David J. Green

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Cohomology of group number 741 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) · (t14  +  t13  −  2·t12  +  2·t11  −  t10  +  2·t9  +  2·t6  −  2·t5  +  3·t4  −  2·t3  +  2·t2  +  1)

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

• The a-invariants are -∞,-4,-5,-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 17 minimal generators of maximal degree 16:

1. a_1_2, a nilpotent element of degree 1
2. b_1_0, an element of degree 1
3. b_1_1, an element of degree 1
4. a_2_3, a nilpotent element of degree 2
5. a_2_4, a nilpotent 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. b_5_21, an element of degree 5
11. b_8_43, an element of degree 8
12. b_9_50, an element of degree 9
13. b_9_51, an element of degree 9
14. b_9_53, an element of degree 9
15. a_10_36, a nilpotent element of degree 10
16. a_10_43, a nilpotent element of degree 10
17. c_16_141, 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 87 minimal relations of maximal degree 20:

1. a_1_2·b_1_0
2. b_1_0·b_1_1
3. a_1_2·b_1_1
4. a_2_3·b_1_1
5. a_2_4·b_1_0
6. a_2_4·a_1_2 + a_2_3·a_1_2
7. b_2_6·b_1_0 + b_2_5·b_1_1 + a_1_2³
8. a_2_3·a_2_4 + a_2_3²
9. a_2_4² + a_2_3²
10. b_2_5·a_1_2² + a_2_3²
11. b_2_5·b_2_6·b_1_1 + b_2_5²·b_1_1 + b_2_6·a_1_2³
12. b_1_1·b_5_19 + b_2_6²·b_1_1² + a_2_3·b_2_6·a_1_2²
13. a_1_2·b_5_19 + a_2_4·b_2_5·b_2_6 + a_2_4·b_2_5² + b_2_6²·a_1_2² + a_2_3²·b_2_6
14. b_1_0·b_5_20 + b_2_5²·b_1_0² + a_2_3·b_1_0⁴ + a_2_3³
15. a_1_2·b_5_20 + a_2_3·b_2_6² + a_2_3·b_2_5·b_2_6 + a_2_3²·b_2_5
16. b_1_1·b_5_21 + a_2_4·b_2_6² + a_2_3·b_2_6² + a_2_3·b_2_6·a_1_2²
17. b_1_0·b_5_21 + b_1_0·b_5_19 + b_2_5·b_1_0⁴ + b_2_5²·b_1_0² + a_2_4·b_2_5²
       + a_2_3·b_1_0⁴ + a_2_3·b_2_5²
18. b_2_5²·b_2_6·a_1_2 + b_2_5³·a_1_2 + a_2_4·b_5_19 + a_2_4·b_2_6²·b_1_1
       + a_2_3·b_2_6²·a_1_2 + a_2_3·b_2_5·b_2_6·a_1_2
19. b_2_5·b_2_6²·a_1_2 + b_2_5²·b_2_6·a_1_2 + a_2_3·b_5_20 + a_2_3·b_2_5²·b_1_0
       + a_2_3·b_2_5²·a_1_2
20. b_2_6·b_5_19 + b_2_6³·b_1_1 + b_2_5·b_5_20 + b_2_5³·b_1_0 + b_2_6³·a_1_2
       + b_2_5·b_2_6²·a_1_2 + b_2_5³·a_1_2 + a_2_3·b_2_5·b_1_0³ + a_1_2²·b_5_21
       + a_2_3·b_2_5·b_2_6·a_1_2 + a_2_3·b_2_5²·a_1_2 + a_2_3²·b_2_6·a_1_2
       + a_2_3²·b_2_5·a_1_2
21. b_2_5²·b_2_6·a_1_2 + b_2_5³·a_1_2 + a_2_4·b_5_21 + a_2_3·b_5_21 + a_2_3·b_5_19
       + a_2_3·b_2_5·b_1_0³ + a_2_3·b_2_5²·b_1_0 + a_2_3·b_2_6²·a_1_2
       + a_2_3·b_2_5·b_2_6·a_1_2 + b_2_6²·a_1_2³ + a_2_3²·b_2_6·a_1_2
       + a_2_3²·b_2_5·a_1_2
22. a_2_3²·b_2_6²·a_1_2 + a_2_3²·b_2_5·b_2_6·a_1_2
23. b_8_43·b_1_1 + b_2_6·b_1_1²·b_5_20 + b_2_6³·b_1_1³ + b_2_6⁴·b_1_1
       + a_2_4·b_2_6·b_5_20 + a_2_3·b_2_6·b_5_20 + b_2_6³·a_1_2³
24. b_1_0⁴·b_5_19 + b_8_43·b_1_0 + b_2_5·b_1_0²·b_5_19 + b_2_5⁴·b_1_0
       + a_2_4·b_2_5·b_5_19 + a_2_3·b_1_0⁷ + a_2_3·b_2_5·b_5_19 + a_2_3·b_2_5·b_1_0⁵
       + a_2_3·b_2_5³·b_1_0 + a_2_3²·b_2_5·b_2_6·a_1_2
25. b_8_43·a_1_2 + b_2_6⁴·a_1_2 + a_2_4·b_2_5·b_5_19 + a_2_3·b_2_6·b_5_21
       + a_2_3·b_2_6·b_5_20 + a_2_3·b_2_5·b_5_21 + a_2_3·b_2_5·b_5_19 + a_2_3·b_2_5²·b_1_0³
       + a_2_3·b_2_5³·b_1_0 + a_2_3·b_2_5³·a_1_2 + a_2_3²·b_5_21 + a_2_3²·b_5_20
       + a_2_3·a_1_2²·b_5_21
26. b_5_19·b_5_20 + b_2_6²·b_1_1·b_5_20 + b_2_5²·b_1_0·b_5_19 + b_2_5²·b_2_6³
       + b_2_5⁴·b_2_6 + a_2_4·b_2_5³·b_2_6 + a_2_4·b_2_5⁴ + a_2_3·b_1_0³·b_5_19
       + a_2_3·b_2_6⁴ + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_6·a_1_2·b_5_21
       + a_2_3·b_2_5·a_1_2·b_5_21 + a_2_3²·b_2_5²·b_2_6 + a_2_3²·b_2_5³
       + a_2_3·b_2_6³·a_1_2² + a_2_3³·b_2_6²
27. b_5_19·b_5_21 + b_5_19² + b_2_6⁴·b_1_1² + b_2_5·b_8_43 + b_2_5·b_2_6⁴
       + b_2_5²·b_2_6³ + b_2_5⁵ + b_2_6²·a_1_2·b_5_21 + b_2_5·b_2_6·a_1_2·b_5_21
       + b_2_5²·a_1_2·b_5_21 + a_2_4·b_2_6⁴ + a_2_4·b_2_5³·b_2_6 + a_2_3·b_1_0³·b_5_19
       + a_2_3·b_2_6⁴ + a_2_3·b_2_5·b_1_0⁶ + a_2_3·b_2_5²·b_1_0⁴
       + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_5³·b_2_6 + a_2_3·b_2_5⁴ + b_2_6⁴·a_1_2²
       + a_2_3²·b_2_6³ + a_2_3²·b_2_5·b_2_6² + a_2_3²·b_2_5²·b_2_6 + a_2_3²·b_2_5³
       + b_2_6·a_1_2³·b_5_21 + a_2_3·b_2_6³·a_1_2² + a_2_3²·a_1_2·b_5_21
       + a_2_3³·b_2_6² + a_2_3³·b_2_5·b_2_6 + a_2_3³·b_2_5²
28. b_5_20·b_5_21 + b_5_19·b_5_20 + b_2_6·b_8_43 + b_2_6⁴·b_1_1² + b_2_6⁵
       + b_2_5·b_2_6⁴ + b_2_5³·b_1_0⁴ + b_2_5⁴·b_1_0² + b_2_5⁴·b_2_6
       + b_2_5·b_2_6·a_1_2·b_5_21 + b_2_5²·a_1_2·b_5_21 + a_2_3·b_2_6⁴
       + a_2_3·b_2_5·b_1_0⁶ + a_2_3·b_2_5·b_2_6³ + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_5⁴
       + a_2_3²·b_2_5²·b_2_6 + b_2_6·a_1_2³·b_5_21 + a_2_3²·a_1_2·b_5_21
       + a_2_3³·b_2_5²
29. b_2_5·b_2_6·a_1_2·b_5_21 + b_2_5²·a_1_2·b_5_21 + a_2_4·b_2_5³·b_2_6 + a_2_4·b_2_5⁴
       + a_2_3·b_1_0³·b_5_19 + a_2_3·b_8_43 + a_2_3·b_2_6⁴ + a_2_3·b_2_5·b_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_5³·b_2_6 + a_2_3·b_2_5⁴
       + a_2_3·b_2_5·a_1_2·b_5_21 + a_2_3²·b_2_5·b_2_6² + a_2_3²·b_2_5³
       + a_2_3²·a_1_2·b_5_21 + a_2_3³·b_2_5²
30. b_2_5·b_2_6·a_1_2·b_5_21 + b_2_5²·a_1_2·b_5_21 + a_2_4·b_8_43
       + a_2_4·b_2_6·b_1_1·b_5_20 + a_2_4·b_2_6³·b_1_1² + a_2_4·b_2_6⁴
       + a_2_3·b_2_5·b_2_6³ + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_5·a_1_2·b_5_21
