17·a_1_0·b_1_3²·b_3_10 + b_4_16²·c_4_19·a_1_0·b_1_3
       + b_4_16²·c_4_18·a_1_0·b_1_3 + b_4_16²·c_4_17·a_1_0·b_1_3 + c_4_19²·b_1_3³·b_3_9
       + c_4_18·c_4_19·b_1_3³·b_3_9 + c_4_18·c_4_19·b_1_3⁶ + c_4_18²·b_1_3³·b_3_10
       + c_4_18²·b_1_3³·b_3_9 + c_4_17·c_4_19·b_1_3³·b_3_10 + c_4_17·c_4_19·b_1_3³·b_3_9
       + c_4_17·c_4_18·b_1_3³·b_3_9 + c_4_17·c_4_18·b_1_3⁶ + c_4_17²·b_1_3³·b_3_10
       + c_4_17²·b_1_3³·b_3_9 + c_4_17²·b_1_3⁶ + b_4_16·c_4_19²·b_1_3²
       + b_4_16·c_4_18·c_4_19·b_1_3² + b_4_16·c_4_17·c_4_19·b_1_3²
       + c_4_19²·a_1_0·b_1_3²·b_3_10 + c_4_19²·a_1_0·b_1_3⁵
       + c_4_18²·a_1_0·b_1_3²·b_3_10 + c_4_18²·a_1_0·b_1_3²·b_3_9
       + c_4_17·c_4_19·a_1_0·b_1_3²·b_3_10 + c_4_17·c_4_19·a_1_0·b_1_3⁵
       + c_4_17·c_4_18·a_1_0·b_1_3²·b_3_9 + c_4_17·c_4_18·a_1_0·b_1_3⁵
       + c_4_17²·a_1_0·b_1_3²·b_3_10 + c_4_17²·a_1_0·b_1_3²·b_3_9
       + b_4_16·c_4_19²·a_1_0·b_1_3 + b_4_16·c_4_17·c_4_19·a_1_0·b_1_3
       + b_4_16·c_4_17²·a_1_0·b_1_3 + c_4_19²·a_1_0³·a_3_5 + c_4_18²·a_1_0³·a_3_5
94. b_6_38·b_8_67 + b_4_16²·b_1_3³·b_3_10 + b_4_16²·b_6_38 + b_4_16²·b_6_36
       + b_6_36·a_1_0·b_1_3⁷ + b_6_36²·a_1_0·b_1_3 + b_4_16²·a_1_0·b_1_3²·b_3_9
       + c_4_18·b_6_36·b_1_3·b_3_10 + c_4_18·b_6_36·b_1_3⁴ + c_4_17·b_6_36·b_1_3·b_3_9
       + b_4_16·c_4_19·b_1_3³·b_3_10 + b_4_16·c_4_19·b_6_36 + b_4_16·c_4_18·b_6_38
       + b_4_16·c_4_18·b_6_36 + b_4_16·c_4_17·b_1_3³·b_3_10 + b_4_16·c_4_17·b_6_36
       + b_4_16²·c_4_19·b_1_3² + b_4_16²·c_4_18·b_1_3² + b_4_16²·c_4_17·b_1_3²
       + c_4_19·b_6_36·a_1_0·b_3_9 + c_4_18·b_6_36·a_1_0·b_3_10 + c_4_18·b_6_36·a_1_0·b_3_9
       + c_4_18·b_6_36·a_1_0·b_1_3³ + c_4_17·b_6_36·a_1_0·b_3_9
       + c_4_17·b_6_36·a_1_0·b_1_3³ + b_4_16·c_4_19·a_1_0·b_1_3²·b_3_10
       + b_4_16·c_4_19·a_1_0·b_1_3²·b_3_9 + b_4_16·c_4_17·b_1_3·a_5_22
       + b_4_16·c_4_17·a_1_0·b_1_3²·b_3_10 + b_4_16²·c_4_19·a_1_0·b_1_3
       + c_4_18·c_4_19·b_1_3³·b_3_10 + c_4_18·c_4_19·b_1_3³·b_3_9 + c_4_18·c_4_19·b_1_3⁶
