David J. Green

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Cohomology of group number 647 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 3 minimal generators and exponent 8.
• It is non-abelian.
• It has p-Rank 3.
• Its center has rank 1.
• It has 3 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 3 and depth 1.
• The depth coincides with the Duflot bound.
• The Poincaré series is

  ( − 1) · (t13  −  2·t12  +  2·t11  −  t10  +  2·t9  +  t8  −  2·t7  +  3·t6  −  3·t5  +  3·t4  −  2·t3  +  2·t2  +  1)

  (t  −  1)3 · (t2  +  1) · (t4  +  1) · (t8  +  1)

• The a-invariants are -∞,-9,-3,-3. 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 15 minimal generators of maximal degree 16:

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. a_2_3, a nilpotent element of degree 2
5. b_2_4, an element of degree 2
6. b_2_5, an element of degree 2
7. b_2_6, an element of degree 2
8. b_5_19, an element of degree 5
9. b_5_20, an element of degree 5
10. a_9_32, a nilpotent element of degree 9
11. b_9_43, an element of degree 9
12. b_9_44, an element of degree 9
13. a_10_38, a nilpotent element of degree 10
14. b_10_53, an element of degree 10
15. c_16_113, a Duflot regular element of degree 16

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 64 minimal relations of maximal degree 20:

1. a_1_1² + a_1_0²
2. a_1_0·a_1_1 + a_1_0²
3. a_1_0·b_1_2
4. a_2_3·a_1_1 + a_2_3·a_1_0
5. b_2_4·a_1_1 + a_2_3·b_1_2 + a_2_3·a_1_1
6. b_2_4·a_1_0 + a_2_3·a_1_1
7. b_2_5·b_1_2 + b_2_4·b_1_2 + b_2_6·a_1_1 + b_2_6·a_1_0 + b_2_5·a_1_1 + b_2_5·a_1_0 + a_1_0³
8. a_2_3² + a_2_3·a_1_0²
9. a_2_3·b_1_2² + a_2_3·b_2_4 + a_2_3·a_1_0²
10. b_2_4·b_1_2² + b_2_4² + b_2_6·a_1_1·b_1_2 + a_2_3·a_1_0²
11. b_2_6²·a_1_1 + b_2_6²·a_1_0 + b_2_5·b_2_6·a_1_1 + b_2_5·b_2_6·a_1_0
       + a_2_3·b_2_6·b_1_2 + b_2_5·a_1_0³
12. b_1_2·b_5_19 + b_2_6·b_1_2⁴ + b_2_6²·b_1_2² + b_2_4·b_2_6² + b_2_4·b_2_5²
       + b_2_4²·b_2_6 + b_2_4³ + a_2_3·b_2_6² + a_2_3·b_2_5² + a_2_3·b_2_4·b_2_6
       + a_2_3·b_2_4²
13. b_2_4·b_2_5² + b_2_4³ + a_1_1·b_5_19 + a_1_0·b_5_19 + b_2_6·a_1_1·b_1_2³
       + a_2_3·b_2_5² + a_2_3·b_2_4·b_2_6 + a_2_3·b_2_4² + a_2_3·b_2_6·a_1_0²
14. a_1_1·b_5_20 + a_1_1·b_5_19 + a_2_3·b_2_6² + a_2_3·b_2_5·b_2_6 + a_2_3·b_2_4·b_2_6
       + b_2_6²·a_1_0² + b_2_5·b_2_6·a_1_0² + a_2_3·b_2_6·a_1_0² + a_2_3·b_2_5·a_1_0²
15. b_2_4·b_2_5² + b_2_4³ + a_1_1·b_5_19 + a_1_0·b_5_20 + b_2_6·a_1_1·b_1_2³
       + a_2_3·b_2_6² + a_2_3·b_2_5·b_2_6 + a_2_3·b_2_5² + a_2_3·b_2_4² + b_2_6²·a_1_0²
       + b_2_5·b_2_6·a_1_0²
16. b_2_4·b_5_19 + b_2_5³·a_1_1 + b_2_5³·a_1_0 + a_2_3·b_5_19 + a_2_3·b_2_4·b_2_6·b_1_2
       + a_2_3·b_2_4²·b_1_2 + b_2_6²·a_1_0³ + b_2_5·b_2_6·a_1_0³ + b_2_5²·a_1_0³
       + a_2_3·b_2_6·a_1_0³
17. b_2_4·b_5_19 + b_2_5³·a_1_1 + b_2_5³·a_1_0 + a_2_3·b_5_20 + a_2_3·b_2_4·b_2_6·b_1_2
       + a_2_3·b_2_4²·b_1_2 + b_2_5²·a_1_0³
18. b_2_5·b_2_6²·a_1_0³ + b_2_5²·b_2_6·a_1_0³
19. b_2_4·b_2_5·b_5_20 + b_2_4²·b_5_20 + b_2_5⁴·a_1_1 + b_2_5⁴·a_1_0 + a_2_3·b_2_5·b_5_19
       + a_2_3·b_2_4³·b_1_2 + b_2_5³·a_1_0³
20. b_5_20² + b_5_19² + b_2_4·b_2_6⁴ + b_2_5·b_2_6·a_1_1·b_5_19
       + b_2_5·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_5²·b_2_6² + b_2_5·a_1_0³·b_5_19
       + a_2_3·b_2_5·b_2_6²·a_1_0² + a_2_3·b_2_5²·b_2_6·a_1_0²
21. a_2_3·b_2_5·b_2_6³ + a_2_3·b_2_5²·b_2_6² + a_1_1·a_9_32 + b_2_6⁴·a_1_0²
       + b_2_5·b_2_6³·a_1_0² + b_2_5³·b_2_6·a_1_0² + a_2_3·b_2_6·a_1_0·b_5_19
       + b_2_6·a_1_0³·b_5_19 + a_2_3·b_2_6³·a_1_0² + a_2_3·b_2_5²·b_2_6·a_1_0²
22. a_2_3·b_2_5·b_2_6³ + a_2_3·b_2_5²·b_2_6² + a_1_0·a_9_32 + b_2_6⁴·a_1_0²
       + b_2_5·b_2_6³·a_1_0² + b_2_5³·b_2_6·a_1_0² + a_2_3·b_2_6·a_1_0·b_5_19
       + b_2_6·a_1_0³·b_5_19 + a_2_3·b_2_6³·a_1_0² + a_2_3·b_2_5·b_2_6²·a_1_0²
       + a_2_3·b_2_5²·b_2_6·a_1_0²
23. b_2_6·b_1_2³·b_5_20 + b_2_6²·b_1_2⁶ + b_2_6³·b_1_2⁴ + b_2_4²·b_1_2·b_5_20
       + b_1_2·a_9_32 + a_1_1·b_9_43 + b_2_6·a_1_1·b_1_2⁷ + b_2_6²·a_1_0·b_5_19
       + b_2_5·b_2_6·a_1_1·b_5_19 + b_2_5·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_5·b_2_6³
       + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_4³·b_2_6 + b_2_6⁴·a_1_0²
       + b_2_5³·b_2_6·a_1_0² + a_2_3·b_2_5·a_1_0·b_5_19 + b_2_6·a_1_0³·b_5_19
       + b_2_5·a_1_0³·b_5_19 + a_2_3·b_2_5·b_2_6²·a_1_0² + a_2_3·b_2_5³·a_1_0²
24. a_1_0·b_9_43 + b_2_6²·a_1_0·b_5_19 + a_2_3·b_2_5·b_2_6³ + a_2_3·b_2_5²·b_2_6²
       + b_2_6⁴·a_1_0² + b_2_5³·b_2_6·a_1_0² + a_2_3·b_2_5·a_1_0·b_5_19
       + b_2_6·a_1_0³·b_5_19 + a_2_3·b_2_6³·a_1_0² + a_2_3·b_2_5²·b_2_6·a_1_0²
       + a_2_3·b_2_5³·a_1_0²
25. b_1_2·b_9_44 + b_1_2·b_9_43 + b_1_2⁵·b_5_20 + b_2_6²·b_1_2·b_5_20 + b_2_6²·b_1_2⁶
       + b_2_6⁴·b_1_2² + b_2_4·b_2_6·b_1_2·b_5_20 + b_2_4²·b_1_2·b_5_20 + b_2_4²·b_2_6³
       + b_2_4³·b_2_6² + b_2_4⁴·b_2_6 + b_1_2·a_9_32 + b_2_5·b_2_6·a_1_1·b_5_19
       + b_2_5·b_2_6·a_1_0·b_5_19 + b_2_5²·a_1_1·b_5_19 + b_2_5²·a_1_0·b_5_19
       + b_2_6·a_1_0³·b_5_19 + a_2_3·b_2_5²·b_2_6·a_1_0²
26. b_5_19² + b_2_6·b_1_2³·b_5_20 + b_2_6³·b_1_2⁴ + b_2_6⁴·b_1_2² + b_2_5·b_2_6⁴
       + b_2_5⁴·b_2_6 + b_2_5⁵ + b_2_4²·b_1_2·b_5_20 + b_2_4³·b_2_6² + b_2_4⁴·b_2_6