       + a_2_3²·b_2_5·b_2_6² + a_2_3²·b_2_5³ + b_2_6·a_1_2³·b_5_21
       + a_2_3·b_2_6³·a_1_2² + a_2_3³·b_2_6² + a_2_3³·b_2_5²
31. b_1_1·b_9_50 + b_1_1⁵·b_5_20 + b_2_6³·b_1_1⁴ + a_2_4·b_1_1³·b_5_20
       + a_2_4·b_2_6·b_1_1·b_5_20 + a_2_4·b_2_6·b_1_1⁶ + a_2_4·b_2_6³·b_1_1²
       + b_2_6·a_1_2³·b_5_21 + a_2_3³·b_2_6²
32. b_5_19² + b_1_0·b_9_50 + b_2_6⁴·b_1_1² + b_2_5²·b_1_0·b_5_19 + b_2_5²·b_1_0⁶
       + b_2_5³·b_2_6² + b_2_5⁴·b_1_0² + b_2_5⁵ + a_2_3·b_1_0³·b_5_19 + a_2_3·b_1_0⁸
       + a_2_3·b_2_5·b_1_0·b_5_19 + a_2_3·b_2_5²·b_1_0⁴ + b_2_6⁴·a_1_2²
       + a_2_3²·b_2_5·b_2_6² + a_2_3²·a_1_2·b_5_21 + a_2_3³·b_2_6² + a_2_3³·b_2_5²
33. b_5_21² + b_5_19² + b_2_6⁴·b_1_1² + b_2_5·b_2_6⁴ + b_2_5²·b_1_0⁶
       + b_2_5⁴·b_1_0² + b_2_5⁴·b_2_6 + a_1_2·b_9_50 + b_2_6²·a_1_2·b_5_21
       + b_2_5·b_2_6·a_1_2·b_5_21 + b_2_5²·a_1_2·b_5_21 + a_2_4·b_2_5⁴ + a_2_3·b_2_6⁴
       + a_2_3·b_2_5·b_2_6³ + a_2_3·b_2_5²·b_2_6² + a_2_3·b_2_5³·b_2_6
       + a_2_3²·b_2_6³ + a_2_3²·b_2_5³ + a_2_3²·a_1_2·b_5_21 + a_2_3³·b_2_5·b_2_6
34. b_5_20² + b_1_1·b_9_51 + b_2_6·b_1_1³·b_5_20 + b_2_6²·b_1_1·b_5_20
       + b_2_6⁴·b_1_1² + b_2_5·b_2_6⁴ + b_2_5³·b_2_6² + b_2_5⁴·b_1_0²
       + a_2_4·b_1_1³·b_5_20 + a_2_4·b_2_6·b_1_1⁶ + a_2_4·b_2_5³·b_2_6
       + a_2_3·b_2_5³·b_2_6 + a_2_3²·b_2_5³ + b_2_6·a_1_2³·b_5_21
       + a_2_3·b_2_6³·a_1_2² + a_2_3²·a_1_2·b_5_21 + a_2_3³·b_2_6² + a_2_3³·b_2_5²
35. b_1_0·b_9_51 + b_8_43·b_1_0² + b_2_5²·b_1_0·b_5_19 + b_2_5²·b_1_0⁶
       + b_2_5³·b_1_0⁴ + b_2_5⁴·b_1_0² + a_2_4·b_2_5⁴ + a_2_3·b_2_5³·b_1_0²
       + a_2_3·b_2_5⁴ + a_2_3²·a_1_2·b_5_21 + a_2_3³·b_2_6²
36. b_5_21² + b_5_19·b_5_20 + b_5_19² + b_2_6²·b_1_1·b_5_20 + b_2_6⁴·b_1_1²
       + b_2_5·b_2_6⁴ + b_2_5²·b_1_0·b_5_19 + b_2_5²·b_1_0⁶ + b_2_5²·b_2_6³
       + b_2_5⁴·b_1_0² + a_1_2·b_9_51 + b_2_6²·a_1_2·b_5_21 + b_2_5·b_2_6·a_1_2·b_5_21
       + a_2_4·b_2_5³·b_2_6 + a_2_3·b_1_0³·b_5_19 + a_2_3·b_2_5·b_2_6³
       + a_2_3·b_2_5³·b_2_6 + b_2_6⁴·a_1_2² + a_2_3·b_2_5·a_1_2·b_5_21 + a_2_3²·b_2_6³
       + a_2_3²·b_2_5²·b_2_6 + b_2_6·a_1_2³·b_5_21
37. b_5_20² + b_1_1·b_9_53 + b_1_1⁵·b_5_20 + b_2_6·b_1_1³·b_5_20 + b_2_6²·b_1_1⁶
       + b_2_6³·b_1_1⁴ + b_2_6⁴·b_1_1² + b_2_5·b_2_6⁴ + b_2_5³·b_2_6²
       + b_2_5⁴·b_1_0² + a_2_4·b_1_1³·b_5_20 + a_2_4·b_2_6²·b_1_1⁴ + a_2_4·b_2_6⁴
       + a_2_3·b_2_6⁴ + a_2_3²·b_2_5³ + b_2_6·a_1_2³·b_5_21 + a_2_3³·b_2_6²
       + a_2_3³·b_2_5·b_2_6
38. b_5_19² + b_1_0·b_9_53 + b_8_43·b_1_0² + b_2_6⁴·b_1_1² + b_2_5·b_1_0³·b_5_19
       + b_2_5²·b_1_0·b_5_19 + b_2_5³·b_1_0⁴ + b_2_5³·b_2_6² + b_2_5⁴·b_1_0²
       + b_2_5⁵ + a_2_4·b_2_5³·b_2_6 + a_2_3·b_2_5²·b_1_0⁴ + a_2_3·b_2_5³·b_2_6
       + b_2_6⁴·a_1_2² + a_2_3²·b_2_5·b_2_6² + a_2_3³·b_2_6² + a_2_3³·b_2_5·b_2_6
       + a_2_3³·b_2_5²
39. b_5_21² + b_5_19·b_5_20 + b_5_19² + b_2_6²·b_1_1·b_5_20 + b_2_6⁴·b_1_1²
       + b_2_5·b_2_6⁴ + b_2_5²·b_1_0·b_5_19 + b_2_5²·b_1_0⁶ + b_2_5²·b_2_6³
       + b_2_5⁴·b_1_0² + a_1_2·b_9_53 + b_2_5·b_2_6·a_1_2·b_5_21 + b_2_5²·a_1_2·b_5_21
       + a_2_4·b_2_5³·b_2_6 + a_2_3·b_1_0³·b_5_19 + a_2_3·b_2_6⁴ + a_2_3·b_2_5²·b_2_6²
       + a_2_3²·b_2_6³ + a_2_3²·b_2_5²·b_2_6 + a_2_3²·b_2_5³ + b_2_6·a_1_2³·b_5_21
       + a_2_3³·b_2_5²
40. a_2_4·b_9_50 + a_2_4·b_1_1⁴·b_5_20 + a_2_4·b_2_6³·b_1_1³ + a_2_3·b_9_51
       + a_2_3·b_8_43·b_1_0 + a_2_3·b_2_5²·b_5_21 + a_2_3·b_2_5²·b_1_0⁵
       + a_2_3·b_2_6⁴·a_1_2 + a_2_3²·b_2_6·b_5_21 + a_2_3·b_2_6·a_1_2²·b_5_21
       + a_2_3²·b_2_5³·a_1_2
41. b_2_6·b_9_53 + b_2_6·b_9_51 + b_2_6·b_1_1⁴·b_5_20 + b_2_6³·b_5_21 + b_2_6³·b_5_20
       + b_2_6³·b_1_1⁵ + b_2_6⁴·b_1_1³ + b_2_5·b_9_53 + b_2_5·b_9_50 + b_2_5·b_8_43·b_1_0
       + b_2_5·b_2_6²·b_5_21 + b_2_5·b_2_6²·b_5_20 + b_2_5²·b_1_0²·b_5_19
       + b_2_5²·b_2_6·b_5_21 + b_2_5²·b_2_6·b_5_20 + b_2_5³·b_5_20 + b_2_5³·b_1_0⁵
       + b_2_5⁴·b_1_0³ + b_2_5⁵·b_1_1 + b_2_5⁵·b_1_0 + b_2_6⁵·a_1_2
       + a_2_4·b_2_6²·b_1_1⁵ + a_2_4·b_2_6³·b_1_1³ + a_2_3·b_2_5·b_1_0²·b_5_19
       + a_2_3·b_2_5·b_1_0⁷ + a_2_3·b_2_5·b_2_6·b_5_20 + a_2_3·b_2_5²·b_5_21
       + a_2_3·b_2_5⁴·b_1_0 + a_1_2²·b_9_50 + a_2_3²·b_2_6·b_5_21 + a_2_3²·b_2_6·b_5_20
       + a_2_3²·b_2_5·b_5_21 + a_2_3²·b_2_5·b_5_20 + a_2_3²·b_2_5·b_5_19 + b_2_6⁴·a_1_2³
       + a_2_3·b_2_6·a_1_2²·b_5_21 + a_2_3²·b_2_5³·a_1_2 + a_2_3³·b_5_21 + a_2_3³·b_5_19
42. a_2_3·b_9_53 + a_2_3·b_9_50 + a_2_3·b_8_43·b_1_0 + a_2_3·b_2_6²·b_5_21
       + a_2_3·b_2_6²·b_5_20 + a_2_3·b_2_5·b_1_0²·b_5_19 + a_2_3·b_2_5²·b_5_20
       + a_2_3·b_2_5²·b_1_0⁵ + a_2_3·b_2_5³·b_1_0³ + a_2_3·b_2_5⁴·b_1_0
       + a_2_3·b_2_5⁴·a_1_2 + a_2_3²·b_2_6·b_5_21 + a_2_3²·b_2_5·b_5_21
       + a_2_3²·b_2_5·b_5_20 + a_2_3²·b_2_5·b_5_19 + a_2_3·b_2_6·a_1_2²·b_5_21
       + a_2_3²·b_2_5³·a_1_2 + a_2_3³·b_5_21 + a_2_3³·b_5_19
43. a_2_4·b_9_53 + a_2_4·b_9_51 + a_2_4·b_1_1⁴·b_5_20 + a_2_4·b_2_6²·b_5_20
       + a_2_4·b_2_6²·b_1_1⁵ + a_2_4·b_2_6³·b_1_1³ + a_2_4·b_2_5²·b_5_19
       + a_2_3·b_2_6²·b_5_21 + a_2_3·b_2_5²·b_5_21 + a_2_3·b_2_5²·b_5_20
       + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_5³·b_1_0³ + a_2_3·b_2_6⁴·a_1_2
       + a_2_3·b_2_5⁴·a_1_2 + a_2_3²·b_2_5·b_5_21 + a_2_3²·b_2_5·b_5_20
       + a_2_3²·b_2_5·b_5_19 + b_2_6⁴·a_1_2³ + a_2_3·b_2_6·a_1_2²·b_5_21