       + c_4_18²·b_1_3³·b_3_10 + c_4_17·c_4_19·b_1_3³·b_3_10
       + c_4_17·c_4_19·b_1_3³·b_3_9 + c_4_17·c_4_19·b_1_3⁶ + c_4_17·c_4_18·b_1_3³·b_3_10
       + c_4_17·c_4_18·b_1_3³·b_3_9 + c_4_17·c_4_18·b_1_3⁶ + c_4_17²·b_1_3³·b_3_10
       + c_4_17²·b_1_3³·b_3_9 + c_4_17²·b_1_3⁶ + b_4_16·c_4_18·c_4_19·b_1_3²
       + b_4_16·c_4_18²·b_1_3² + c_4_18·c_4_19·a_1_0·b_1_3²·b_3_10
       + c_4_18·c_4_19·a_1_0·b_1_3⁵ + c_4_17·c_4_19·a_1_0·b_1_3²·b_3_10
       + c_4_17·c_4_19·a_1_0·b_1_3⁵ + c_4_17·c_4_18·a_1_0·b_1_3²·b_3_10
       + c_4_17·c_4_18·a_1_0·b_1_3⁵ + c_4_17²·a_1_0·b_1_3²·b_3_10
       + b_4_16·c_4_18²·a_1_0·b_1_3 + b_4_16·c_4_17·c_4_18·a_1_0·b_1_3
       + b_4_16·c_4_17²·a_1_0·b_1_3 + c_4_19²·a_1_0³·a_3_5 + c_4_17·c_4_19·a_1_0³·a_3_5
95. b_8_67² + b_6_36²·b_1_3·b_3_9 + b_6_36²·b_1_3⁴ + b_4_16²·b_6_36·b_1_3²
       + b_4_16³·b_1_3·b_3_9 + b_4_16²·b_6_36·a_1_0·b_1_3 + b_4_16³·a_1_0·b_3_10
       + b_4_16³·a_1_0·b_1_3³ + c_4_19·b_6_36² + b_4_16²·c_4_19·b_1_3·b_3_10
       + b_4_16²·c_4_19·b_1_3·b_3_9 + b_4_16²·c_4_18·b_1_3·b_3_9
       + b_4_16²·c_4_17·b_1_3·b_3_10 + b_4_16³·c_4_18 + b_4_16³·c_4_17
       + b_4_16²·c_4_19·a_1_0·b_3_10 + b_4_16²·c_4_19·a_1_0·b_3_9
       + b_4_16²·c_4_19·a_1_0·b_1_3³ + b_4_16²·c_4_18·a_1_0·b_3_10
       + b_4_16²·c_4_17·a_1_0·b_3_9 + c_4_19²·b_1_3⁵·b_3_10 + c_4_19²·b_1_3⁸
       + c_4_18²·b_1_3⁵·b_3_9 + c_4_17²·b_1_3⁵·b_3_10 + c_4_17²·b_1_3⁸
       + b_4_16²·c_4_19² + b_4_16²·c_4_18·c_4_19 + b_4_16²·c_4_18²
       + b_4_16²·c_4_17·c_4_19 + b_4_16²·c_4_17·c_4_18 + c_4_19²·a_1_0·b_1_3⁴·b_3_10
       + c_4_19²·a_1_0·b_1_3⁴·b_3_9 + c_4_17²·a_1_0·b_1_3⁴·b_3_10
       + c_4_17²·a_1_0·b_1_3⁴·b_3_9 + b_4_16·c_4_19²·a_1_0·b_1_3³
       + b_4_16·c_4_17·c_4_19·a_1_0·b_1_3³ + b_4_16·c_4_17·c_4_18·a_1_0·b_1_3³
       + b_4_16·c_4_17²·a_1_0·b_1_3³ + c_4_19³·b_1_3⁴ + c_4_18·c_4_19²·b_1_3⁴
       + c_4_18²·c_4_19·b_1_3⁴ + c_4_17·c_4_19²·b_1_3⁴ + c_4_17²·c_4_19·b_1_3⁴
       + c_4_17²·c_4_18·b_1_3⁴ + c_4_17³·b_1_3⁴