       + b_2_4⁵ + b_1_2·a_9_32 + a_1_1·b_9_44 + b_2_6²·a_1_0·b_5_19
       + b_2_5·b_2_6·a_1_1·b_5_19 + a_2_3·b_2_6⁴ + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_4⁴
       + b_2_6⁴·a_1_0² + b_2_5²·b_2_6²·a_1_0² + a_2_3·b_2_5²·b_2_6·a_1_0²
       + a_2_3·b_2_5³·a_1_0²
27. b_5_19² + b_2_6²·b_1_2⁶ + b_2_6⁴·b_1_2² + b_2_5·b_2_6⁴ + b_2_5⁴·b_2_6
       + b_2_5⁵ + b_2_4³·b_2_6² + b_2_4⁴·b_2_6 + b_2_4⁵ + a_1_0·b_9_44
       + b_2_6²·a_1_0·b_5_19 + b_2_5·b_2_6·a_1_1·b_5_19 + b_2_5²·a_1_1·b_5_19
       + b_2_5²·a_1_0·b_5_19 + a_2_3·b_2_6⁴ + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_4³·b_2_6
       + a_2_3·b_2_4⁴ + b_2_6⁴·a_1_0² + b_2_5²·b_2_6²·a_1_0² + b_2_5·a_1_0³·b_5_19
       + a_2_3·b_2_6³·a_1_0² + a_2_3·b_2_5·b_2_6²·a_1_0²
       + a_2_3·b_2_5²·b_2_6·a_1_0² + a_2_3·b_2_5³·a_1_0²
28. a_2_3·a_9_32 + a_2_3·b_2_6⁴·a_1_0 + a_2_3·b_2_5²·b_2_6²·a_1_0
       + a_2_3·b_2_5³·b_2_6·a_1_0
29. b_2_4²·b_2_6·b_5_20 + b_2_4²·b_2_6³·b_1_2 + b_2_4³·b_5_20 + b_2_4³·b_2_6²·b_1_2
       + b_2_4·a_9_32 + a_2_3·b_9_43 + a_2_3·b_2_6²·b_5_19 + a_2_3·b_2_5²·b_2_6²·a_1_0
       + a_1_0²·a_9_32 + b_2_6⁴·a_1_0³ + a_2_3·b_2_5·a_1_0²·b_5_19
30. b_2_6²·b_1_2²·b_5_20 + b_2_6³·b_1_2⁵ + b_2_6⁴·b_1_2³ + b_2_5·b_9_43
       + b_2_5·b_2_6²·b_5_20 + b_2_5²·b_2_6·b_5_20 + b_2_5²·b_2_6·b_5_19 + b_2_4·b_9_43
       + b_2_4·b_2_6²·b_5_20 + b_2_4²·b_2_6·b_5_20 + b_2_4²·b_2_6³·b_1_2 + b_2_4³·b_5_20
       + b_2_4³·b_2_6²·b_1_2 + b_2_6·a_9_32 + b_2_6⁵·a_1_0 + b_2_5·b_2_6⁴·a_1_0
       + b_2_5⁴·b_2_6·a_1_1 + b_2_5⁵·a_1_1 + b_2_5⁵·a_1_0 + b_2_4·a_9_32
       + a_2_3·b_2_6²·b_5_19 + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_4³·b_2_6·b_1_2
       + a_2_3·b_2_4⁴·b_1_2 + a_1_0²·b_9_44 + b_2_6²·a_1_0²·b_5_19
       + b_2_5·b_2_6·a_1_0²·b_5_19 + b_2_5²·a_1_0²·b_5_19 + a_2_3·b_2_5²·b_2_6²·a_1_0
       + a_2_3·b_2_5³·b_2_6·a_1_0 + a_2_3·b_2_5⁴·a_1_0 + a_1_0²·a_9_32 + b_2_5⁴·a_1_0³
       + a_2_3·b_2_6·a_1_0²·b_5_19 + a_2_3·b_2_5·a_1_0²·b_5_19
31. b_2_4·b_9_44 + b_2_4·b_9_43 + b_2_4·b_2_6²·b_5_20 + b_2_4·b_2_6⁴·b_1_2
       + b_2_4³·b_5_20 + b_2_4³·b_2_6²·b_1_2 + b_2_4⁴·b_2_6·b_1_2 + b_2_5⁵·a_1_1
       + b_2_5⁵·a_1_0 + a_2_3·b_9_44 + a_2_3·b_2_4³·b_2_6·b_1_2 + a_2_3·b_2_4⁴·b_1_2
       + a_2_3·b_2_6⁴·a_1_0 + a_2_3·b_2_5³·b_2_6·a_1_0 + a_1_0²·a_9_32
       + b_2_5³·b_2_6·a_1_0³ + a_2_3·b_2_5·a_1_0²·b_5_19
32. b_2_6²·b_1_2²·b_5_20 + b_2_6³·b_1_2⁵ + b_2_6⁴·b_1_2³ + b_2_4·b_2_6²·b_5_20
       + b_2_4·b_2_6⁴·b_1_2 + b_2_4²·b_2_6·b_5_20 + a_1_1·b_1_2·b_9_43 + a_10_38·b_1_2
       + b_2_5⁴·b_2_6·a_1_1 + b_2_5⁴·b_2_6·a_1_0 + b_2_4·a_9_32 + a_2_3·b_2_6²·b_5_19
       + a_2_3·b_2_6⁴·a_1_0 + a_2_3·b_2_5²·b_2_6²·a_1_0 + a_2_3·b_2_5³·b_2_6·a_1_0
       + b_2_5³·b_2_6·a_1_0³ + b_2_5⁴·a_1_0³ + a_2_3·b_2_6·a_1_0²·b_5_19
33. b_2_4·b_9_44 + b_2_4·b_9_43 + b_2_4·b_2_6²·b_5_20 + b_2_4·b_2_6⁴·b_1_2
       + b_2_4²·b_2_6·b_5_20 + b_2_4²·b_2_6³·b_1_2 + b_2_4⁴·b_2_6·b_1_2 + b_2_5⁵·a_1_1
       + b_2_5⁵·a_1_0 + b_2_4·a_9_32 + a_2_3·b_2_6²·b_5_19 + a_2_3·b_2_5·b_2_6·b_5_19
       + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_4⁴·b_1_2 + a_10_38·a_1_1 + b_2_6²·a_1_0²·b_5_19
       + b_2_5·b_2_6·a_1_0²·b_5_19 + b_2_5²·a_1_0²·b_5_19 + a_2_3·b_2_6⁴·a_1_0
       + a_2_3·b_2_5²·b_2_6²·a_1_0 + a_2_3·b_2_5³·b_2_6·a_1_0 + a_2_3·b_2_5⁴·a_1_0
       + a_1_0²·a_9_32 + b_2_5³·b_2_6·a_1_0³ + b_2_5⁴·a_1_0³
       + a_2_3·b_2_6·a_1_0²·b_5_19
34. b_2_4·b_9_44 + b_2_4·b_9_43 + b_2_4·b_2_6²·b_5_20 + b_2_4·b_2_6⁴·b_1_2
       + b_2_4²·b_2_6·b_5_20 + b_2_4²·b_2_6³·b_1_2 + b_2_4⁴·b_2_6·b_1_2 + b_2_5⁵·a_1_1
       + b_2_5⁵·a_1_0 + b_2_4·a_9_32 + a_2_3·b_2_6²·b_5_19 + a_2_3·b_2_5·b_2_6·b_5_19
       + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_4⁴·b_1_2 + a_10_38·a_1_0 + b_2_6²·a_1_0²·b_5_19
       + b_2_5·b_2_6·a_1_0²·b_5_19 + b_2_5²·a_1_0²·b_5_19 + a_2_3·b_2_6⁴·a_1_0
       + a_2_3·b_2_5²·b_2_6²·a_1_0 + a_2_3·b_2_5³·b_2_6·a_1_0 + a_2_3·b_2_5⁴·a_1_0
       + a_1_0²·a_9_32 + b_2_5³·b_2_6·a_1_0³ + b_2_5⁴·a_1_0³
       + a_2_3·b_2_6·a_1_0²·b_5_19
35. b_1_2²·b_9_43 + b_10_53·b_1_2 + b_2_6²·b_1_2²·b_5_20 + b_2_6²·b_1_2⁷
       + b_2_6³·b_1_2⁵ + b_2_6⁴·b_1_2³ + b_2_6⁵·b_1_2 + b_2_4·b_9_43
       + b_2_4·b_2_6⁴·b_1_2 + b_2_4²·b_2_6·b_5_20 + b_2_4³·b_2_6²·b_1_2 + b_2_4⁵·b_1_2
       + b_2_6·a_1_1·b_1_2⁸ + b_2_5⁵·a_1_1 + b_2_5⁵·a_1_0 + b_2_4·a_9_32
       + a_2_3·b_2_6²·b_5_19 + a_2_3·b_2_4⁴·b_1_2 + a_2_3·b_2_5²·b_2_6²·a_1_0
       + a_1_0²·a_9_32 + b_2_6⁴·a_1_0³ + b_2_5⁴·a_1_0³
36. b_2_4·b_9_44 + b_2_4·b_9_43 + b_2_4·b_2_6²·b_5_20 + b_2_4·b_2_6⁴·b_1_2
       + b_2_4³·b_5_20 + b_2_4³·b_2_6²·b_1_2 + b_2_4⁴·b_2_6·b_1_2 + a_1_1·b_1_2·b_9_43
       + b_10_53·a_1_1 + b_2_6⁵·a_1_0 + b_2_5·b_2_6⁴·a_1_0 + b_2_5⁴·b_2_6·a_1_1
       + b_2_5⁵·a_1_0 + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_4³·b_2_6·b_1_2
       + a_2_3·b_2_4⁴·b_1_2 + b_2_5²·a_1_0²·b_5_19 + a_2_3·b_2_5³·b_2_6·a_1_0
37. b_2_4·b_9_44 + b_2_4·b_9_43 + b_2_4·b_2_6²·b_5_20 + b_2_4·b_2_6⁴·b_1_2
       + b_2_4²·b_2_6·b_5_20 + b_2_4²·b_2_6³·b_1_2 + b_2_4⁴·b_2_6·b_1_2 + b_10_53·a_1_0
       + b_2_6⁵·a_1_0 + b_2_5·b_2_6⁴·a_1_0 + b_2_5⁴·b_2_6·a_1_0 + b_2_5⁵·a_1_1