       + a_2_3²·b_2_5³·a_1_2 + a_2_3³·b_5_21 + a_2_3³·b_5_19
44. a_10_36·b_1_1 + a_2_4·b_9_51 + a_2_4·b_9_50 + a_2_4·b_2_6²·b_1_1⁵
       + a_2_4·b_2_6³·b_1_1³ + a_2_4·b_2_5²·b_5_19 + a_2_3·b_2_5²·b_5_21
       + a_2_3·b_2_5²·b_5_19 + a_2_3·b_2_5³·b_1_0³ + a_2_3·b_2_5⁴·b_1_0
       + a_2_3·b_2_6⁴·a_1_2 + a_2_3²·b_2_6·b_5_21 + a_2_3·b_2_6·a_1_2²·b_5_21
       + a_2_3³·b_5_21 + a_2_3³·b_5_19
45. a_10_36·b_1_0 + a_2_4·b_9_50 + a_2_4·b_1_1⁴·b_5_20 + a_2_4·b_2_6³·b_1_1³
       + a_2_3·b_9_50 + a_2_3·b_8_43·b_1_0 + a_2_3·b_2_5·b_1_0⁷ + a_2_3·b_2_5³·b_1_0³
       + a_2_3³·b_5_21 + a_2_3³·b_5_19
46. a_1_2²·b_9_50 + a_10_36·a_1_2 + b_2_6²·a_1_2²·b_5_21 + a_2_3·b_2_5⁴·a_1_2
       + a_2_3²·b_2_6·b_5_21 + a_2_3²·b_2_5·b_5_21
47. a_10_43·b_1_1 + a_2_4·b_2_6²·b_5_20 + a_2_4·b_2_6²·b_1_1⁵ + a_2_4·b_2_6³·b_1_1³
       + a_2_3·b_2_6²·b_5_20 + b_2_6⁴·a_1_2³ + a_2_3·b_2_6·a_1_2²·b_5_21
       + a_2_3²·b_2_5³·a_1_2 + a_2_3³·b_5_19
48. a_10_43·b_1_0 + a_2_4·b_9_50 + a_2_4·b_1_1⁴·b_5_20 + a_2_4·b_2_6³·b_1_1³
       + a_2_3·b_9_50 + a_2_3·b_8_43·b_1_0 + a_2_3·b_2_5·b_1_0²·b_5_19
       + a_2_3·b_2_5³·b_1_0³ + a_2_3·b_2_5⁴·b_1_0 + a_2_3³·b_5_21 + a_2_3³·b_5_19
49. a_2_4·b_9_50 + a_2_4·b_1_1⁴·b_5_20 + a_2_4·b_2_6³·b_1_1³ + a_2_3·b_2_6²·b_5_21
       + a_2_3·b_2_6²·b_5_20 + a_2_3·b_2_5·b_2_6·b_5_21 + a_1_2²·b_9_50 + a_10_43·a_1_2
       + a_2_3·b_2_6⁴·a_1_2 + a_2_3²·b_2_5·b_5_20 + a_2_3²·b_2_5·b_5_19 + a_2_3³·b_5_19
50. a_2_4·a_10_36 + a_2_3·a_10_36 + a_2_3³·b_2_6³ + a_2_3³·b_2_5²·b_2_6
51. a_2_3·a_10_36 + a_2_3·b_2_5²·a_1_2·b_5_21 + a_2_3²·b_2_6⁴ + a_2_3²·b_2_5·b_2_6³
       + a_2_3²·b_2_5⁴ + a_10_43·a_1_2² + a_2_3·b_2_6⁴·a_1_2² + a_2_3³·b_2_6³
       + a_2_3³·b_2_5²·b_2_6 + a_2_3³·b_2_5³
52. b_2_5·a_1_2·b_9_50 + a_2_3·b_2_6·b_8_43 + a_2_3·b_2_6⁵ + a_2_3·a_10_43 + a_2_3·a_10_36
       + a_2_3·b_2_6²·a_1_2·b_5_21 + a_2_3·b_2_5²·a_1_2·b_5_21 + a_2_3²·b_2_6⁴
       + a_2_3²·b_2_5·b_2_6³ + a_2_3²·b_2_5³·b_2_6 + a_2_3²·b_2_6·a_1_2·b_5_21
       + a_2_3³·b_2_5·b_2_6² + a_2_3³·b_2_5²·b_2_6
53. b_2_5·a_1_2·b_9_50 + a_2_3·b_2_6·b_8_43 + a_2_3·b_2_6⁵ + a_2_4·a_10_43 + a_2_3·a_10_36
       + a_2_3·b_2_6²·a_1_2·b_5_21 + a_2_3·b_2_5²·a_1_2·b_5_21 + a_2_3²·b_2_6⁴
       + a_2_3²·b_2_5·b_2_6³ + a_2_3²·b_2_5³·b_2_6 + b_2_6²·a_1_2³·b_5_21
       + a_2_3·b_2_6⁴·a_1_2² + a_2_3³·b_2_5²·b_2_6
54. b_1_0⁴·b_9_50 + b_8_43·b_5_21 + b_8_43·b_5_20 + b_2_6·b_1_1²·b_9_51
       + b_2_6²·b_1_1⁴·b_5_20 + b_2_6⁴·b_5_21 + b_2_6⁴·b_5_20 + b_2_6⁵·b_1_1³
       + b_2_5·b_1_0²·b_9_50 + b_2_5·b_8_43·b_1_0³ + b_2_5·b_2_6·b_9_51
       + b_2_5·b_2_6·b_9_50 + b_2_5²·b_1_0⁹ + b_2_5²·b_8_43·b_1_0 + b_2_5²·b_2_6²·b_5_21
       + b_2_5²·b_2_6²·b_5_20 + b_2_5³·b_1_0⁷ + b_2_5³·b_2_6·b_5_20 + b_2_5⁴·b_5_20
       + b_2_5⁴·b_5_19 + b_2_5⁴·b_1_0⁵ + b_2_5⁶·b_1_1 + b_2_5⁶·b_1_0 + a_2_4·b_2_6·b_9_51
       + a_2_4·b_2_6·b_1_1⁴·b_5_20 + a_2_4·b_2_6²·b_1_1²·b_5_20 + a_2_4·b_2_6²·b_1_1⁷
       + a_2_3·b_1_0¹¹ + a_2_3·b_2_6³·b_5_21 + a_2_3·b_2_5·b_9_50 + a_2_3·b_2_5·b_1_0⁹
       + a_2_3·b_2_5·b_8_43·b_1_0 + a_2_3·b_2_5·b_2_6²·b_5_21
       + a_2_3·b_2_5²·b_1_0²·b_5_19 + a_2_3·b_2_5²·b_2_6·b_5_21 + a_2_3·b_2_5³·b_5_21
       + a_2_3·b_2_5³·b_5_20 + a_2_3·b_2_5³·b_5_19 + a_2_3·b_2_5³·b_1_0⁵
       + a_2_3·b_2_5⁵·b_1_0 + b_2_6·a_10_36·a_1_2 + b_2_6³·a_1_2²·b_5_21
       + a_2_3·b_2_5⁵·a_1_2 + a_2_3²·b_2_6²·b_5_20 + a_2_3²·b_2_5²·b_5_21
       + a_2_3²·b_2_5²·b_5_19 + a_2_3²·b_2_5⁴·a_1_2 + a_2_3³·b_2_5·b_5_21
       + a_2_3³·b_2_5·b_5_19
55. b_8_43·b_5_21 + b_8_43·b_5_20 + b_8_43·b_5_19 + b_2_6·b_1_1²·b_9_51
       + b_2_6²·b_1_1⁴·b_5_20 + b_2_6³·b_1_1²·b_5_20 + b_2_6⁴·b_5_21 + b_2_6⁴·b_5_20
       + b_2_6⁶·b_1_1 + b_2_5·b_8_43·b_1_0³ + b_2_5·b_2_6³·b_5_20 + b_2_5³·b_2_6·b_5_21
       + b_2_5⁴·b_5_21 + b_2_5⁴·b_5_20 + b_2_5⁴·b_5_19 + b_2_5⁵·b_1_0³ + b_2_5⁶·b_1_1
       + b_2_6⁶·a_1_2 + b_2_5⁶·a_1_2 + a_2_4·b_2_6·b_9_51 + a_2_4·b_2_6·b_1_1⁴·b_5_20
       + a_2_4·b_2_6²·b_1_1²·b_5_20 + a_2_4·b_2_6²·b_1_1⁷ + a_2_4·b_2_6³·b_5_20
       + a_2_3·b_2_5·b_2_6²·b_5_21 + a_2_3·b_2_5²·b_1_0²·b_5_19 + a_2_3·b_2_5³·b_5_20
       + a_2_3·b_2_5³·b_5_19 + a_2_3·b_2_5⁵·b_1_0 + b_2_6³·a_1_2²·b_5_21
       + b_2_5·a_10_43·a_1_2 + a_2_3²·b_2_6²·b_5_21 + a_2_3²·b_2_5·b_2_6·b_5_21
       + a_2_3²·b_2_5·b_2_6·b_5_20 + a_2_3²·b_2_5²·b_5_21 + a_2_3²·b_2_5⁴·a_1_2
       + a_2_3³·b_2_5·b_5_21
56. b_1_0⁴·b_9_50 + b_8_43·b_5_21 + b_2_6⁴·b_5_21 + b_2_5·b_1_0²·b_9_50
       + b_2_5·b_8_43·b_1_0³ + b_2_5·b_2_6·b_9_51 + b_2_5·b_2_6·b_9_50
       + b_2_5·b_2_6³·b_5_21 + b_2_5·b_2_6³·b_5_20 + b_2_5²·b_1_0⁹
       + b_2_5²·b_2_6²·b_5_21 + b_2_5³·b_1_0⁷ + b_2_5³·b_2_6·b_5_21
       + b_2_5³·b_2_6·b_5_20 + b_2_5⁴·b_5_20 + b_2_5⁴·b_5_19 + b_2_5⁴·b_1_0⁵
       + b_2_5⁶·b_1_0 + a_2_4·b_2_6³·b_5_20 + a_2_4·b_2_6⁵·b_1_1 + a_2_4·b_2_5³·b_5_19
       + a_2_3·b_1_0¹¹ + a_2_3·b_8_43·b_1_0³ + a_2_3·b_2_5·b_9_50 + a_2_3·b_2_5·b_1_0⁹
       + a_2_3·b_2_5·b_8_43·b_1_0 + a_2_3·b_2_5·b_2_6²·b_5_21 + a_2_3·b_2_5·b_2_6²·b_5_20
       + a_2_3·b_2_5²·b_1_0²·b_5_19 + a_2_3·b_2_5³·b_1_0⁵ + a_2_3·b_2_5⁴·b_1_0³
       + a_2_3·b_2_5⁵·b_1_0 + b_2_6·a_10_43·a_1_2 + a_2_3²·b_2_6²·b_5_21
       + a_2_3²·b_2_6²·b_5_20 + a_2_3²·b_2_5·b_2_6·b_5_21 + a_2_3²·b_2_5·b_2_6·b_5_20