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Ring generators

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Data used for Benson′s test

• Benson′s completion test succeeded in degree 16.
• 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_17, a Duflot regular element of degree 4
  2. c_4_18, a Duflot regular element of degree 4
  3. c_4_19, a Duflot regular element of degree 4
  4. b_1_3², an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 8, 10].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group

Ring generators

Ring relations

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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. a_1_2 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_5 → 0, an element of degree 3
6. a_3_6 → 0, an element of degree 3
7. a_3_7 → 0, an element of degree 3
8. a_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_4_16 → 0, an element of degree 4
12. c_4_17 → c_1_2⁴, an element of degree 4
13. c_4_18 → c_1_2⁴ + c_1_0⁴, an element of degree 4
14. c_4_19 → c_1_1⁴, an element of degree 4
15. a_5_22 → 0, an element of degree 5
16. b_6_36 → 0, an element of degree 6
17. b_6_38 → 0, an element of degree 6
18. b_8_67 → 0, an element of degree 8

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. a_1_2 → 0, an element of degree 1
4. b_1_3 → c_1_3, an element of degree 1
5. a_3_5 → 0, an element of degree 3
6. a_3_6 → 0, an element of degree 3
7. a_3_7 → 0, an element of degree 3
8. a_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_0·c_1_3² + c_1_0²·c_1_3, an element of degree 3
10. b_3_10 → c_1_1·c_1_3² + c_1_1²·c_1_3, an element of degree 3
11. b_4_16 → c_1_2²·c_1_3², an element of degree 4
12. c_4_17 → c_1_2²·c_1_3² + c_1_2⁴, an element of degree 4
13. c_4_18 → c_1_2·c_1_3³ + c_1_2²·c_1_3² + 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
14. c_4_19 → c_1_2·c_1_3³ + c_1_2²·c_1_3² + 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
15. a_5_22 → 0, an element of degree 5
16. b_6_36 → c_1_2²·c_1_3⁴ + c_1_2⁴·c_1_3² + c_1_1·c_1_2·c_1_3⁴ + c_1_1²·c_1_2·c_1_3³
       + c_1_0·c_1_1·c_1_3⁴ + c_1_0·c_1_1²·c_1_3³ + c_1_0²·c_1_3⁴
       + c_1_0²·c_1_1·c_1_3³ + c_1_0²·c_1_1²·c_1_3² + c_1_0⁴·c_1_3², an element of degree 6
17. b_6_38 → c_1_2·c_1_3⁵ + c_1_2³·c_1_3³ + c_1_1·c_1_3⁵ + c_1_1²·c_1_3⁴ + c_1_0·c_1_3⁵
       + c_1_0·c_1_2²·c_1_3³ + c_1_0²·c_1_2²·c_1_3² + c_1_0⁴·c_1_3², an element of degree 6
18. b_8_67 → c_1_2·c_1_3⁷ + c_1_2⁴·c_1_3⁴ + c_1_1·c_1_2·c_1_3⁶ + c_1_1·c_1_2²·c_1_3⁵
       + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3³ + c_1_1²·c_1_2·c_1_3⁵
       + c_1_1²·c_1_2³·c_1_3³ + c_1_1²·c_1_2⁴·c_1_3² + c_1_1³·c_1_3⁵
       + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁵·c_1_3³ + c_1_1⁶·c_1_3²
       + c_1_0·c_1_3⁷ + c_1_0·c_1_1·c_1_3⁶ + c_1_0·c_1_1·c_1_2²·c_1_3⁴
       + c_1_0·c_1_1²·c_1_3⁵ + c_1_0·c_1_1²·c_1_2²·c_1_3³ + c_1_0²·c_1_3⁶
       + c_1_0²·c_1_2²·c_1_3⁴ + c_1_0²·c_1_1·c_1_3⁵ + c_1_0²·c_1_1·c_1_2²·c_1_3³
       + c_1_0²·c_1_1²·c_1_3⁴ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0⁴·c_1_2²·c_1_3², an element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128