       + b_2_4·a_9_32 + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_4⁴·b_1_2 + b_2_5²·a_1_0²·b_5_19
       + a_2_3·b_2_6⁴·a_1_0 + a_2_3·b_2_5²·b_2_6²·a_1_0 + b_2_5³·b_2_6·a_1_0³
       + a_2_3·b_2_5·a_1_0²·b_5_19
38. b_2_4³·b_1_2·b_5_20 + b_2_4⁴·b_2_6² + b_2_4·a_10_38 + a_2_3·b_2_4⁴·b_2_6
       + a_2_3·b_2_6²·a_1_0·b_5_19 + a_2_3·b_2_5·b_2_6·a_1_0·b_5_19
       + a_2_3·b_2_5²·a_1_0·b_5_19 + a_10_38·a_1_0² + b_2_5²·a_1_0³·b_5_19
       + a_2_3·b_2_5²·b_2_6²·a_1_0² + a_2_3·b_2_5³·b_2_6·a_1_0²
       + a_2_3·b_2_5⁴·a_1_0²
39. a_2_3·a_10_38 + a_2_3·b_2_6²·a_1_0·b_5_19 + a_2_3·b_2_5·b_2_6·a_1_0·b_5_19
       + a_2_3·b_2_5²·a_1_0·b_5_19 + a_10_38·a_1_0² + b_2_5²·a_1_0³·b_5_19
       + a_2_3·b_2_6⁴·a_1_0² + a_2_3·b_2_5³·b_2_6·a_1_0² + a_2_3·b_2_5⁴·a_1_0²
40. b_2_4·b_10_53 + b_2_4·b_2_6⁵ + b_2_4²·b_2_6⁴ + b_2_4³·b_1_2·b_5_20
       + b_2_4⁴·b_2_6² + b_2_4⁶ + b_10_53·a_1_1·b_1_2 + a_10_38·b_1_2²
       + b_2_6·b_1_2·a_9_32 + b_2_5³·a_1_1·b_5_19 + b_2_5³·a_1_0·b_5_19 + b_2_4·b_1_2·a_9_32
       + a_2_3·b_2_5³·b_2_6² + a_2_3·b_2_5⁴·b_2_6 + a_2_3·b_2_5⁵ + a_2_3·b_2_4⁴·b_2_6
       + b_2_6·a_1_0·a_9_32 + b_2_6⁵·a_1_0² + b_2_5·a_1_0·a_9_32 + b_2_5²·b_2_6³·a_1_0²
       + b_2_5³·b_2_6²·a_1_0² + b_2_5⁴·b_2_6·a_1_0² + a_2_3·b_2_5²·a_1_0·b_5_19
       + a_10_38·a_1_0² + b_2_6²·a_1_0³·b_5_19 + b_2_5·b_2_6·a_1_0³·b_5_19
       + a_2_3·b_2_6⁴·a_1_0² + a_2_3·b_2_5²·b_2_6²·a_1_0²
       + a_2_3·b_2_5³·b_2_6·a_1_0²
41. a_2_3·b_10_53 + a_2_3·b_2_6⁵ + a_2_3·b_2_5³·b_2_6² + a_2_3·b_2_5⁴·b_2_6
       + a_2_3·b_2_5⁵ + a_2_3·b_2_4⁴·b_2_6 + b_2_6·a_1_0·a_9_32 + b_2_6⁵·a_1_0²
       + b_2_5·a_1_0·a_9_32 + b_2_5²·b_2_6³·a_1_0² + b_2_5³·b_2_6²·a_1_0²
       + b_2_5⁴·b_2_6·a_1_0² + a_2_3·b_2_5²·a_1_0·b_5_19 + a_10_38·a_1_0²
       + b_2_5²·a_1_0³·b_5_19 + a_2_3·b_2_6⁴·a_1_0² + a_2_3·b_2_5³·b_2_6·a_1_0²
       + a_2_3·b_2_5⁴·a_1_0²
42. b_2_5·b_2_6³·b_5_20 + b_2_5·b_2_6³·b_5_19 + b_2_5²·b_2_6²·b_5_20
       + b_2_5²·b_2_6²·b_5_19 + b_2_4·b_2_6⁵·b_1_2 + b_2_4²·b_2_6⁴·b_1_2
       + b_2_6·b_10_53·a_1_1 + b_2_6·a_10_38·b_1_2 + b_2_6²·a_9_32 + b_2_5·b_2_6·a_9_32
       + b_2_5²·b_2_6⁴·a_1_0 + b_2_5⁵·b_2_6·a_1_0 + b_2_4·a_10_38·b_1_2
       + b_2_4·b_2_6·a_9_32 + b_2_4²·a_9_32 + a_2_3·b_2_4·b_9_43 + b_2_6·a_10_38·a_1_0
       + b_2_5·a_1_0²·b_9_44 + b_2_5·b_2_6²·a_1_0²·b_5_19 + b_2_5²·b_2_6·a_1_0²·b_5_19
       + b_2_5³·a_1_0²·b_5_19 + a_2_3·b_2_5⁴·b_2_6·a_1_0 + b_2_6⁵·a_1_0³
       + b_2_5⁵·a_1_0³ + a_2_3·b_2_6²·a_1_0²·b_5_19 + a_2_3·b_2_5·b_2_6·a_1_0²·b_5_19
43. b_5_20·b_9_44 + b_5_20·b_9_43 + b_5_19·b_9_44 + b_5_19·b_9_43 + b_2_6⁴·b_1_2·b_5_20
       + b_2_6⁵·b_1_2⁴ + b_2_6⁶·b_1_2² + b_2_5·b_2_6·b_5_19·b_5_20
       + b_2_5²·b_5_19·b_5_20 + b_2_5²·b_2_6⁵ + b_2_5³·b_2_6⁴ + b_2_5⁵·b_2_6²
       + b_2_5⁷ + b_2_4³·b_2_6⁴ + b_2_4⁴·b_2_6³ + b_2_4⁵·b_2_6² + b_2_4⁷
       + b_1_2⁵·a_9_32 + a_10_38·b_1_2⁴ + b_2_6·b_1_2³·a_9_32 + b_2_6·a_1_1·b_1_2¹¹
       + b_2_6·a_10_38·b_1_2² + b_2_6²·a_1_0·b_9_44 + b_2_6²·a_10_38 + b_2_5·b_2_6·a_10_38
       + b_2_5·b_2_6³·a_1_0·b_5_19 + b_2_5²·a_1_0·b_9_44 + b_2_5³·b_2_6·a_1_1·b_5_19
       + b_2_5⁴·a_1_1·b_5_19 + b_2_5⁴·a_1_0·b_5_19 + b_2_4·b_2_6·b_1_2·a_9_32
       + a_2_3·b_2_5⁴·b_2_6² + a_2_3·b_2_5⁵·b_2_6 + a_2_3·b_2_4·b_1_2·b_9_43
       + a_2_3·b_2_4⁶ + b_2_6²·a_1_0·a_9_32 + b_2_5²·a_1_0·a_9_32
       + b_2_5³·b_2_6³·a_1_0² + b_2_5⁴·b_2_6²·a_1_0² + a_2_3·b_2_6³·a_1_0·b_5_19
       + a_2_3·b_2_5·b_2_6²·a_1_0·b_5_19 + b_2_6³·a_1_0³·b_5_19 + b_2_5·a_10_38·a_1_0²
       + b_2_5³·a_1_0³·b_5_19 + a_2_3·b_2_6⁵·a_1_0² + a_2_3·b_2_5⁵·a_1_0²
       + b_2_5·a_1_0³·a_9_32
44. b_2_5·b_2_6·b_5_19·b_5_20 + b_2_5²·b_5_19·b_5_20 + b_2_5²·b_10_53 + b_2_5⁵·b_2_6²
       + b_2_5⁶·b_2_6 + b_2_4²·b_2_6⁵ + b_2_4³·b_2_6⁴ + b_2_4⁵·b_2_6² + b_2_4⁶·b_2_6
       + b_2_4⁷ + b_5_20·a_9_32 + b_2_6·b_1_2³·a_9_32 + b_2_6²·b_1_2·a_9_32
       + b_2_6⁴·a_1_0·b_5_19 + b_2_5·b_2_6·a_1_0·b_9_44 + b_2_5·b_2_6³·a_1_0·b_5_19
       + b_2_5²·a_1_0·b_9_44 + b_2_5²·a_10_38 + b_2_5²·b_2_6²·a_1_0·b_5_19
       + b_2_4²·b_1_2·a_9_32 + b_2_4²·a_10_38 + a_2_3·b_2_6⁶ + a_2_3·b_2_5⁴·b_2_6²
       + a_2_3·b_2_5⁶ + a_2_3·b_2_4⁵·b_2_6 + a_2_3·b_2_4⁶ + b_2_6⁶·a_1_0²
       + b_2_5·b_2_6⁵·a_1_0² + b_2_5²·a_1_0·a_9_32 + b_2_5²·b_2_6⁴·a_1_0²
       + b_2_5³·b_2_6³·a_1_0² + b_2_5⁴·b_2_6²·a_1_0² + b_2_5⁶·a_1_0²
       + a_2_3·b_2_5²·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_5³·a_1_0·b_5_19
       + b_2_6·a_10_38·a_1_0² + b_2_6³·a_1_0³·b_5_19 + b_2_5·a_10_38·a_1_0²
       + a_2_3·b_2_5³·b_2_6²·a_1_0² + a_2_3·b_2_5⁴·b_2_6·a_1_0²
       + a_2_3·b_2_5⁵·a_1_0²
45. b_5_20·a_9_32 + b_5_19·a_9_32 + b_2_6·b_10_53·a_1_1·b_1_2 + b_2_6·a_10_38·b_1_2²
       + b_2_6²·b_1_2·a_9_32 + b_2_4²·b_1_2·a_9_32 + b_2_4²·a_10_38 + a_2_3·b_2_6⁶
       + a_2_3·b_2_5⁴·b_2_6² + a_2_3·b_2_4·b_1_2·b_9_43 + b_2_6⁶·a_1_0²
       + b_2_5·b_2_6·a_1_0·a_9_32 + a_2_3·b_2_6³·a_1_0·b_5_19 + b_2_6³·a_1_0³·b_5_19
       + b_2_5·a_10_38·a_1_0² + b_2_5³·a_1_0³·b_5_19 + a_2_3·b_2_6⁵·a_1_0²
       + a_2_3·b_2_5³·b_2_6²·a_1_0² + a_2_3·b_2_5⁴·b_2_6·a_1_0²
       + a_2_3·b_2_5⁵·a_1_0² + b_2_5·a_1_0³·a_9_32
46. b_5_20·b_9_44 + b_5_20·b_9_43 + b_5_19·b_9_44 + b_2_6·b_10_53·b_1_2²