       + a_2_3²·b_2_5²·b_5_21 + a_2_3²·b_2_5²·b_5_20 + a_2_3²·b_2_5²·b_5_19
       + b_2_6⁵·a_1_2³ + a_2_3·b_2_6²·a_1_2²·b_5_21 + a_2_3²·b_2_5⁴·a_1_2
57. b_1_0⁴·b_9_50 + b_8_43·b_5_21 + b_8_43·b_5_20 + b_2_6·b_1_1²·b_9_51
       + b_2_6²·b_1_1⁴·b_5_20 + b_2_6⁴·b_5_21 + b_2_6⁴·b_5_20 + b_2_6⁵·b_1_1³
       + b_2_5·b_1_0²·b_9_50 + b_2_5·b_8_43·b_1_0³ + b_2_5²·b_1_0⁹
       + b_2_5²·b_8_43·b_1_0 + b_2_5²·b_2_6²·b_5_21 + b_2_5²·b_2_6²·b_5_20
       + b_2_5³·b_1_0⁷ + b_2_5³·b_2_6·b_5_21 + b_2_5³·b_2_6·b_5_20 + b_2_5⁴·b_5_20
       + b_2_5⁴·b_5_19 + b_2_5⁴·b_1_0⁵ + b_2_5⁶·b_1_0 + b_2_5⁶·a_1_2 + a_2_4·b_2_6·b_9_51
       + a_2_4·b_2_6·b_1_1⁴·b_5_20 + a_2_4·b_2_6²·b_1_1²·b_5_20 + a_2_4·b_2_6²·b_1_1⁷
       + a_2_4·b_2_5³·b_5_19 + a_2_3·b_1_0¹¹ + a_2_3·b_2_6³·b_5_21 + a_2_3·b_2_6³·b_5_20
       + a_2_3·b_2_5·b_9_50 + a_2_3·b_2_5·b_1_0⁹ + a_2_3·b_2_5·b_8_43·b_1_0
       + a_2_3·b_2_5·b_2_6²·b_5_20 + a_2_3·b_2_5²·b_1_0²·b_5_19
       + a_2_3·b_2_5²·b_2_6·b_5_21 + a_2_3·b_2_5²·b_2_6·b_5_20 + a_2_3·b_2_5³·b_5_21
       + a_2_3·b_2_5³·b_5_19 + a_2_3·b_2_5³·b_1_0⁵ + a_2_3·b_2_5⁵·a_1_2
       + a_2_3²·b_2_6²·b_5_20 + a_2_3²·b_2_5·b_2_6·b_5_20 + a_2_3²·b_2_5²·b_5_21
       + b_2_6⁵·a_1_2³ + a_2_3·a_10_43·a_1_2 + a_2_3³·b_2_6·b_5_21 + a_2_3³·b_2_5·b_5_21
       + a_10_43·a_1_2³
58. b_5_21·b_9_53 + b_5_21·b_9_51 + b_5_20·b_9_53 + b_5_20·b_9_51 + b_5_19·b_9_53
       + b_5_19·b_9_51 + b_1_1⁵·b_9_51 + b_2_6·b_1_1⁷·b_5_20 + b_2_6²·b_1_1·b_9_51
       + b_2_6²·b_1_1⁵·b_5_20 + b_2_6⁵·b_1_1⁴ + b_2_6⁶·b_1_1² + b_2_5·b_1_0³·b_9_50
       + b_2_5·b_2_6²·b_8_43 + b_2_5·b_2_6⁶ + b_2_5²·b_8_43·b_1_0²
       + b_2_5³·b_1_0³·b_5_19 + b_2_5³·b_8_43 + b_2_5⁴·b_1_0·b_5_19 + b_2_5⁵·b_1_0⁴
       + b_2_5⁶·b_1_0² + b_2_5⁷ + b_2_6²·a_1_2·b_9_50 + b_2_6⁴·a_1_2·b_5_21
       + b_2_5²·a_10_36 + a_2_4·b_1_1⁷·b_5_20 + a_2_4·b_2_6·b_1_1⁵·b_5_20
       + a_2_4·b_2_6·b_1_1¹⁰ + a_2_4·b_2_6²·b_1_1³·b_5_20 + a_2_4·b_2_6⁵·b_1_1²
       + a_2_4·b_2_6⁶ + a_2_4·b_2_5⁵·b_2_6 + a_2_3·b_2_5·b_1_0¹⁰
       + a_2_3·b_2_5·b_8_43·b_1_0² + a_2_3·b_2_5·b_2_6·b_8_43
       + a_2_3·b_2_5²·b_1_0³·b_5_19 + a_2_3·b_2_5²·b_1_0⁸ + a_2_3·b_2_5²·b_2_6⁴
       + a_2_3·b_2_5³·b_1_0·b_5_19 + a_2_3·b_2_5³·b_1_0⁶ + a_2_3·b_2_5⁶
       + a_2_3·b_2_6³·a_1_2·b_5_21 + a_2_3·b_2_5³·a_1_2·b_5_21 + a_2_3²·b_2_6⁵
       + a_2_3²·b_2_5·b_8_43 + a_2_3²·b_2_5·b_2_6⁴ + a_2_3²·b_2_5²·b_2_6³
       + a_2_3²·b_2_5⁴·b_2_6 + b_2_6³·a_1_2³·b_5_21 + a_2_3·b_2_6⁵·a_1_2²
       + a_2_3³·b_2_5³·b_2_6 + a_2_3³·b_2_5⁴
59. b_5_21·b_9_53 + b_5_21·b_9_50 + b_5_20·b_9_53 + b_5_20·b_9_51 + b_1_1⁵·b_9_51
       + b_8_43·b_1_0·b_5_19 + b_2_6·b_1_1⁷·b_5_20 + b_2_6²·b_1_1·b_9_51
       + b_2_6⁴·b_1_1·b_5_20 + b_2_6⁴·b_1_1⁶ + b_2_6⁶·b_1_1² + b_2_5·b_1_0³·b_9_50
       + b_2_5·b_8_43·b_1_0⁴ + b_2_5²·b_1_0·b_9_50 + b_2_5²·b_8_43·b_1_0²
       + b_2_5³·b_2_6⁴ + b_2_5⁴·b_1_0·b_5_19 + b_2_5⁴·b_2_6³ + b_2_6²·a_10_36
       + b_2_5⁴·a_1_2·b_5_21 + a_2_4·b_1_1⁷·b_5_20 + a_2_4·b_2_6·b_1_1⁵·b_5_20
       + a_2_4·b_2_6·b_1_1¹⁰ + a_2_4·b_2_6²·b_1_1³·b_5_20 + a_2_4·b_2_6³·b_1_1⁶
       + a_2_4·b_2_5⁵·b_2_6 + a_2_4·b_2_5⁶ + a_2_3·b_2_5·b_1_0·b_9_50
       + a_2_3·b_2_5·b_8_43·b_1_0² + a_2_3·b_2_5·b_2_6⁵ + a_2_3·b_2_5²·b_1_0³·b_5_19
       + a_2_3·b_2_5²·b_8_43 + a_2_3·b_2_5³·b_1_0⁶ + a_2_3·b_2_5⁴·b_2_6²
       + a_2_3·b_2_5⁵·b_1_0² + a_2_3·b_2_5⁵·b_2_6 + b_2_6⁶·a_1_2²
       + a_2_3²·b_2_6·b_8_43 + a_2_3²·b_2_6⁵ + a_2_3²·b_2_5²·b_2_6³
       + b_2_6³·a_1_2³·b_5_21 + a_2_3·b_2_6⁵·a_1_2² + a_2_3³·b_8_43
       + a_2_3³·b_2_5²·b_2_6² + a_2_3³·b_2_5³·b_2_6 + a_2_3³·b_2_5⁴
60. b_5_19·b_9_53 + b_5_19·b_9_50 + b_8_43·b_1_0·b_5_19 + b_2_6²·b_1_1·b_9_51
       + b_2_6⁴·b_1_1·b_5_20 + b_2_6⁴·b_1_1⁶ + b_2_5·b_1_0³·b_9_50 + b_2_5·b_2_6²·b_8_43
       + b_2_5·b_2_6⁶ + b_2_5²·b_8_43·b_1_0² + b_2_5³·b_1_0³·b_5_19 + b_2_5³·b_1_0⁸
       + b_2_5³·b_2_6⁴ + b_2_5⁵·b_1_0⁴ + b_2_5⁶·b_2_6 + b_2_6⁴·a_1_2·b_5_21
       + a_2_4·b_2_6²·b_1_1³·b_5_20 + a_2_4·b_2_6³·b_1_1·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁴
       + a_2_4·b_2_6⁵·b_1_1² + a_2_4·b_2_6⁶ + a_2_4·b_2_5⁵·b_2_6 + a_2_4·b_2_5⁶
       + a_2_3·b_1_0³·b_9_50 + a_2_3·b_8_43·b_1_0⁴ + a_2_3·b_2_6²·b_8_43 + a_2_3·b_2_6⁶
       + a_2_3·b_2_5·b_1_0·b_9_50 + a_2_3·b_2_5·b_1_0¹⁰ + a_2_3·b_2_5·b_2_6·b_8_43
       + a_2_3·b_2_5²·b_1_0³·b_5_19 + a_2_3·b_2_5²·b_8_43 + a_2_3·b_2_5³·b_1_0·b_5_19
       + a_2_3·b_2_5³·b_1_0⁶ + a_2_3·b_2_5⁴·b_2_6² + a_2_3·b_2_5⁵·b_1_0²
       + a_2_3·b_2_6³·a_1_2·b_5_21 + a_2_3²·b_2_6·b_8_43 + a_2_3²·b_2_6⁵
       + a_2_3²·b_2_5·b_8_43 + a_2_3²·b_2_5⁴·b_2_6 + a_2_3²·b_2_5⁵
       + b_2_6·a_10_43·a_1_2² + b_2_6³·a_1_2³·b_5_21 + a_2_3·b_2_6⁵·a_1_2²
       + a_2_3²·b_2_5²·a_1_2·b_5_21 + a_2_3³·b_2_5³·b_2_6 + a_2_3³·b_2_5⁴
61. b_5_21·b_9_53 + b_5_21·b_9_51 + b_5_20·b_9_53 + b_5_20·b_9_51 + b_5_20·b_9_50
       + b_5_19·b_9_50 + b_2_6²·b_1_1·b_9_51 + b_2_6³·b_1_1³·b_5_20 + b_2_6³·b_8_43
       + b_2_6⁵·b_1_1⁴ + b_2_6⁷ + b_2_5²·b_8_43·b_1_0² + b_2_5²·b_2_6·b_8_43
       + b_2_5²·b_2_6⁵ + b_2_5³·b_1_0³·b_5_19 + b_2_5³·b_1_0⁸ + b_2_5⁴·b_1_0⁶
       + b_2_5⁴·b_2_6³ + b_2_5⁵·b_2_6² + b_2_5⁶·b_1_0² + b_2_5⁶·b_2_6 + b_2_5⁷
       + b_2_6²·a_1_2·b_9_50 + b_2_6²·a_10_43 + b_2_5·b_2_6·a_10_36 + b_2_5²·a_10_43
       + b_2_5⁴·a_1_2·b_5_21 + a_2_4·b_1_1³·b_9_51 + a_2_4·b_2_6·b_1_1·b_9_51
       + a_2_4·b_2_6·b_1_1⁵·b_5_20 + a_2_4·b_2_6³·b_1_1·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁴
       + a_2_4·b_2_5⁵·b_2_6 + a_2_4·b_2_5⁶ + a_2_3·b_8_43·b_1_0⁴ + a_2_3·b_2_6²·b_8_43
       + a_2_3·b_2_5·b_1_0·b_9_50 + a_2_3·b_2_5·b_8_43·b_1_0² + a_2_3·b_2_5·b_2_6·b_8_43
       + a_2_3·b_2_5·b_2_6⁵ + a_2_3·b_2_5²·b_1_0⁸ + a_2_3·b_2_5³·b_1_0·b_5_19
       + a_2_3·b_2_5³·b_1_0⁶ + a_2_3·b_2_5³·b_2_6³ + a_2_3·b_2_5⁵·b_2_6
       + b_2_6⁶·a_1_2² + a_2_3·b_2_6³·a_1_2·b_5_21 + a_2_3·b_2_5·a_10_43
       + a_2_3²·b_2_5³·b_2_6² + a_2_3²·b_2_5⁵ + a_2_3·b_2_6⁵·a_1_2²
       + a_2_3²·b_2_5²·a_1_2·b_5_21 + a_2_3³·b_8_43 + a_2_3³·b_2_5²·b_2_6²
62. b_5_21·b_9_53 + b_5_21·b_9_51 + b_5_20·b_9_53 + b_5_20·b_9_51 + b_5_19·b_9_53
       + b_1_1⁵·b_9_51 + b_8_43·b_1_0·b_5_19 + b_2_6·b_1_1⁷·b_5_20 + b_2_6²·b_1_1⁵·b_5_20
       + b_2_6⁵·b_1_1⁴ + b_2_6⁶·b_1_1² + b_2_5·b_1_0³·b_9_50 + b_2_5²·b_1_0·b_9_50
       + b_2_5²·b_2_6·b_8_43 + b_2_5²·b_2_6⁵ + b_2_5³·b_2_6⁴ + b_2_5⁴·b_1_0⁶
       + b_2_5⁴·b_2_6³ + b_2_5⁵·b_1_0⁴ + b_2_5⁵·b_2_6² + b_2_5⁶·b_1_0² + b_2_5⁷
       + b_2_6⁴·a_1_2·b_5_21 + b_2_5·b_2_6·a_10_43 + b_2_5·b_2_6·a_10_36 + b_2_5²·a_10_43
       + b_2_5⁴·a_1_2·b_5_21 + a_2_4·b_1_1⁷·b_5_20 + a_2_4·b_2_6·b_1_1⁵·b_5_20
       + a_2_4·b_2_6·b_1_1¹⁰ + a_2_4·b_2_6²·b_1_1³·b_5_20 + a_2_4·b_2_6⁵·b_1_1²
       + a_2_4·b_2_6⁶ + a_2_3·b_2_5·b_1_0¹⁰ + a_2_3·b_2_5·b_8_43·b_1_0²
       + a_2_3·b_2_5·b_2_6·b_8_43 + a_2_3·b_2_5·b_2_6⁵ + a_2_3·b_2_5²·b_1_0³·b_5_19
       + a_2_3·b_2_5²·b_1_0⁸ + a_2_3·b_2_5²·b_8_43 + a_2_3·b_2_5⁴·b_2_6²
       + a_2_3·b_2_5⁵·b_1_0² + b_2_6⁶·a_1_2² + a_2_3·b_2_6·a_10_43
       + a_2_3·b_2_5³·a_1_2·b_5_21 + a_2_3²·b_2_6⁵ + a_2_3²·b_2_5²·b_2_6³
       + a_2_3²·b_2_5³·b_2_6² + a_2_3²·b_2_5⁴·b_2_6 + a_2_3²·b_2_5⁵
       + a_2_3²·b_2_5²·a_1_2·b_5_21 + a_2_3³·b_8_43 + a_2_3³·b_2_5²·b_2_6²
       + a_2_3³·b_2_5³·b_2_6
63. b_5_20·b_9_53 + b_5_20·b_9_51 + b_1_1⁵·b_9_51 + b_2_6·b_1_1⁷·b_5_20
       + b_2_6²·b_1_1·b_9_51 + b_2_6³·b_8_43 + b_2_6⁴·b_1_1⁶ + b_2_6⁷
       + b_2_5²·b_1_0·b_9_50 + b_2_5²·b_2_6·b_8_43 + b_2_5³·b_1_0³·b_5_19
       + b_2_5³·b_2_6⁴ + b_2_5⁴·b_1_0·b_5_19 + b_2_5⁴·b_2_6³ + b_2_5⁵·b_2_6²
       + b_2_5⁶·b_1_0² + a_2_4·b_1_1⁷·b_5_20 + a_2_4·b_2_6·b_1_1⁵·b_5_20
       + a_2_4·b_2_6·b_1_1¹⁰ + a_2_4·b_2_6³·b_1_1⁶ + a_2_4·b_2_5⁵·b_2_6
       + a_2_3·b_1_0³·b_9_50 + a_2_3·b_2_6²·b_8_43 + a_2_3·b_2_5·b_8_43·b_1_0²
       + a_2_3·b_2_5·b_2_6·b_8_43 + a_2_3·b_2_5²·b_1_0⁸ + a_2_3·b_2_5²·b_8_43
       + a_2_3·b_2_5³·b_2_6³ + a_2_3·b_2_5⁴·b_1_0⁴ + a_2_3·b_2_5⁴·b_2_6²
       + a_2_3·b_2_6³·a_1_2·b_5_21 + a_2_3·b_2_5³·a_1_2·b_5_21 + a_2_3²·b_2_5·b_2_6⁴
       + a_2_3²·b_2_5²·b_2_6³ + a_2_3²·b_2_5³·b_2_6² + a_2_3²·b_2_5⁵
       + a_2_3²·a_10_43 + a_2_3²·b_2_5²·a_1_2·b_5_21 + a_2_3³·b_8_43
       + a_2_3³·b_2_5²·b_2_6² + a_2_3³·b_2_5³·b_2_6
64. b_2_5·b_2_6²·b_9_50 + b_2_5·b_2_6⁴·b_5_21 + b_2_5·b_2_6⁴·b_5_20
       + b_2_5²·b_2_6³·b_5_21 + b_2_5³·b_9_51 + b_2_5³·b_8_43·b_1_0
       + b_2_5³·b_2_6²·b_5_21 + b_2_5³·b_2_6²·b_5_20 + b_2_5⁴·b_2_6·b_5_21
       + b_2_5⁵·b_5_21 + b_2_5⁵·b_1_0⁵ + a_10_43·b_5_20 + a_10_43·b_5_19 + a_10_36·b_5_19
       + b_2_5⁷·a_1_2 + a_2_4·b_2_6⁵·b_1_1³ + a_2_4·b_2_6⁶·b_1_1 + a_2_4·b_2_5⁴·b_5_19
       + a_2_3·b_2_6⁴·b_5_21 + a_2_3·b_2_5·b_1_0²·b_9_50 + a_2_3·b_2_5·b_8_43·b_1_0³
       + a_2_3·b_2_5·b_2_6³·b_5_21 + a_2_3·b_2_5²·b_9_50 + a_2_3·b_2_5²·b_2_6²·b_5_20
       + a_2_3·b_2_5³·b_1_0²·b_5_19 + a_2_3·b_2_5³·b_1_0⁷ + a_2_3·b_2_5⁴·b_5_21
       + a_2_3·b_2_5⁵·b_1_0³ + a_2_3·b_2_5⁶·b_1_0 + b_2_6⁴·a_1_2²·b_5_21
       + a_2_3·b_2_6⁶·a_1_2 + a_2_3·b_2_5⁶·a_1_2 + a_2_3²·b_2_6³·b_5_21
       + a_2_3²·b_2_6³·b_5_20 + a_2_3²·b_2_5·b_2_6²·b_5_21
       + a_2_3²·b_2_5²·b_2_6·b_5_21 + a_2_3²·b_2_5²·b_2_6·b_5_20
       + a_2_3²·b_2_5³·b_5_19 + b_2_6⁶·a_1_2³ + a_2_3·b_2_5·a_10_43·a_1_2
       + a_2_3²·b_2_5⁵·a_1_2 + a_2_3³·b_2_6²·b_5_21 + a_2_3³·b_2_5²·b_5_21
       + b_2_6·a_10_43·a_1_2³
65. b_2_5·b_2_6²·b_9_50 + b_2_5·b_2_6⁴·b_5_21 + b_2_5·b_2_6⁴·b_5_20
       + b_2_5²·b_2_6³·b_5_21 + b_2_5³·b_9_51 + b_2_5³·b_8_43·b_1_0
       + b_2_5³·b_2_6²·b_5_21 + b_2_5³·b_2_6²·b_5_20 + b_2_5⁴·b_2_6·b_5_21
       + b_2_5⁵·b_5_21 + b_2_5⁵·b_1_0⁵ + a_1_2·b_5_21·b_9_50 + a_10_43·b_5_20
       + a_10_43·b_5_19 + a_10_36·b_5_21 + b_2_5⁷·a_1_2 + a_2_4·b_2_6²·b_9_51
       + a_2_4·b_2_6²·b_1_1⁴·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁵ + a_2_4·b_2_6⁵·b_1_1³
       + a_2_4·b_2_6⁶·b_1_1 + a_2_4·b_2_5⁴·b_5_19 + a_2_3·b_2_5·b_2_6³·b_5_20
       + a_2_3·b_2_5²·b_1_0⁹ + a_2_3·b_2_5²·b_8_43·b_1_0 + a_2_3·b_2_5²·b_2_6²·b_5_20
       + a_2_3·b_2_5³·b_1_0²·b_5_19 + a_2_3·b_2_5⁴·b_5_21 + a_2_3·b_2_5⁴·b_5_20
       + a_2_3·b_2_5⁴·b_1_0⁵ + b_2_6²·a_10_43·a_1_2 + b_2_6⁴·a_1_2²·b_5_21
       + b_2_5·b_2_6·a_10_43·a_1_2 + a_2_3²·b_2_5·b_2_6²·b_5_20 + a_2_3²·b_2_5³·b_5_21
       + b_2_6⁶·a_1_2³ + a_2_3·b_2_5·a_10_43·a_1_2 + a_2_3³·b_2_5·b_2_6·b_5_21
       + a_2_3³·b_2_5²·b_5_21 + a_2_3³·b_2_5²·b_5_19
66. b_2_5²·b_2_6·b_9_50 + b_2_5²·b_2_6³·b_5_21 + b_2_5²·b_2_6³·b_5_20
       + b_2_5³·b_9_51 + b_2_5³·b_8_43·b_1_0 + b_2_5³·b_2_6²·b_5_20 + b_2_5⁴·b_2_6·b_5_21
       + b_2_5⁵·b_5_21 + b_2_5⁵·b_1_0⁵ + a_10_43·b_5_19 + a_10_36·b_5_19 + b_2_5⁷·a_1_2