       + b_2_6²·b_5_19·b_5_20 + b_2_6²·b_10_53 + b_2_6³·b_1_2⁸ + b_2_6⁷ + b_2_5·b_2_6⁶
       + b_2_5²·b_5_19·b_5_20 + b_2_5³·b_2_6⁴ + b_2_5⁴·b_2_6³ + b_2_5⁵·b_2_6²
       + b_2_5⁶·b_2_6 + b_2_5⁷ + b_2_4·b_2_6⁶ + b_2_4²·b_2_6⁵ + b_2_4³·b_2_6⁴
       + b_2_4⁴·b_2_6³ + b_2_4⁷ + b_5_20·a_9_32 + b_5_19·a_9_32 + b_1_2⁵·a_9_32
       + a_10_38·b_1_2⁴ + b_2_6·b_1_2³·a_9_32 + b_2_6·a_1_1·b_1_2¹¹
       + b_2_6·a_10_38·b_1_2² + b_2_6²·a_1_0·b_9_44 + b_2_6⁴·a_1_0·b_5_19
       + b_2_5·b_2_6·a_1_0·b_9_44 + b_2_5·b_2_6·a_10_38 + b_2_5·b_2_6³·a_1_0·b_5_19
       + b_2_5²·a_1_0·b_9_44 + b_2_5³·b_2_6·a_1_1·b_5_19 + b_2_5³·b_2_6·a_1_0·b_5_19
       + a_2_3·b_2_6·b_1_2·b_9_43 + a_2_3·b_2_5⁴·b_2_6² + a_2_3·b_2_5⁶
       + a_2_3·b_2_4·b_1_2·b_9_43 + a_2_3·b_2_4⁵·b_2_6 + b_2_6²·a_1_0·a_9_32
       + b_2_5·b_2_6·a_1_0·a_9_32 + b_2_5²·a_1_0·a_9_32 + b_2_5³·b_2_6³·a_1_0²
       + b_2_5⁴·b_2_6²·a_1_0² + a_2_3·b_2_6³·a_1_0·b_5_19
       + a_2_3·b_2_5²·b_2_6·a_1_0·b_5_19 + b_2_5·a_10_38·a_1_0²
       + a_2_3·b_2_5³·b_2_6²·a_1_0² + a_2_3·b_2_5⁵·a_1_0²
47. a_10_38·b_5_20 + a_10_38·b_5_19 + b_2_4²·a_10_38·b_1_2 + b_2_4²·b_2_6·a_9_32
       + b_2_4³·a_9_32 + a_2_3·b_2_6⁴·b_5_19 + a_2_3·b_2_5³·b_2_6·b_5_19
       + a_2_3·b_2_4·b_2_6·b_9_43 + a_2_3·b_2_4²·b_9_43 + a_2_3·b_2_4⁵·b_2_6·b_1_2
       + b_2_6²·a_1_0²·b_9_44 + b_2_5·b_2_6·a_1_0²·b_9_44 + a_2_3·b_2_5⁴·b_2_6²·a_1_0
       + a_2_3·b_2_5⁵·b_2_6·a_1_0 + a_2_3·b_2_6³·a_1_0²·b_5_19 + b_2_6·a_10_38·a_1_0³
48. b_10_53·b_5_19 + b_2_6·b_10_53·b_1_2³ + b_2_6²·b_10_53·b_1_2 + b_2_6⁵·b_5_19
       + b_2_6⁶·b_1_2³ + b_2_6⁷·b_1_2 + b_2_5·b_2_6⁴·b_5_19 + b_2_5³·b_2_6²·b_5_20
       + b_2_5³·b_2_6²·b_5_19 + b_2_5⁴·b_2_6·b_5_19 + b_2_5⁵·b_5_20 + b_2_4·b_2_6⁶·b_1_2
       + b_2_4²·b_2_6⁵·b_1_2 + b_2_4³·b_2_6⁴·b_1_2 + b_2_4⁶·b_2_6·b_1_2 + a_10_38·b_5_19
       + b_2_6·a_10_38·b_1_2³ + b_2_6³·a_9_32 + b_2_6⁷·a_1_0 + b_2_5²·b_2_6·a_9_32
       + b_2_5³·a_9_32 + b_2_5⁴·b_2_6³·a_1_0 + b_2_5⁶·b_2_6·a_1_1 + b_2_5⁷·a_1_1
       + b_2_5⁷·a_1_0 + b_2_4²·a_10_38·b_1_2 + b_2_4²·b_2_6·a_9_32 + b_2_4³·a_9_32
       + a_2_3·b_2_6⁴·b_5_19 + a_2_3·b_2_5³·b_2_6·b_5_19 + a_2_3·b_2_5⁴·b_5_19
       + a_2_3·b_2_4·b_2_6·b_9_43 + a_2_3·b_2_4⁵·b_2_6·b_1_2 + a_2_3·b_2_4⁶·b_1_2
       + a_1_0·b_5_19·a_9_32 + b_2_6²·a_10_38·a_1_0 + b_2_6⁴·a_1_0²·b_5_19
       + b_2_5·b_2_6·a_1_0²·b_9_44 + b_2_5·b_2_6·a_10_38·a_1_0
       + b_2_5·b_2_6³·a_1_0²·b_5_19 + b_2_5²·b_2_6²·a_1_0²·b_5_19
       + b_2_5³·b_2_6·a_1_0²·b_5_19 + b_2_5⁴·a_1_0²·b_5_19 + a_2_3·b_2_5⁶·a_1_0
       + b_2_6⁶·a_1_0³ + b_2_5·b_2_6·a_1_0²·a_9_32 + b_2_5²·a_1_0²·a_9_32
       + a_2_3·b_2_6³·a_1_0²·b_5_19 + a_2_3·b_2_5²·b_2_6·a_1_0²·b_5_19
       + a_2_3·b_2_5³·a_1_0²·b_5_19
49. b_2_5·b_10_53·b_5_20 + b_2_5·b_2_6⁵·b_5_19 + b_2_5²·b_2_6⁴·b_5_19
       + b_2_5⁴·b_2_6²·b_5_20 + b_2_5⁴·b_2_6²·b_5_19 + b_2_5⁵·b_2_6·b_5_20
       + b_2_5⁶·b_5_19 + b_2_4·b_2_6⁷·b_1_2 + b_2_4²·b_2_6⁶·b_1_2 + b_2_4⁴·b_2_6⁴·b_1_2
       + b_2_4⁵·b_2_6³·b_1_2 + b_2_4⁶·b_2_6²·b_1_2 + b_2_6³·a_10_38·b_1_2
       + b_2_6⁴·a_9_32 + b_2_6⁸·a_1_0 + b_2_5·a_10_38·b_5_19 + b_2_5²·b_2_6⁶·a_1_0
       + b_2_5³·b_2_6·a_9_32 + b_2_5⁴·a_9_32 + b_2_5⁴·b_2_6⁴·a_1_0 + b_2_5⁵·b_2_6³·a_1_0
       + b_2_5⁷·b_2_6·a_1_1 + b_2_5⁸·a_1_1 + b_2_5⁸·a_1_0 + b_2_4·b_2_6³·a_9_32
       + b_2_4³·b_2_6·a_9_32 + a_2_3·b_2_6⁵·b_5_19 + a_2_3·b_2_5³·b_2_6²·b_5_19
       + a_2_3·b_2_5⁵·b_5_19 + a_2_3·b_2_4³·b_9_43 + a_2_3·b_2_4⁷·b_1_2
       + b_2_6⁵·a_1_0²·b_5_19 + b_2_5·a_1_0·b_5_19·a_9_32 + b_2_5·b_2_6²·a_10_38·a_1_0
       + b_2_5·b_2_6⁴·a_1_0²·b_5_19 + b_2_5²·b_2_6·a_10_38·a_1_0
       + b_2_5⁴·b_2_6·a_1_0²·b_5_19 + b_2_5⁵·a_1_0²·b_5_19 + a_2_3·b_2_5⁵·b_2_6²·a_1_0
       + a_2_3·b_2_5⁷·a_1_0 + a_10_38·a_1_0²·b_5_19 + b_2_6³·a_1_0²·a_9_32
       + b_2_6⁷·a_1_0³ + b_2_5·b_2_6²·a_1_0²·a_9_32 + b_2_5⁷·a_1_0³
       + a_2_3·b_2_5²·b_2_6²·a_1_0²·b_5_19 + a_2_3·b_2_5⁴·a_1_0²·b_5_19
50. a_9_32² + b_2_6⁸·a_1_0² + b_2_5·b_2_6³·a_1_0·a_9_32 + b_2_5·b_2_6⁷·a_1_0²
       + b_2_5²·b_2_6²·a_1_0·a_9_32 + b_2_5³·b_2_6⁵·a_1_0² + b_2_5⁵·b_2_6³·a_1_0²
       + b_2_5⁶·b_2_6²·a_1_0² + b_2_6·a_1_0²·b_5_19·a_9_32 + b_2_6⁵·a_1_0³·b_5_19
51. a_9_32·b_9_44 + a_9_32·b_9_43 + b_2_6·b_1_2⁷·a_9_32 + b_2_6³·b_1_2³·a_9_32
       + b_2_6⁴·a_1_0·b_9_44 + b_2_6⁶·a_1_0·b_5_19 + b_2_5·b_2_6·b_5_19·a_9_32
       + b_2_5·b_2_6³·a_1_0·b_9_44 + b_2_5·b_2_6³·a_10_38 + b_2_5·b_2_6⁵·a_1_0·b_5_19
       + b_2_5²·b_5_19·a_9_32 + b_2_5²·b_2_6²·a_10_38 + b_2_5³·b_2_6·a_1_0·b_9_44
       + b_2_5⁵·b_2_6·a_1_0·b_5_19 + b_2_4·b_2_6³·b_1_2·a_9_32
       + b_2_4²·b_2_6²·b_1_2·a_9_32 + a_9_32² + b_2_6·a_1_0²·b_5_19·b_9_44
       + b_2_6·a_10_38·a_1_0·b_5_19 + b_2_6⁴·a_1_0·a_9_32 + b_2_6⁸·a_1_0²
       + b_2_5·b_2_6³·a_1_0·a_9_32 + b_2_5·b_2_6⁷·a_1_0² + b_2_5²·b_2_6⁶·a_1_0²
       + b_2_5³·b_2_6·a_1_0·a_9_32 + b_2_5³·b_2_6⁵·a_1_0² + b_2_5⁴·a_1_0·a_9_32
       + b_2_5⁴·b_2_6⁴·a_1_0² + b_2_5⁵·b_2_6³·a_1_0² + b_2_5⁷·b_2_6·a_1_0²
       + a_2_3·b_2_6⁵·a_1_0·b_5_19 + a_2_3·b_2_5⁴·b_2_6·a_1_0·b_5_19
       + b_2_6³·a_10_38·a_1_0² + b_2_6⁵·a_1_0³·b_5_19 + b_2_5·a_1_0²·b_5_19·a_9_32
       + b_2_5⁴·b_2_6·a_1_0³·b_5_19