       + a_2_4·b_2_6²·b_9_51 + a_2_4·b_2_6²·b_1_1⁴·b_5_20 + a_2_4·b_2_6⁴·b_5_20
       + a_2_4·b_2_6⁵·b_1_1³ + a_2_4·b_2_5⁴·b_5_19 + a_2_3·b_2_6⁴·b_5_21
       + a_2_3·b_2_5·b_1_0²·b_9_50 + a_2_3·b_2_5·b_8_43·b_1_0³
       + a_2_3·b_2_5·b_2_6³·b_5_20 + a_2_3·b_2_5²·b_8_43·b_1_0
       + a_2_3·b_2_5²·b_2_6²·b_5_21 + a_2_3·b_2_5²·b_2_6²·b_5_20
       + a_2_3·b_2_5³·b_1_0⁷ + a_2_3·b_2_5³·b_2_6·b_5_21 + a_2_3·b_2_5⁴·b_5_21
       + a_2_3·b_2_5⁴·b_5_20 + a_2_3·b_2_5⁶·b_1_0 + b_2_6⁴·a_1_2²·b_5_21
       + b_2_5·b_2_6·a_10_43·a_1_2 + a_2_3²·b_2_6³·b_5_21 + a_2_3²·b_2_5²·b_2_6·b_5_21
       + a_2_3²·b_2_5³·b_5_20 + b_2_6⁶·a_1_2³ + a_2_3·b_2_6·a_10_43·a_1_2
       + a_2_3·b_2_5·a_10_43·a_1_2 + a_2_3³·b_2_6²·b_5_21 + a_2_3³·b_2_5·b_2_6·b_5_21
       + a_2_3³·b_2_5²·b_5_19
67. b_8_43·b_1_0³·b_5_19 + b_8_43² + b_2_6²·b_1_1³·b_9_51 + b_2_6³·b_1_1⁵·b_5_20
       + b_2_6⁴·b_1_1³·b_5_20 + b_2_6⁸ + b_2_5·b_8_43·b_1_0·b_5_19
       + b_2_5⁴·b_1_0³·b_5_19 + b_2_5⁴·b_2_6⁴ + b_2_5⁵·b_1_0·b_5_19 + b_2_5⁵·b_2_6³
       + b_2_5⁷·b_2_6 + b_2_5⁸ + a_2_4·b_2_6²·b_1_1⁵·b_5_20 + a_2_4·b_2_6³·b_1_1⁸
       + a_2_4·b_2_5⁶·b_2_6 + a_2_4·b_2_5⁷ + a_2_3·b_8_43·b_1_0⁶
       + a_2_3·b_2_5·b_1_0³·b_9_50 + a_2_3·b_2_5·b_8_43·b_1_0⁴
       + a_2_3·b_2_5²·b_1_0·b_9_50 + a_2_3·b_2_5²·b_2_6·b_8_43 + a_2_3·b_2_5²·b_2_6⁵
       + a_2_3·b_2_5³·b_1_0³·b_5_19 + a_2_3·b_2_5³·b_1_0⁸ + a_2_3·b_2_5³·b_8_43
       + a_2_3·b_2_5³·b_2_6⁴ + a_2_3·b_2_5⁴·b_1_0·b_5_19 + a_2_3·b_2_5⁴·b_2_6³
       + a_2_3·b_2_5⁵·b_2_6² + a_2_3·b_2_6²·a_10_43 + a_2_3·b_2_6⁴·a_1_2·b_5_21
       + a_2_3·b_2_5²·a_10_43 + a_2_3·b_2_5⁴·a_1_2·b_5_21 + a_2_3²·b_2_6²·b_8_43
       + a_2_3²·b_2_5·b_2_6⁵ + a_2_3²·b_2_5²·b_2_6⁴ + a_2_3²·b_2_5³·b_2_6³
       + a_2_3²·b_2_5⁴·b_2_6² + a_2_3²·b_2_5⁶ + b_2_6²·a_10_43·a_1_2²
       + a_2_3²·b_2_5·a_10_43 + a_2_3²·b_2_5³·a_1_2·b_5_21 + a_2_3³·b_2_5³·b_2_6²
68. b_1_0³·b_5_19·b_9_50 + b_8_43·b_9_53 + b_8_43²·b_1_0 + b_2_6·b_1_1·b_5_20·b_9_51
       + b_2_6·b_1_1⁶·b_9_51 + b_2_6²·b_1_1⁸·b_5_20 + b_2_6³·b_1_1⁶·b_5_20
       + b_2_6⁴·b_9_51 + b_2_6⁴·b_1_1⁴·b_5_20 + b_2_6⁶·b_5_21 + b_2_6⁶·b_5_20
       + b_2_5·b_1_0·b_5_19·b_9_50 + b_2_5·b_8_43·b_1_0²·b_5_19 + b_2_5²·b_8_43·b_1_0⁵
       + b_2_5³·b_8_43·b_1_0³ + b_2_5³·b_2_6³·b_5_20 + b_2_5⁴·b_9_53 + b_2_5⁴·b_9_51
       + b_2_5⁴·b_2_6²·b_5_21 + b_2_5⁴·b_2_6²·b_5_20 + b_2_5⁵·b_1_0²·b_5_19
       + b_2_5⁵·b_2_6·b_5_21 + b_2_5⁵·b_2_6·b_5_20 + b_2_5⁶·b_5_21 + b_2_5⁷·b_1_0³
       + b_2_5⁸·b_1_1 + b_2_6·a_10_43·b_5_21 + b_2_6·a_10_43·b_5_20 + b_2_6·a_10_36·b_5_21
       + b_2_6·a_10_36·b_5_20 + b_2_6⁸·a_1_2 + b_2_5·a_10_43·b_5_21 + b_2_5⁸·a_1_2
       + a_2_4·b_2_6·b_1_1⁸·b_5_20 + a_2_4·b_2_6²·b_1_1⁶·b_5_20 + a_2_4·b_2_6²·b_1_1¹¹
       + a_2_4·b_2_6³·b_1_1⁴·b_5_20 + a_2_4·b_2_6⁵·b_5_20 + a_2_4·b_2_6⁶·b_1_1³
       + a_2_4·b_2_6⁷·b_1_1 + a_2_3·b_8_43·b_1_0⁷ + a_2_3·b_2_6⁵·b_5_20
       + a_2_3·b_2_5·b_2_6⁴·b_5_20 + a_2_3·b_2_5²·b_1_0¹¹ + a_2_3·b_2_5²·b_2_6³·b_5_20
       + a_2_3·b_2_5³·b_1_0⁹ + a_2_3·b_2_5⁴·b_1_0⁷ + a_2_3·b_2_5⁵·b_5_21
       + a_2_3·b_2_5⁵·b_5_19 + a_2_3·b_2_5⁵·b_1_0⁵ + a_2_3·b_2_5⁶·b_1_0³
       + a_2_3·b_2_5⁷·b_1_0 + b_2_6³·a_10_36·a_1_2 + b_2_5³·a_10_43·a_1_2
       + a_2_3·b_2_6⁷·a_1_2 + a_2_3·b_2_5⁷·a_1_2 + a_2_3²·b_2_6⁴·b_5_21
       + a_2_3²·b_2_5·b_2_6³·b_5_20 + a_2_3²·b_2_5²·b_2_6²·b_5_21
       + a_2_3²·b_2_5²·b_2_6²·b_5_20 + a_2_3²·b_2_5³·b_2_6·b_5_21
       + a_2_3²·b_2_5³·b_2_6·b_5_20 + a_2_3²·b_2_5⁴·b_5_21
       + a_2_3³·b_2_5·b_2_6²·b_5_21 + a_2_3³·b_2_5²·b_2_6·b_5_21
       + a_2_3³·b_2_5³·b_5_21 + b_2_6²·a_10_43·a_1_2³
69. b_1_0³·b_5_19·b_9_50 + b_8_43·b_9_50 + b_2_6·b_1_1⁶·b_9_51 + b_2_6²·b_1_1⁸·b_5_20
       + b_2_6⁴·b_9_50 + b_2_6⁴·b_1_1⁴·b_5_20 + b_2_6⁵·b_1_1⁷ + b_2_6⁶·b_1_1⁵
       + b_2_5·b_1_0·b_5_19·b_9_50 + b_2_5³·b_2_6³·b_5_20 + b_2_5⁴·b_9_51 + b_2_5⁴·b_9_50
       + b_2_5⁴·b_8_43·b_1_0 + b_2_5⁶·b_5_21 + b_2_5⁶·b_5_20 + b_2_5⁶·b_1_0⁵
       + b_2_5⁸·b_1_1 + b_2_5⁸·b_1_0 + b_2_6·a_10_43·b_5_21 + b_2_6·a_10_43·b_5_20
       + b_2_6·a_10_36·b_5_21 + b_2_5·a_10_43·b_5_21 + b_2_5⁸·a_1_2
       + a_2_4·b_2_6·b_1_1⁸·b_5_20 + a_2_4·b_2_6²·b_1_1²·b_9_51
       + a_2_4·b_2_6²·b_1_1⁶·b_5_20 + a_2_4·b_2_6²·b_1_1¹¹ + a_2_4·b_2_6³·b_9_51
       + a_2_4·b_2_6³·b_1_1⁴·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁷ + a_2_4·b_2_6⁵·b_5_20
       + a_2_4·b_2_6⁷·b_1_1 + a_2_4·b_2_5⁵·b_5_19 + a_2_3·b_8_43·b_1_0²·b_5_19
       + a_2_3·b_2_6⁵·b_5_21 + a_2_3·b_2_6⁵·b_5_20 + a_2_3·b_2_5·b_8_43·b_5_19
       + a_2_3·b_2_5·b_2_6⁴·b_5_21 + a_2_3·b_2_5²·b_1_0¹¹ + a_2_3·b_2_5³·b_1_0⁹
       + a_2_3·b_2_5³·b_2_6²·b_5_20 + a_2_3·b_2_5⁴·b_1_0²·b_5_19
       + a_2_3·b_2_5⁴·b_2_6·b_5_21 + a_2_3·b_2_5⁴·b_2_6·b_5_20 + a_2_3·b_2_5⁵·b_5_19
       + a_2_3·b_2_5⁵·b_1_0⁵ + a_2_3·b_2_5⁶·b_1_0³ + b_2_6³·a_10_43·a_1_2
       + b_2_6³·a_10_36·a_1_2 + b_2_5³·a_10_43·a_1_2 + a_2_3²·b_2_6⁴·b_5_21
       + a_2_3²·b_2_6⁴·b_5_20 + a_2_3²·b_2_5·b_2_6³·b_5_20
       + a_2_3²·b_2_5²·b_2_6²·b_5_21 + a_2_3²·b_2_5³·b_2_6·b_5_21
       + a_2_3²·b_2_5⁴·b_5_20 + a_2_3·b_2_5·b_2_6·a_10_43·a_1_2
       + a_2_3·b_2_5²·a_10_43·a_1_2 + a_2_3²·b_2_5⁶·a_1_2 + a_2_3³·b_2_5·b_2_6²·b_5_21
       + a_2_3³·b_2_5³·b_5_21
70. b_1_0³·b_5_19·b_9_50 + b_8_43·b_9_53 + b_8_43·b_9_51 + b_2_6·b_1_1⁶·b_9_51
       + b_2_6²·b_1_1⁸·b_5_20 + b_2_6³·b_1_1²·b_9_51 + b_2_6³·b_1_1⁶·b_5_20
       + b_2_6⁴·b_1_1⁴·b_5_20 + b_2_6⁶·b_5_21 + b_2_6⁶·b_5_20 + b_2_5·b_1_0·b_5_19·b_9_50
       + b_2_5·b_8_43·b_1_0²·b_5_19 + b_2_5²·b_8_43·b_5_19 + b_2_5³·b_2_6³·b_5_21
       + b_2_5⁴·b_9_53 + b_2_5⁴·b_9_51 + b_2_5⁴·b_8_43·b_1_0 + b_2_5⁴·b_2_6²·b_5_21
       + b_2_5⁵·b_1_0²·b_5_19 + b_2_5⁵·b_2_6·b_5_21 + b_2_5⁵·b_2_6·b_5_20 + b_2_5⁶·b_5_19
       + b_2_5⁸·b_1_0 + b_2_6⁸·a_1_2 + b_2_5·a_10_36·b_5_19 + b_2_5⁸·a_1_2
       + a_2_4·b_2_6·b_1_1⁴·b_9_51 + a_2_4·b_2_6·b_1_1⁸·b_5_20 + a_2_4·b_2_6²·b_1_1¹¹
       + a_2_4·b_2_6³·b_9_51 + a_2_4·b_2_6⁵·b_1_1⁵ + a_2_4·b_2_6⁶·b_1_1³
       + a_2_4·b_2_5⁵·b_5_19 + a_2_3·b_8_43·b_1_0⁷ + a_2_3·b_2_5·b_2_6⁴·b_5_21
       + a_2_3·b_2_5²·b_1_0¹¹ + a_2_3·b_2_5²·b_2_6³·b_5_21 + a_2_3·b_2_5³·b_9_50
       + a_2_3·b_2_5³·b_1_0⁹ + a_2_3·b_2_5⁴·b_1_0²·b_5_19 + a_2_3·b_2_5⁴·b_2_6·b_5_21
       + a_2_3·b_2_5⁵·b_5_20 + a_2_3·b_2_5⁶·b_1_0³ + a_2_3·b_2_5⁷·b_1_0
       + a_2_3·a_10_43·b_5_20 + a_2_3·a_10_43·b_5_19 + a_2_3²·b_2_5²·b_2_6²·b_5_20
       + a_2_3²·b_2_5³·b_2_6·b_5_21 + a_2_3²·b_2_5⁴·b_5_20 + a_2_3²·b_2_5⁴·b_5_19
       + b_2_6⁷·a_1_2³ + a_2_3·b_2_6²·a_10_43·a_1_2 + a_2_3·b_2_5·b_2_6·a_10_43·a_1_2
       + a_2_3³·b_2_5³·b_5_19
71. b_9_53² + b_9_51² + b_9_50·b_9_53 + b_9_50·b_9_51 + b_2_6²·b_5_21·b_9_50
       + b_2_6²·b_1_1⁵·b_9_51 + b_2_6²·b_1_1⁹·b_5_20 + b_2_6³·b_1_1⁷·b_5_20
       + b_2_6⁴·b_1_1·b_9_51 + b_2_6⁴·b_1_1⁵·b_5_20 + b_2_6⁴·b_1_1¹⁰ + b_2_6⁵·b_1_1⁸
       + b_2_6⁵·b_8_43 + b_2_6⁶·b_1_1⁶ + b_2_6⁹ + b_2_5·b_1_0²·b_5_19·b_9_50
       + b_2_5·b_2_6·b_5_21·b_9_50 + b_2_5²·b_5_19·b_9_50 + b_2_5²·b_8_43·b_1_0·b_5_19
       + b_2_5³·b_1_0³·b_9_50 + b_2_5⁴·b_2_6·b_8_43 + b_2_5⁴·b_2_6⁵
       + b_2_5⁵·b_1_0³·b_5_19 + b_2_5⁵·b_1_0⁸ + b_2_5⁶·b_1_0⁶ + b_2_5⁷·b_1_0⁴
       + b_2_5⁷·b_2_6² + b_2_5⁸·b_1_0² + b_2_5⁹ + b_8_43·a_10_43 + b_8_43·a_10_36
       + b_2_6⁴·a_1_2·b_9_50 + b_2_6⁴·a_10_36 + b_2_6⁶·a_1_2·b_5_21 + b_2_5⁴·a_10_43
       + b_2_5⁶·a_1_2·b_5_21 + a_2_4·b_1_1⁷·b_9_51 + a_2_4·b_2_6·b_5_20·b_9_51
       + a_2_4·b_2_6·b_1_1⁹·b_5_20 + a_2_4·b_2_6²·b_1_1³·b_9_51
       + a_2_4·b_2_6³·b_1_1·b_9_51 + a_2_4·b_2_6⁴·b_1_1⁸ + a_2_4·b_2_6⁵·b_1_1⁶
       + a_2_4·b_2_6⁷·b_1_1² + a_2_4·b_2_5⁸ + a_2_3·b_1_0²·b_5_19·b_9_50
       + a_2_3·b_8_43² + a_2_3·b_2_6⁴·b_8_43 + a_2_3·b_2_5·b_5_19·b_9_50
       + a_2_3·b_2_5·b_8_43·b_1_0·b_5_19 + a_2_3·b_2_5·b_8_43·b_1_0⁶
       + a_2_3·b_2_5·b_2_6³·b_8_43 + a_2_3·b_2_5·b_2_6⁷ + a_2_3·b_2_5²·b_1_0³·b_9_50
       + a_2_3·b_2_5²·b_1_0¹² + a_2_3·b_2_5³·b_1_0¹⁰ + a_2_3·b_2_5³·b_2_6·b_8_43
       + a_2_3·b_2_5³·b_2_6⁵ + a_2_3·b_2_5⁴·b_1_0³·b_5_19 + a_2_3·b_2_5⁴·b_1_0⁸
       + a_2_3·b_2_5⁵·b_1_0⁶ + a_2_3·b_2_5⁵·b_2_6³ + a_2_3·b_2_5⁶·b_2_6²
       + a_2_3·b_2_5⁷·b_1_0² + a_2_3·b_2_5⁸ + b_2_6·a_10_36·a_1_2·b_5_21
       + a_2_3·b_2_5·b_2_6²·a_10_43 + a_2_3·b_2_5²·b_2_6·a_10_43 + a_2_3·b_2_5³·a_10_43
       + a_2_3²·b_2_6³·b_8_43 + a_2_3²·b_2_6⁷ + a_2_3²·b_2_5·b_2_6²·b_8_43
       + a_2_3²·b_2_5·b_2_6⁶ + a_2_3²·b_2_5²·b_2_6·b_8_43 + a_2_3²·b_2_5³·b_8_43
       + a_2_3²·b_2_5⁴·b_2_6³ + a_2_3²·b_2_5⁷ + b_2_6⁵·a_1_2³·b_5_21
       + a_2_3·a_10_43·a_1_2·b_5_21 + a_2_3²·b_2_5·b_2_6·a_10_43 + a_2_3²·b_2_5²·a_10_43
       + a_2_3²·b_2_5⁴·a_1_2·b_5_21 + a_2_3³·b_2_5²·b_8_43 + a_2_3³·b_2_5⁴·b_2_6²
       + a_2_3³·b_2_5⁵·b_2_6
72. b_8_43·a_10_36 + b_2_6⁴·a_10_36 + b_2_5³·b_2_6·a_10_36 + b_2_5⁴·a_10_36
       + a_2_4·b_2_6·b_5_20·b_9_51 + a_2_4·b_2_6·b_1_1⁵·b_9_51
       + a_2_4·b_2_6²·b_1_1⁷·b_5_20 + a_2_4·b_2_6³·b_1_1·b_9_51
       + a_2_4·b_2_6³·b_1_1⁵·b_5_20 + a_2_3·b_1_0²·b_5_19·b_9_50 + a_2_3·b_8_43²
       + a_2_3·b_2_6⁸ + a_2_3·b_2_5·b_5_19·b_9_50 + a_2_3·b_2_5·b_8_43·b_1_0⁶
       + a_2_3·b_2_5²·b_2_6²·b_8_43 + a_2_3·b_2_5²·b_2_6⁶
       + a_2_3·b_2_5³·b_8_43·b_1_0² + a_2_3·b_2_5³·b_2_6·b_8_43 + a_2_3·b_2_5³·b_2_6⁵
       + a_2_3·b_2_5⁴·b_1_0³·b_5_19 + a_2_3·b_2_5⁵·b_1_0·b_5_19 + a_2_3·b_2_5⁵·b_1_0⁶
       + a_2_3·b_2_5⁶·b_2_6² + a_2_3·b_2_5⁷·b_1_0² + a_2_3·b_2_5⁸
       + b_2_6·a_10_43·a_1_2·b_5_21 + b_2_5·a_10_43·a_1_2·b_5_21
       + a_2_3²·b_2_5·b_2_6²·b_8_43 + a_2_3²·b_2_5²·b_2_6⁵ + a_2_3²·b_2_5³·b_8_43
       + a_2_3²·b_2_5⁶·b_2_6 + b_2_6³·a_10_43·a_1_2² + b_2_6⁵·a_1_2³·b_5_21
       + a_2_3·a_10_43·a_1_2·b_5_21 + a_2_3²·b_2_5·b_2_6·a_10_43 + a_2_3²·b_2_5²·a_10_43
       + a_2_3³·b_2_5⁴·b_2_6² + a_2_3³·b_2_5⁵·b_2_6 + a_2_3³·b_2_5⁶
73. b_9_50·b_9_53 + b_9_50² + b_1_1⁴·b_5_20·b_9_51 + b_8_43·b_1_0·b_9_50
       + b_2_6²·b_5_21·b_9_50 + b_2_6²·b_1_1⁵·b_9_51 + b_2_6²·b_1_1⁹·b_5_20
       + b_2_6³·b_1_1³·b_9_51 + b_2_6³·b_1_1⁷·b_5_20 + b_2_6⁴·b_1_1⁵·b_5_20
       + b_2_6⁵·b_1_1³·b_5_20 + b_2_6⁵·b_1_1⁸ + b_2_6⁵·b_8_43 + b_2_6⁶·b_1_1·b_5_20
       + b_2_6⁶·b_1_1⁶ + b_2_6⁸·b_1_1² + b_2_6⁹ + b_2_5·b_1_0²·b_5_19·b_9_50
       + b_2_5·b_2_6⁴·b_8_43 + b_2_5·b_2_6⁸ + b_2_5²·b_8_43·b_1_0·b_5_19
       + b_2_5²·b_2_6³·b_8_43 + b_2_5²·b_2_6⁷ + b_2_5³·b_2_6²·b_8_43 + b_2_5³·b_2_6⁶
       + b_2_5⁴·b_1_0¹⁰ + b_2_5⁴·b_8_43·b_1_0² + b_2_5⁵·b_1_0⁸ + b_2_5⁶·b_1_0·b_5_19
       + b_2_5⁶·b_1_0⁶ + b_2_6⁴·a_1_2·b_9_50 + b_2_6⁴·a_10_43 + b_2_5·b_2_6³·a_10_43
       + b_2_5²·b_2_6²·a_10_43 + b_2_5³·b_2_6·a_10_43 + a_2_4·b_1_1²·b_5_20·b_9_51