52. b_9_43·b_9_44 + b_9_43² + b_10_53·b_1_2³·b_5_20 + b_2_6²·b_5_20·b_9_43
       + b_2_6²·b_5_19·b_9_44 + b_2_6²·b_10_53·b_1_2⁴ + b_2_6³·b_1_2¹²
       + b_2_6³·b_10_53·b_1_2² + b_2_6⁴·b_1_2·b_9_43 + b_2_6⁴·b_1_2¹⁰ + b_2_6⁴·b_10_53
       + b_2_6⁶·b_1_2·b_5_20 + b_2_6⁶·b_1_2⁶ + b_2_6⁹ + b_2_5·b_2_6⁸
       + b_2_5⁴·b_5_19·b_5_20 + b_2_5⁴·b_10_53 + b_2_5⁵·b_2_6⁴
       + b_2_4·b_2_6·b_5_20·b_9_43 + b_2_4·b_2_6³·b_1_2·b_9_43 + b_2_4²·b_2_6⁷
       + b_2_4³·b_2_6·b_1_2·b_9_43 + b_2_4³·b_2_6⁶ + b_2_4⁴·b_2_6⁵ + b_2_4⁹
       + a_9_32·b_9_43 + b_2_6·b_1_2⁷·a_9_32 + b_2_6·a_10_38·b_1_2⁶ + b_2_6²·b_5_19·a_9_32
       + b_2_6²·b_1_2⁵·a_9_32 + b_2_6³·b_1_2³·a_9_32 + b_2_6³·a_10_38·b_1_2²
       + b_2_6⁴·a_1_0·b_9_44 + b_2_6⁴·a_10_38 + b_2_6⁶·a_1_0·b_5_19
       + b_2_5·b_2_6·b_5_19·a_9_32 + b_2_5·b_2_6³·a_10_38 + b_2_5²·b_5_19·a_9_32
       + b_2_5²·b_2_6²·a_10_38 + b_2_5³·b_2_6·a_1_0·b_9_44 + b_2_5⁴·a_1_0·b_9_44
       + b_2_5⁴·a_10_38 + b_2_5⁴·b_2_6²·a_1_0·b_5_19 + b_2_5⁶·a_1_1·b_5_19
       + b_2_5⁶·a_1_0·b_5_19 + b_2_4²·b_2_6²·b_1_2·a_9_32 + b_2_4³·b_2_6·b_1_2·a_9_32
       + b_2_4⁴·b_1_2·a_9_32 + a_2_3·b_2_6⁸ + a_2_3·b_2_4²·b_2_6·b_1_2·b_9_43
       + b_2_5·a_1_0²·b_5_19·b_9_44 + b_2_5·a_10_38·a_1_0·b_5_19
       + b_2_5²·b_2_6²·a_1_0·a_9_32 + b_2_5³·b_2_6·a_1_0·a_9_32 + b_2_5⁷·b_2_6·a_1_0²
       + b_2_5⁸·a_1_0² + a_2_3·b_2_6⁵·a_1_0·b_5_19 + a_2_3·b_2_5³·b_2_6²·a_1_0·b_5_19
       + a_2_3·b_2_5⁴·b_2_6·a_1_0·b_5_19 + b_2_6³·a_10_38·a_1_0²
       + b_2_5·a_1_0²·b_5_19·a_9_32 + b_2_5·b_2_6²·a_10_38·a_1_0²
       + b_2_5²·b_2_6·a_10_38·a_1_0² + a_2_3·b_2_5⁶·b_2_6·a_1_0²
       + b_2_5³·a_1_0³·a_9_32
53. b_9_43² + b_10_53·b_1_2³·b_5_20 + b_10_53·b_1_2⁸ + b_2_6·b_10_53·b_1_2·b_5_20
       + b_2_6²·b_1_2¹⁴ + b_2_6³·b_1_2¹² + b_2_6³·b_10_53·b_1_2² + b_2_6⁴·b_1_2¹⁰
       + b_2_6⁵·b_1_2⁸ + b_2_6⁶·b_1_2·b_5_20 + b_2_6⁶·b_1_2⁶ + b_2_6⁸·b_1_2²
       + b_2_5·b_2_6⁸ + b_2_5⁴·b_2_6⁵ + b_2_5⁵·b_2_6⁴ + b_2_4·b_2_6·b_5_20·b_9_43
       + b_2_4²·b_5_20·b_9_43 + b_2_4³·b_2_6·b_1_2·b_9_43 + b_2_4⁶·b_2_6³
       + b_2_4⁷·b_2_6² + b_1_2⁹·a_9_32 + b_2_6·a_1_1·b_1_2¹⁵ + b_2_6²·b_1_2⁵·a_9_32
       + b_2_6⁴·a_1_0·b_9_44 + b_2_6⁶·a_1_0·b_5_19 + b_2_5·b_2_6⁵·a_1_0·b_5_19
       + b_2_5⁵·b_2_6·a_1_1·b_5_19 + b_2_5⁵·b_2_6·a_1_0·b_5_19
       + b_2_4·b_2_6³·b_1_2·a_9_32 + b_2_4²·b_2_6²·b_1_2·a_9_32
       + b_2_4³·b_2_6·b_1_2·a_9_32 + b_2_4⁴·b_1_2·a_9_32 + b_2_4⁴·a_10_38 + a_2_3·b_2_6⁸
       + a_2_3·b_2_4⁷·b_2_6 + a_2_3·b_2_4⁸ + b_2_6⁴·a_1_0·a_9_32 + b_2_6⁸·a_1_0²
       + b_2_5·b_2_6³·a_1_0·a_9_32 + b_2_5²·b_2_6²·a_1_0·a_9_32
       + b_2_5³·b_2_6·a_1_0·a_9_32 + b_2_5³·b_2_6⁵·a_1_0² + b_2_5⁴·b_2_6⁴·a_1_0²
       + b_2_5⁵·b_2_6³·a_1_0² + a_2_3·b_2_5³·b_2_6²·a_1_0·b_5_19
       + b_2_6³·a_10_38·a_1_0² + b_2_6⁵·a_1_0³·b_5_19 + b_2_5·a_1_0²·b_5_19·a_9_32
       + a_2_3·b_2_6⁷·a_1_0² + a_2_3·b_2_5⁵·b_2_6²·a_1_0²
       + a_2_3·b_2_5⁶·b_2_6·a_1_0² + a_2_3·b_2_5⁷·a_1_0² + b_2_5³·a_1_0³·a_9_32
       + c_16_113·b_1_2²
54. b_2_6·b_10_53·b_1_2·b_5_20 + b_2_6²·b_10_53·b_1_2⁴ + b_2_6³·b_10_53·b_1_2²
       + b_2_6⁶·b_1_2·b_5_20 + b_2_6⁷·b_1_2⁴ + b_2_6⁸·b_1_2²
       + b_2_4·b_2_6·b_5_20·b_9_43 + b_2_4·b_2_6³·b_1_2·b_9_43 + b_2_4²·b_5_20·b_9_43
       + b_2_4²·b_2_6²·b_1_2·b_9_43 + b_2_4³·b_2_6⁶ + b_2_4⁷·b_2_6² + a_9_32·b_9_43
       + a_10_38·b_1_2⁸ + b_2_6·b_1_2⁷·a_9_32 + b_2_6·a_10_38·b_1_2⁶
       + b_2_6²·b_5_19·a_9_32 + b_2_6³·b_1_2³·a_9_32 + b_2_6⁴·b_1_2·a_9_32
       + b_2_5⁵·b_2_6·a_1_1·b_5_19 + b_2_5⁵·b_2_6·a_1_0·b_5_19
       + b_2_4·b_2_6³·b_1_2·a_9_32 + b_2_4⁴·b_1_2·a_9_32 + a_2_3·b_2_5⁶·b_2_6²
       + a_2_3·b_2_4³·b_1_2·b_9_43 + a_2_3·b_2_4⁷·b_2_6 + a_2_3·b_2_4⁸
       + b_2_6⁴·a_1_0·a_9_32 + b_2_5·b_2_6³·a_1_0·a_9_32 + b_2_5·b_2_6⁷·a_1_0²
       + b_2_5³·b_2_6⁵·a_1_0² + b_2_5⁴·a_1_0·a_9_32 + b_2_5⁵·b_2_6³·a_1_0²
       + b_2_5⁶·b_2_6²·a_1_0² + b_2_5⁷·b_2_6·a_1_0²
       + a_2_3·b_2_5³·b_2_6²·a_1_0·b_5_19 + b_2_5²·b_2_6·a_10_38·a_1_0²
       + a_2_3·b_2_6⁷·a_1_0² + c_16_113·a_1_1·b_1_2
55. b_9_44² + b_9_43² + b_2_6²·b_1_2¹⁴ + b_2_6⁶·b_1_2⁶ + b_2_5·b_2_6⁸
       + b_2_5³·b_2_6⁶ + b_2_5⁶·b_2_6³ + b_2_5⁷·b_2_6² + b_2_5⁸·b_2_6 + b_2_5⁹
       + b_2_4·b_2_6⁸ + b_2_4⁶·b_2_6³ + b_2_4⁷·b_2_6² + b_2_4⁸·b_2_6 + b_2_4⁹
       + b_2_6⁴·a_1_0·b_9_44 + b_2_6⁶·a_1_0·b_5_19 + b_2_5·b_2_6⁵·a_1_0·b_5_19
       + b_2_5²·b_2_6⁴·a_1_0·b_5_19 + b_2_5⁴·a_1_0·b_9_44 + b_2_5⁵·b_2_6·a_1_0·b_5_19
       + b_2_5⁶·a_1_1·b_5_19 + b_2_5⁶·a_1_0·b_5_19 + a_2_3·b_2_6⁸ + a_2_3·b_2_4⁷·b_2_6
       + a_2_3·b_2_4⁸ + a_9_32² + b_2_6⁸·a_1_0² + b_2_5·a_1_0²·b_5_19·b_9_44
       + b_2_5·b_2_6³·a_1_0·a_9_32 + b_2_5·b_2_6⁷·a_1_0² + b_2_5²·b_2_6²·a_1_0·a_9_32
       + b_2_5²·b_2_6⁶·a_1_0² + b_2_5³·b_2_6·a_1_0·a_9_32 + b_2_5³·b_2_6⁵·a_1_0²
       + b_2_5⁴·a_1_0·a_9_32 + b_2_5⁴·b_2_6⁴·a_1_0² + b_2_5⁵·b_2_6³·a_1_0²
       + b_2_5⁶·b_2_6²·a_1_0² + b_2_5⁷·b_2_6·a_1_0² + a_2_3·b_2_6⁵·a_1_0·b_5_19
       + a_2_3·b_2_5³·b_2_6²·a_1_0·b_5_19 + b_2_6³·a_10_38·a_1_0²
       + b_2_5·a_1_0²·b_5_19·a_9_32 + b_2_5³·a_10_38·a_1_0²
       + b_2_5⁴·b_2_6·a_1_0³·b_5_19 + a_2_3·b_2_5⁶·b_2_6·a_1_0² + c_16_113·a_1_0²
56. a_10_38·a_9_32 + b_2_6²·a_1_0·b_5_19·a_9_32 + b_2_6⁴·a_10_38·a_1_0
       + b_2_6⁶·a_1_0²·b_5_19 + b_2_5·b_2_6·a_1_0·b_5_19·a_9_32
       + b_2_5·b_2_6³·a_1_0²·b_9_44 + b_2_5²·a_1_0·b_5_19·a_9_32
       + b_2_5²·b_2_6²·a_1_0²·b_9_44 + b_2_5²·b_2_6²·a_10_38·a_1_0
       + b_2_5³·b_2_6·a_10_38·a_1_0 + b_2_5⁴·b_2_6²·a_1_0²·b_5_19
       + b_2_5⁵·b_2_6·a_1_0²·b_5_19 + b_2_5·b_2_6³·a_1_0²·a_9_32
       + b_2_5³·b_2_6·a_1_0²·a_9_32 + b_2_5⁴·a_1_0²·a_9_32 + b_2_5⁷·b_2_6·a_1_0³
       + b_2_5·a_1_0³·b_5_19·a_9_32
57. b_10_53·b_9_44 + b_10_53·b_9_43 + b_10_53·b_1_2⁴·b_5_20 + b_2_6²·b_10_53·b_5_20
       + b_2_6²·b_10_53·b_1_2⁵ + b_2_6⁴·b_10_53·b_1_2 + b_2_6⁵·b_9_44 + b_2_6⁵·b_9_43
       + b_2_6⁶·b_1_2⁷ + b_2_6⁷·b_5_20 + b_2_6⁹·b_1_2 + b_2_5·b_2_6⁴·b_9_44
       + b_2_5⁴·b_2_6·b_9_44 + b_2_5⁵·b_9_44 + b_2_5⁷·b_5_20 + b_2_5⁷·b_5_19
       + b_2_4·b_2_6⁴·b_9_43 + b_2_4·b_2_6⁶·b_5_20 + b_2_4·b_2_6⁸·b_1_2
       + b_2_4³·b_2_6⁶·b_1_2 + b_2_4⁴·b_2_6·b_9_43 + b_2_4⁵·b_9_43 + b_10_53·a_9_32
       + a_10_38·b_9_44 + a_10_38·b_9_43 + b_2_6·a_10_38·b_1_2⁷
       + b_2_6²·a_1_0·b_5_19·b_9_44 + b_2_6⁵·a_9_32 + b_2_5·b_2_6·a_1_0·b_5_19·b_9_44
       + b_2_5·b_2_6·a_10_38·b_5_19 + b_2_5·b_2_6⁴·a_9_32 + b_2_5·b_2_6⁸·a_1_0
       + b_2_5²·b_2_6³·a_9_32 + b_2_5³·b_2_6⁶·a_1_0 + b_2_5⁴·b_2_6·a_9_32
       + b_2_5⁴·b_2_6⁵·a_1_0 + b_2_5⁷·b_2_6²·a_1_0 + b_2_4·b_2_6⁴·a_9_32
       + b_2_4²·b_2_6³·a_9_32 + b_2_4⁴·a_10_38·b_1_2 + a_2_3·b_2_6⁶·b_5_19
       + a_2_3·b_2_4⁷·b_2_6·b_1_2 + b_2_5·b_2_6·a_1_0·b_5_19·a_9_32
       + b_2_5·b_2_6³·a_10_38·a_1_0 + b_2_5·b_2_6⁵·a_1_0²·b_5_19
       + b_2_5²·b_2_6²·a_1_0²·b_9_44 + b_2_5³·b_2_6·a_10_38·a_1_0
       + b_2_5³·b_2_6³·a_1_0²·b_5_19 + b_2_5⁴·a_1_0²·b_9_44 + b_2_5⁴·a_10_38·a_1_0
       + b_2_5⁴·b_2_6²·a_1_0²·b_5_19 + b_2_5⁶·a_1_0²·b_5_19 + a_2_3·b_2_5⁸·a_1_0
       + b_2_6·a_10_38·a_1_0²·b_5_19 + b_2_6⁴·a_1_0²·a_9_32
       + b_2_5·a_10_38·a_1_0²·b_5_19 + b_2_5²·b_2_6²·a_1_0²·a_9_32
       + b_2_5⁷·b_2_6·a_1_0³ + b_2_5⁸·a_1_0³ + a_2_3·b_2_5⁴·b_2_6·a_1_0²·b_5_19
       + b_2_5·a_1_0³·b_5_19·a_9_32
58. b_2_6²·b_10_53·b_5_20 + b_2_6³·b_10_53·b_1_2³ + b_2_6⁴·b_10_53·b_1_2
       + b_2_6⁷·b_5_20 + b_2_6⁸·b_1_2³ + b_2_6⁹·b_1_2 + b_2_5·b_2_6⁶·b_5_19
       + b_2_5⁴·b_2_6³·b_5_19 + b_2_5⁵·b_2_6²·b_5_20 + b_2_4·b_2_6·b_1_2·b_5_20·b_9_43
       + b_2_4·b_2_6⁶·b_5_20 + b_2_4·b_2_6⁸·b_1_2 + b_2_4²·b_2_6³·b_9_43
       + b_2_4²·b_2_6⁷·b_1_2 + b_2_4⁵·b_2_6⁴·b_1_2 + b_2_4⁶·b_2_6³·b_1_2
       + b_1_2·a_9_32·b_9_43 + b_10_53·a_9_32 + a_10_38·b_9_43 + a_10_38·b_1_2⁹
       + b_2_6·b_1_2⁸·a_9_32 + b_2_6²·b_1_2⁶·a_9_32 + b_2_6³·b_1_2⁴·a_9_32
       + b_2_6⁵·a_9_32 + b_2_5·b_2_6⁴·a_9_32 + b_2_5⁴·b_2_6⁵·a_1_0 + b_2_5⁵·a_9_32
       + b_2_5⁶·b_2_6³·a_1_0 + b_2_5⁷·b_2_6²·a_1_0 + b_2_5⁸·b_2_6·a_1_1
       + b_2_5⁸·b_2_6·a_1_0 + b_2_4·b_2_6⁴·a_9_32 + b_2_4³·b_2_6²·a_9_32
       + b_2_4⁴·a_10_38·b_1_2 + b_2_4⁴·b_2_6·a_9_32 + a_2_3·b_2_4⁷·b_2_6·b_1_2
       + a_2_3·b_2_4⁸·b_1_2 + a_10_38·a_9_32 + b_2_6⁴·a_1_0²·b_9_44
       + b_2_5²·b_2_6²·a_10_38·a_1_0 + b_2_5²·b_2_6⁴·a_1_0²·b_5_19
       + b_2_5³·b_2_6·a_10_38·a_1_0 + b_2_5³·b_2_6³·a_1_0²·b_5_19
       + b_2_5⁴·a_1_0²·b_9_44 + b_2_5⁴·b_2_6²·a_1_0²·b_5_19
       + b_2_5⁵·b_2_6·a_1_0²·b_5_19 + b_2_5⁶·a_1_0²·b_5_19 + a_2_3·b_2_6⁸·a_1_0
       + a_2_3·b_2_5⁶·b_2_6²·a_1_0 + a_2_3·b_2_5⁷·b_2_6·a_1_0 + a_2_3·b_2_5⁸·a_1_0
       + b_2_6·a_10_38·a_1_0²·b_5_19 + b_2_6⁴·a_1_0²·a_9_32 + b_2_6⁸·a_1_0³
       + b_2_5²·b_2_6²·a_1_0²·a_9_32 + b_2_5³·b_2_6·a_1_0²·a_9_32
       + b_2_5⁴·a_1_0²·a_9_32 + b_2_5⁷·b_2_6·a_1_0³ + b_2_5⁸·a_1_0³
       + b_2_6³·a_10_38·a_1_0³ + c_16_113·a_1_1·b_1_2²
59. b_10_53·b_9_43 + b_10_53·b_1_2⁴·b_5_20 + b_10_53·b_1_2⁹
       + b_2_6²·b_1_2·b_5_20·b_9_43 + b_2_6²·b_1_2¹⁵ + b_2_6²·b_10_53·b_5_20
       + b_2_6³·b_1_2¹³ + b_2_6⁵·b_9_43 + b_2_6⁷·b_5_20 + b_2_5⁶·b_2_6·b_5_20
       + b_2_5⁶·b_2_6·b_5_19 + b_2_4·b_2_6·b_1_2·b_5_20·b_9_43 + b_2_4·b_2_6⁶·b_5_20
       + b_2_4²·b_1_2·b_5_20·b_9_43 + b_2_4²·b_2_6³·b_9_43 + b_2_4²·b_2_6⁷·b_1_2
       + b_2_4³·b_2_6²·b_9_43 + b_2_4³·b_2_6⁶·b_1_2 + b_2_4⁴·b_2_6⁵·b_1_2
       + b_2_4⁵·b_9_43 + b_2_4⁹·b_1_2 + b_1_2·a_9_32·b_9_43 + b_1_2¹⁰·a_9_32 + a_10_38·b_9_43
       + b_2_6·a_1_1·b_1_2¹⁶ + b_2_6·a_10_38·b_1_2⁷ + b_2_6²·b_1_2⁶·a_9_32
       + b_2_6²·a_10_38·b_5_19 + b_2_6⁴·a_10_38·b_1_2 + b_2_6⁵·a_9_32 + b_2_6⁹·a_1_0
       + b_2_5·b_2_6⁴·a_9_32 + b_2_5³·b_2_6²·a_9_32 + b_2_5⁴·b_2_6⁵·a_1_0
       + b_2_5⁵·b_2_6⁴·a_1_0 + b_2_5⁶·b_2_6³·a_1_0 + b_2_5⁸·b_2_6·a_1_0 + b_2_5⁹·a_1_1
       + b_2_5⁹·a_1_0 + b_2_4·b_2_6⁴·a_9_32 + b_2_4⁴·a_10_38·b_1_2 + b_2_4⁴·b_2_6·a_9_32
       + a_2_3·b_2_6⁶·b_5_19 + a_2_3·b_2_5⁵·b_2_6·b_5_19 + a_2_3·b_2_5⁶·b_5_19
       + a_2_3·b_2_4⁸·b_1_2 + b_2_5·b_2_6³·a_1_0²·b_9_44 + b_2_5²·a_1_0·b_5_19·a_9_32
       + b_2_5²·b_2_6²·a_1_0²·b_9_44 + b_2_5²·b_2_6⁴·a_1_0²·b_5_19
       + b_2_5⁴·b_2_6²·a_1_0²·b_5_19 + b_2_5⁵·b_2_6·a_1_0²·b_5_19
       + a_2_3·b_2_5⁶·b_2_6²·a_1_0 + a_2_3·b_2_5⁸·a_1_0 + b_2_6·a_10_38·a_1_0²·b_5_19
       + b_2_5·b_2_6³·a_1_0²·a_9_32 + b_2_5²·b_2_6²·a_1_0²·a_9_32
       + b_2_5³·b_2_6·a_1_0²·a_9_32 + b_2_5⁸·a_1_0³
       + a_2_3·b_2_5³·b_2_6²·a_1_0²·b_5_19 + a_2_3·b_2_5⁵·a_1_0²·b_5_19
       + b_2_5·a_1_0³·b_5_19·a_9_32 + c_16_113·b_1_2³ + b_2_4·c_16_113·b_1_2
60. b_2_4·b_2_6·b_1_2·b_5_20·b_9_43 + b_2_4²·b_1_2·b_5_20·b_9_43
       + b_2_4²·b_2_6³·b_9_43 + b_2_4³·b_2_6²·b_9_43 + b_1_2·a_9_32·b_9_43
       + b_10_53·a_9_32 + b_2_6²·b_1_2⁶·a_9_32 + b_2_6⁵·a_9_32 + b_2_5·b_2_6⁴·a_9_32
       + b_2_5⁴·b_2_6·a_9_32 + b_2_5⁵·a_9_32 + b_2_4³·b_2_6²·a_9_32 + b_2_4⁴·b_2_6·a_9_32
       + a_2_3·b_2_6⁶·b_5_19 + a_2_3·b_2_5⁴·b_2_6²·b_5_19 + a_2_3·b_2_4³·b_2_6·b_9_43
       + a_2_3·b_2_4⁸·b_1_2 + a_10_38·a_9_32 + b_2_6⁶·a_1_0²·b_5_19
       + b_2_5·b_2_6·a_1_0·b_5_19·a_9_32 + a_2_3·b_2_5⁷·b_2_6·a_1_0
       + b_2_6·a_10_38·a_1_0²·b_5_19 + b_2_6⁸·a_1_0³ + b_2_5·a_10_38·a_1_0²·b_5_19
       + b_2_5²·b_2_6²·a_1_0²·a_9_32 + b_2_5³·b_2_6·a_1_0²·a_9_32
       + b_2_5⁴·a_1_0²·a_9_32 + b_2_5⁸·a_1_0³ + a_2_3·b_2_5³·b_2_6²·a_1_0²·b_5_19
       + a_2_3·b_2_5⁴·b_2_6·a_1_0²·b_5_19 + a_2_3·b_2_5⁵·a_1_0²·b_5_19
       + b_2_6³·a_10_38·a_1_0³ + b_2_5·a_1_0³·b_5_19·a_9_32 + a_2_3·c_16_113·b_1_2
61. b_2_4·b_2_6⁶·b_5_20 + b_2_4·b_2_6⁸·b_1_2 + a_10_38·b_9_44 + a_10_38·b_9_43
       + b_2_6·a_10_38·b_1_2⁷ + b_2_6²·a_1_0·b_5_19·b_9_44 + b_2_6⁴·b_1_2²·a_9_32
       + b_2_6⁴·a_10_38·b_1_2 + b_2_6⁵·a_9_32 + b_2_6⁹·a_1_0
       + b_2_5·b_2_6·a_1_0·b_5_19·b_9_44 + b_2_5·b_2_6·a_10_38·b_5_19 + b_2_5·b_2_6⁴·a_9_32
       + b_2_5·b_2_6⁸·a_1_0 + b_2_5²·a_1_0·b_5_19·b_9_44 + b_2_5²·a_10_38·b_5_19
       + b_2_5²·b_2_6³·a_9_32 + b_2_5³·b_2_6²·a_9_32 + b_2_5⁴·b_2_6⁵·a_1_0
       + b_2_5⁵·b_2_6⁴·a_1_0 + b_2_5⁷·b_2_6²·a_1_0 + b_2_5⁸·b_2_6·a_1_1 + b_2_5⁹·a_1_0
       + b_2_4·b_2_6⁴·a_9_32 + b_2_4²·b_2_6³·a_9_32 + b_2_4³·b_2_6²·a_9_32
       + a_2_3·b_2_5⁴·b_2_6²·b_5_19 + a_2_3·b_2_4⁷·b_2_6·b_1_2 + a_10_38·a_9_32
       + b_2_6²·a_1_0·b_5_19·a_9_32 + b_2_6⁴·a_1_0²·b_9_44 + b_2_6⁶·a_1_0²·b_5_19
       + b_2_5·b_2_6³·a_1_0²·b_9_44 + b_2_5·b_2_6³·a_10_38·a_1_0
       + b_2_5²·a_1_0·b_5_19·a_9_32 + b_2_5²·b_2_6²·a_1_0²·b_9_44
       + b_2_5²·b_2_6²·a_10_38·a_1_0 + b_2_5²·b_2_6⁴·a_1_0²·b_5_19
       + b_2_5³·b_2_6·a_1_0²·b_9_44 + b_2_5³·b_2_6·a_10_38·a_1_0 + b_2_5⁴·a_10_38·a_1_0
       + a_2_3·b_2_5⁶·b_2_6²·a_1_0 + a_2_3·b_2_5⁸·a_1_0 + b_2_6⁴·a_1_0²·a_9_32
       + b_2_6⁸·a_1_0³ + b_2_5·a_10_38·a_1_0²·b_5_19 + b_2_5³·b_2_6·a_1_0²·a_9_32
       + b_2_5⁸·a_1_0³ + b_2_6³·a_10_38·a_1_0³ + a_2_3·c_16_113·a_1_0
62. b_2_4³·b_5_20·b_9_43 + b_2_4³·b_2_6²·b_1_2·b_9_43 + a_10_38·b_1_2·b_9_43
       + a_10_38·b_10_53 + b_2_6³·b_1_2⁵·a_9_32 + b_2_6⁵·a_10_38 + b_2_5·b_2_6⁴·a_10_38
       + b_2_5⁴·b_2_6·a_10_38 + b_2_5⁵·a_10_38 + b_2_4²·b_2_6³·b_1_2·a_9_32
       + b_2_4⁵·b_1_2·a_9_32 + b_2_4⁵·a_10_38 + a_2_3·b_2_5⁷·b_2_6² + a_2_3·b_2_5⁸·b_2_6
       + a_2_3·b_2_4³·b_2_6·b_1_2·b_9_43 + a_2_3·b_2_4⁴·b_1_2·b_9_43 + a_10_38²
       + b_2_6²·a_1_0²·b_5_19·b_9_44 + b_2_6⁵·a_1_0·a_9_32 + b_2_6⁹·a_1_0²
       + b_2_5·b_2_6·a_1_0²·b_5_19·b_9_44 + b_2_5·b_2_6⁴·a_1_0·a_9_32
       + b_2_5²·b_2_6³·a_1_0·a_9_32 + b_2_5³·b_2_6²·a_1_0·a_9_32
       + b_2_5³·b_2_6⁶·a_1_0² + b_2_5⁵·b_2_6⁴·a_1_0² + b_2_5⁶·b_2_6³·a_1_0²
       + a_2_3·b_2_5⁴·b_2_6²·a_1_0·b_5_19 + a_2_3·b_2_5⁶·a_1_0·b_5_19
       + b_2_6²·a_1_0²·b_5_19·a_9_32 + b_2_6⁴·a_10_38·a_1_0²
       + b_2_5²·a_1_0²·b_5_19·a_9_32 + b_2_5²·b_2_6²·a_10_38·a_1_0²
       + b_2_5⁵·b_2_6·a_1_0³·b_5_19 + b_2_5⁶·a_1_0³·b_5_19 + a_2_3·b_2_6⁸·a_1_0²
       + b_2_5⁴·a_1_0³·a_9_32
63. b_10_53·b_1_2⁵·b_5_20 + b_10_53·b_1_2¹⁰ + b_10_53² + b_2_6²·b_1_2¹⁶
       + b_2_6²·b_10_53·b_1_2⁶ + b_2_6³·b_1_2¹⁴ + b_2_6⁵·b_1_2¹⁰ + b_2_6⁶·b_1_2⁸
       + b_2_6⁷·b_1_2⁶ + b_2_6¹⁰ + b_2_5²·b_2_6⁸ + b_2_5⁸·b_2_6² + b_2_5¹⁰
       + b_2_4³·b_2_6⁷ + b_2_4⁴·b_2_6⁶ + b_2_4⁶·b_2_6⁴ + b_2_4⁷·b_2_6³ + b_2_4¹⁰
       + b_1_2¹¹·a_9_32 + b_10_53·b_1_2·a_9_32 + a_10_38·b_1_2¹⁰ + b_2_6·b_1_2⁹·a_9_32
       + b_2_6·a_1_1·b_1_2¹⁷ + b_2_6·a_10_38·b_1_2⁸ + b_2_6⁵·b_1_2·a_9_32
       + b_2_4⁵·a_10_38 + a_2_3·b_2_4⁴·b_1_2·b_9_43 + a_2_3·b_2_4⁸·b_2_6 + a_10_38²
       + b_2_6⁵·a_1_0·a_9_32 + b_2_6⁹·a_1_0² + b_2_5·b_2_6⁴·a_1_0·a_9_32
       + b_2_5²·b_2_6⁷·a_1_0² + b_2_5³·b_2_6²·a_1_0·a_9_32 + b_2_5⁵·a_1_0·a_9_32
       + b_2_5⁵·b_2_6⁴·a_1_0² + b_2_5⁸·b_2_6·a_1_0² + a_2_3·b_2_6⁶·a_1_0·b_5_19
       + a_2_3·b_2_5⁵·b_2_6·a_1_0·b_5_19 + b_2_6²·a_1_0²·b_5_19·a_9_32
       + b_2_6⁴·a_10_38·a_1_0² + b_2_5²·a_1_0²·b_5_19·a_9_32
       + b_2_5²·b_2_6²·a_10_38·a_1_0² + a_2_3·b_2_5⁷·b_2_6·a_1_0²
       + a_2_3·b_2_5⁸·a_1_0² + b_2_5⁴·a_1_0³·a_9_32 + c_16_113·b_1_2⁴
       + b_2_4²·c_16_113 + c_16_113·a_1_1·b_1_2³ + a_2_3·b_2_4·c_16_113
64. a_10_38² + b_2_6⁵·a_1_0·a_9_32 + b_2_6⁹·a_1_0² + b_2_5·b_2_6⁴·a_1_0·a_9_32
       + b_2_5²·b_2_6³·a_1_0·a_9_32 + b_2_5³·b_2_6²·a_1_0·a_9_32
       + b_2_5⁴·b_2_6⁵·a_1_0² + b_2_5⁷·b_2_6²·a_1_0² + b_2_5⁸·b_2_6·a_1_0²
       + b_2_5⁹·a_1_0² + a_2_3·b_2_6⁶·a_1_0·b_5_19 + a_2_3·b_2_5⁴·b_2_6²·a_1_0·b_5_19
       + b_2_6²·a_1_0²·b_5_19·a_9_32 + b_2_6⁴·a_10_38·a_1_0²
       + b_2_5²·a_1_0²·b_5_19·a_9_32 + b_2_5²·b_2_6²·a_10_38·a_1_0²
       + b_2_5⁶·a_1_0³·b_5_19 + a_2_3·b_2_6⁸·a_1_0² + a_2_3·b_2_5⁶·b_2_6²·a_1_0²
       + a_2_3·b_2_5⁷·b_2_6·a_1_0² + b_2_5⁴·a_1_0³·a_9_32 + a_2_3·c_16_113·a_1_0²

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 20.
• 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_16_113, a Duflot regular element of degree 16
  2. b_1_2⁴ + b_2_6² + b_2_5·b_2_6 + b_2_5² + b_2_4·b_2_6 + b_2_4·b_2_5, an element of degree 4
  3. b_2_6, an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, 7, 17, 19].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

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 1

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. a_2_3 → 0, an element of degree 2
5. b_2_4 → 0, an element of degree 2
6. b_2_5 → 0, an element of degree 2
7. b_2_6 → 0, an element of degree 2
8. b_5_19 → 0, an element of degree 5
9. b_5_20 → 0, an element of degree 5
10. a_9_32 → 0, an element of degree 9
11. b_9_43 → 0, an element of degree 9
12. b_9_44 → 0, an element of degree 9
13. a_10_38 → 0, an element of degree 10
14. b_10_53 → 0, an element of degree 10
15. c_16_113 → c_1_0¹⁶, an element of degree 16

Restriction map to a maximal el. ab. subgp. 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 → c_1_1, an element of degree 1
4. a_2_3 → 0, an element of degree 2
5. b_2_4 → 0, an element of degree 2
6. b_2_5 → 0, an element of degree 2
7. b_2_6 → c_1_2² + c_1_1·c_1_2, an element of degree 2
8. b_5_19 → c_1_1·c_1_2⁴ + c_1_1⁴·c_1_2, an element of degree 5
9. b_5_20 → c_1_1·c_1_2⁴ + c_1_1⁴·c_1_2, an element of degree 5
10. a_9_32 → 0, an element of degree 9
11. b_9_43 → c_1_1³·c_1_2⁶ + c_1_1⁴·c_1_2⁵ + c_1_1⁵·c_1_2⁴ + c_1_1⁶·c_1_2³
       + c_1_0²·c_1_1³·c_1_2⁴ + c_1_0²·c_1_1⁵·c_1_2² + c_1_0⁴·c_1_1·c_1_2⁴
       + c_1_0⁴·c_1_1³·c_1_2² + c_1_0⁴·c_1_1⁵ + c_1_0⁸·c_1_1, an element of degree 9
12. b_9_44 → c_1_1⁷·c_1_2² + c_1_1⁸·c_1_2 + c_1_0²·c_1_1³·c_1_2⁴ + c_1_0²·c_1_1⁵·c_1_2²
       + c_1_0⁴·c_1_1·c_1_2⁴ + c_1_0⁴·c_1_1³·c_1_2² + c_1_0⁴·c_1_1⁵ + c_1_0⁸·c_1_1, an element of degree 9
13. a_10_38 → 0, an element of degree 10
14. b_10_53 → c_1_2¹⁰ + c_1_1·c_1_2⁹ + c_1_1⁷·c_1_2³ + c_1_1⁸·c_1_2²
       + c_1_0²·c_1_1⁴·c_1_2⁴ + c_1_0²·c_1_1⁶·c_1_2² + c_1_0⁴·c_1_1²·c_1_2⁴
       + c_1_0⁴·c_1_1⁴·c_1_2² + c_1_0⁴·c_1_1⁶ + c_1_0⁸·c_1_1², an element of degree 10
15. c_16_113 → c_1_1²·c_1_2¹⁴ + c_1_1³·c_1_2¹³ + c_1_1⁵·c_1_2¹¹ + c_1_1⁷·c_1_2⁹
       + c_1_1⁹·c_1_2⁷ + c_1_1¹¹·c_1_2⁵ + c_1_1¹²·c_1_2⁴ + c_1_1¹³·c_1_2³
       + c_1_0²·c_1_1⁸·c_1_2⁶ + c_1_0²·c_1_1⁹·c_1_2⁵ + c_1_0²·c_1_1¹¹·c_1_2³
       + c_1_0²·c_1_1¹²·c_1_2² + c_1_0⁴·c_1_1⁴·c_1_2⁸ + c_1_0⁴·c_1_1⁶·c_1_2⁶
       + c_1_0⁴·c_1_1⁷·c_1_2⁵ + c_1_0⁴·c_1_1⁸·c_1_2⁴ + c_1_0⁴·c_1_1⁹·c_1_2³
       + c_1_0⁴·c_1_1¹¹·c_1_2 + c_1_0⁴·c_1_1¹² + c_1_0⁸·c_1_2⁸
       + c_1_0⁸·c_1_1⁴·c_1_2⁴ + c_1_0⁸·c_1_1⁶·c_1_2² + c_1_0⁸·c_1_1⁷·c_1_2
       + c_1_0¹⁶, an element of degree 16

Restriction map to a maximal el. ab. subgp. 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. a_2_3 → 0, an element of degree 2
5. b_2_4 → 0, an element of degree 2
6. b_2_5 → c_1_1², an element of degree 2
7. b_2_6 → c_1_2², an element of degree 2
8. b_5_19 → c_1_1·c_1_2⁴ + c_1_1⁴·c_1_2 + c_1_1⁵, an element of degree 5
9. b_5_20 → c_1_1·c_1_2⁴ + c_1_1⁴·c_1_2 + c_1_1⁵, an element of degree 5
10. a_9_32 → 0, an element of degree 9
11. b_9_43 → c_1_1·c_1_2⁸ + c_1_1⁴·c_1_2⁵ + c_1_1⁵·c_1_2⁴, an element of degree 9
12. b_9_44 → c_1_1³·c_1_2⁶ + c_1_1⁴·c_1_2⁵ + c_1_1⁵·c_1_2⁴ + c_1_1⁶·c_1_2³
       + c_1_1⁷·c_1_2² + c_1_1⁸·c_1_2 + c_1_1⁹, an element of degree 9
13. a_10_38 → 0, an element of degree 10
14. b_10_53 → c_1_2¹⁰ + c_1_1²·c_1_2⁸ + c_1_1⁸·c_1_2² + c_1_1¹⁰, an element of degree 10
15. c_16_113 → c_1_1⁶·c_1_2¹⁰ + c_1_1⁷·c_1_2⁹ + c_1_1¹⁰·c_1_2⁶ + c_1_1¹¹·c_1_2⁵
       + c_1_1¹²·c_1_2⁴ + c_1_1¹⁶ + c_1_0⁴·c_1_1⁴·c_1_2⁸ + c_1_0⁴·c_1_1⁸·c_1_2⁴
       + c_1_0⁸·c_1_2⁸ + c_1_0⁸·c_1_1⁴·c_1_2⁴ + c_1_0⁸·c_1_1⁸ + c_1_0¹⁶, an element of degree 16

Restriction map to a maximal el. ab. subgp. 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 → c_1_2, an element of degree 1
4. a_2_3 → 0, an element of degree 2
5. b_2_4 → c_1_2², an element of degree 2
6. b_2_5 → c_1_2², an element of degree 2
7. b_2_6 → c_1_1·c_1_2 + c_1_1², an element of degree 2
8. b_5_19 → 0, an element of degree 5
9. b_5_20 → c_1_1²·c_1_2³ + c_1_1⁴·c_1_2, an element of degree 5
10. a_9_32 → 0, an element of degree 9
11. b_9_43 → c_1_2⁹ + c_1_1⁴·c_1_2⁵ + c_1_1⁸·c_1_2 + c_1_0²·c_1_1²·c_1_2⁵
       + c_1_0²·c_1_1⁴·c_1_2³ + c_1_0⁴·c_1_2⁵ + c_1_0⁴·c_1_1²·c_1_2³
       + c_1_0⁴·c_1_1⁴·c_1_2 + c_1_0⁸·c_1_2, an element of degree 9
12. b_9_44 → c_1_2⁹ + c_1_1·c_1_2⁸ + c_1_1²·c_1_2⁷ + c_1_1⁴·c_1_2⁵ + c_1_1⁸·c_1_2
       + c_1_0²·c_1_1²·c_1_2⁵ + c_1_0²·c_1_1⁴·c_1_2³ + c_1_0⁴·c_1_2⁵
       + c_1_0⁴·c_1_1²·c_1_2³ + c_1_0⁴·c_1_1⁴·c_1_2 + c_1_0⁸·c_1_2, an element of degree 9
13. a_10_38 → 0, an element of degree 10
14. b_10_53 → c_1_2¹⁰ + c_1_1⁴·c_1_2⁶ + c_1_1⁵·c_1_2⁵ + c_1_1⁶·c_1_2⁴ + c_1_1⁸·c_1_2²
       + c_1_1⁹·c_1_2 + c_1_1¹⁰, an element of degree 10
15. c_16_113 → c_1_1·c_1_2¹⁵ + c_1_1²·c_1_2¹⁴ + c_1_1³·c_1_2¹³ + c_1_1⁵·c_1_2¹¹
       + c_1_1¹⁰·c_1_2⁶ + c_1_1¹²·c_1_2⁴ + c_1_0²·c_1_1³·c_1_2¹¹
       + c_1_0²·c_1_1⁸·c_1_2⁶ + c_1_0²·c_1_1⁹·c_1_2⁵ + c_1_0²·c_1_1¹⁰·c_1_2⁴
       + c_1_0⁴·c_1_1·c_1_2¹¹ + c_1_0⁴·c_1_1⁴·c_1_2⁸ + c_1_0⁴·c_1_1⁵·c_1_2⁷
       + c_1_0⁴·c_1_1⁶·c_1_2⁶ + c_1_0⁴·c_1_1⁹·c_1_2³ + c_1_0⁴·c_1_1¹⁰·c_1_2²
       + c_1_0⁸·c_1_2⁸ + c_1_0⁸·c_1_1·c_1_2⁷ + c_1_0⁸·c_1_1³·c_1_2⁵
       + c_1_0⁸·c_1_1⁴·c_1_2⁴ + c_1_0⁸·c_1_1⁵·c_1_2³ + c_1_0⁸·c_1_1⁶·c_1_2²
       + c_1_0⁸·c_1_1⁸ + c_1_0¹⁶, an element of degree 16

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128