       + a_2_4·b_1_1⁷·b_9_51 + a_2_4·b_2_6·b_5_20·b_9_51 + a_2_4·b_2_6·b_1_1⁹·b_5_20
       + a_2_4·b_2_6²·b_1_1³·b_9_51 + a_2_4·b_2_6²·b_1_1⁷·b_5_20
       + a_2_4·b_2_6⁴·b_1_1³·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁸ + a_2_4·b_2_6⁵·b_1_1⁶
       + a_2_4·b_2_6⁶·b_1_1⁴ + a_2_4·b_2_5⁷·b_2_6 + a_2_4·b_2_5⁸
       + a_2_3·b_1_0²·b_5_19·b_9_50 + a_2_3·b_8_43² + a_2_3·b_2_5·b_5_19·b_9_50
       + a_2_3·b_2_5·b_2_6³·b_8_43 + a_2_3·b_2_5²·b_1_0³·b_9_50
       + a_2_3·b_2_5²·b_8_43·b_1_0⁴ + a_2_3·b_2_5²·b_2_6⁶ + a_2_3·b_2_5³·b_1_0·b_9_50
       + a_2_3·b_2_5³·b_1_0¹⁰ + a_2_3·b_2_5⁴·b_2_6⁴ + a_2_3·b_2_5⁵·b_1_0·b_5_19
       + a_2_3·b_2_5⁵·b_2_6³ + a_2_3·b_2_5⁶·b_2_6² + a_2_3·b_2_5⁷·b_1_0²
       + b_2_6·a_10_43·a_1_2·b_5_21 + b_2_6·a_10_36·a_1_2·b_5_21
       + b_2_5·a_10_43·a_1_2·b_5_21 + a_2_3·b_2_6⁵·a_1_2·b_5_21 + a_2_3²·b_2_5·b_2_6⁶
       + a_2_3²·b_2_5²·b_2_6·b_8_43 + a_2_3²·b_2_5²·b_2_6⁵ + a_2_3²·b_2_5⁴·b_2_6³
       + a_2_3²·b_2_5⁶·b_2_6 + a_2_3²·b_2_5⁷ + b_2_6⁵·a_1_2³·b_5_21
       + a_2_3·b_2_6⁷·a_1_2² + a_2_3²·b_2_5·b_2_6·a_10_43 + a_2_3²·b_2_5²·a_10_43
       + a_2_3³·b_2_5²·b_8_43 + a_2_3³·b_2_5⁴·b_2_6² + a_2_3³·b_2_5⁵·b_2_6
       + a_2_3³·b_2_5⁶
74. b_9_51·b_9_53 + b_9_51² + b_9_50·b_9_53 + b_9_50² + b_2_6²·b_5_20·b_9_51
       + b_2_6²·b_1_1⁹·b_5_20 + b_2_6³·b_1_1⁷·b_5_20 + b_2_6⁴·b_1_1⁵·b_5_20
       + b_2_6⁵·b_1_1³·b_5_20 + b_2_6⁵·b_1_1⁸ + b_2_6⁵·b_8_43 + b_2_6⁶·b_1_1·b_5_20
       + b_2_6⁶·b_1_1⁶ + b_2_6⁸·b_1_1² + b_2_6⁹ + b_2_5·b_1_0²·b_5_19·b_9_50
       + b_2_5·b_8_43² + b_2_5·b_2_6·b_5_21·b_9_50 + b_2_5·b_2_6⁸ + b_2_5²·b_5_19·b_9_50
       + b_2_5²·b_2_6³·b_8_43 + b_2_5²·b_2_6⁷ + b_2_5³·b_1_0³·b_9_50
       + b_2_5³·b_8_43·b_1_0⁴ + b_2_5³·b_2_6²·b_8_43 + b_2_5⁴·b_2_6⁵
       + b_2_5⁵·b_1_0³·b_5_19 + b_2_5⁵·b_1_0⁸ + b_2_5⁵·b_2_6⁴ + b_2_5⁶·b_2_6³
       + b_2_5⁷·b_1_0⁴ + b_2_5⁷·b_2_6² + b_2_5⁸·b_2_6 + b_8_43·a_10_43
       + b_2_6⁴·a_1_2·b_9_50 + b_2_6⁴·a_10_36 + b_2_5²·b_2_6²·a_10_43
       + b_2_5³·b_2_6·a_10_43 + b_2_5³·b_2_6·a_10_36 + b_2_5⁴·a_10_43 + b_2_5⁴·a_10_36
       + b_2_5⁶·a_1_2·b_5_21 + a_2_4·b_1_1²·b_5_20·b_9_51 + a_2_4·b_1_1⁷·b_9_51
       + a_2_4·b_2_6·b_5_20·b_9_51 + a_2_4·b_2_6·b_1_1⁵·b_9_51 + a_2_4·b_2_6·b_1_1⁹·b_5_20
       + a_2_4·b_2_6²·b_1_1⁷·b_5_20 + a_2_4·b_2_6³·b_1_1·b_9_51
       + a_2_4·b_2_6³·b_1_1⁵·b_5_20 + a_2_4·b_2_6⁴·b_1_1³·b_5_20
       + a_2_4·b_2_6⁴·b_1_1⁸ + a_2_4·b_2_6⁶·b_1_1⁴ + a_2_4·b_2_5⁸
       + a_2_3·b_8_43·b_1_0⁸ + a_2_3·b_8_43² + a_2_3·b_2_6⁴·b_8_43 + a_2_3·b_2_6⁸
       + a_2_3·b_2_5·b_8_43·b_1_0·b_5_19 + a_2_3·b_2_5·b_8_43·b_1_0⁶
       + a_2_3·b_2_5·b_2_6³·b_8_43 + a_2_3·b_2_5·b_2_6⁷ + a_2_3·b_2_5²·b_1_0³·b_9_50
       + a_2_3·b_2_5²·b_2_6²·b_8_43 + a_2_3·b_2_5³·b_1_0·b_9_50 + a_2_3·b_2_5³·b_1_0¹⁰
       + a_2_3·b_2_5⁴·b_1_0³·b_5_19 + a_2_3·b_2_5⁴·b_2_6⁴ + a_2_3·b_2_5⁵·b_1_0·b_5_19
       + a_2_3·b_2_5⁵·b_2_6³ + a_2_3·b_2_5⁶·b_1_0⁴ + a_2_3·b_2_5⁷·b_1_0²
       + a_2_3·b_2_5⁷·b_2_6 + a_2_3·b_2_5⁸ + b_2_6⁸·a_1_2² + a_2_3·b_2_6³·a_10_43
       + a_2_3·b_2_5³·a_10_43 + a_2_3²·b_2_6⁷ + a_2_3²·b_2_5·b_2_6²·b_8_43
       + a_2_3²·b_2_5·b_2_6⁶ + a_2_3²·b_2_5²·b_2_6·b_8_43 + a_2_3²·b_2_5²·b_2_6⁵
       + a_2_3²·b_2_5³·b_8_43 + a_2_3²·b_2_5⁴·b_2_6³ + a_2_3²·b_2_5⁶·b_2_6
       + a_2_3·b_2_6⁷·a_1_2² + a_2_3²·b_2_5²·a_10_43 + a_2_3²·b_2_5⁴·a_1_2·b_5_21
       + a_2_3³·b_2_5²·b_8_43
75. b_9_51·b_9_53 + b_9_51² + b_1_1⁴·b_5_20·b_9_51 + b_8_43·b_1_0·b_9_50
       + b_2_6²·b_5_21·b_9_50 + b_2_6²·b_5_20·b_9_51 + b_2_6²·b_1_1⁵·b_9_51
       + b_2_6³·b_1_1³·b_9_51 + b_2_5·b_8_43² + b_2_5·b_2_6⁸ + b_2_5²·b_5_21·b_9_50
       + b_2_5²·b_8_43·b_1_0·b_5_19 + b_2_5²·b_2_6³·b_8_43 + b_2_5²·b_2_6⁷
       + b_2_5³·b_8_43·b_1_0⁴ + b_2_5³·b_2_6²·b_8_43 + b_2_5⁴·b_1_0·b_9_50
       + b_2_5⁴·b_1_0¹⁰ + b_2_5⁴·b_8_43·b_1_0² + b_2_5⁴·b_2_6·b_8_43 + b_2_5⁴·b_2_6⁵
       + b_2_5⁵·b_1_0³·b_5_19 + b_2_5⁶·b_1_0·b_5_19 + b_2_5⁶·b_1_0⁶ + b_2_5⁶·b_2_6³
       + b_2_5⁷·b_1_0⁴ + b_2_6⁴·a_10_36 + b_2_5²·b_2_6²·a_10_43 + b_2_5³·b_2_6·a_10_43
       + b_2_5⁶·a_1_2·b_5_21 + a_2_4·b_2_6·b_1_1⁵·b_9_51 + a_2_4·b_2_6²·b_1_1³·b_9_51
       + a_2_4·b_2_6⁶·b_1_1⁴ + a_2_4·b_2_6⁷·b_1_1² + a_2_4·b_2_5⁸
       + a_2_3·b_8_43·b_1_0⁸ + a_2_3·b_8_43² + a_2_3·b_2_6⁴·b_8_43
       + a_2_3·b_2_5·b_8_43·b_1_0⁶ + a_2_3·b_2_5·b_2_6³·b_8_43 + a_2_3·b_2_5·b_2_6⁷
       + a_2_3·b_2_5²·b_1_0³·b_9_50 + a_2_3·b_2_5²·b_8_43·b_1_0⁴
       + a_2_3·b_2_5²·b_2_6²·b_8_43 + a_2_3·b_2_5³·b_8_43·b_1_0²
       + a_2_3·b_2_5³·b_2_6⁵ + a_2_3·b_2_5⁴·b_2_6⁴ + a_2_3·b_2_5⁵·b_1_0⁶
       + a_2_3·b_2_5⁶·b_1_0⁴ + a_2_3·b_2_5⁸ + b_2_6⁸·a_1_2²
       + b_2_5·a_10_43·a_1_2·b_5_21 + a_2_3·b_2_6⁵·a_1_2·b_5_21
       + a_2_3·b_2_5²·b_2_6·a_10_43 + a_2_3·b_2_5³·a_10_43 + a_2_3²·b_2_6³·b_8_43
       + a_2_3²·b_2_5·b_2_6⁶ + a_2_3²·b_2_5²·b_2_6⁵ + a_2_3²·b_2_5³·b_8_43
       + a_2_3²·b_2_5³·b_2_6⁴ + a_2_3²·b_2_5⁵·b_2_6² + a_2_3²·b_2_5⁶·b_2_6
       + a_2_3²·b_2_5⁷ + b_2_6⁵·a_1_2³·b_5_21 + a_2_3·b_2_6⁷·a_1_2²
       + a_2_3²·b_2_6²·a_10_43 + a_2_3²·b_2_5⁴·a_1_2·b_5_21 + a_2_3³·b_2_5⁵·b_2_6
76. b_9_50·b_9_53 + b_9_50·b_9_51 + b_1_1⁹·b_9_51 + b_8_43·b_1_0¹⁰ + b_8_43²·b_1_0²
       + b_2_6·b_1_1¹¹·b_5_20 + b_2_6²·b_5_21·b_9_50 + b_2_6²·b_1_1⁵·b_9_51
       + b_2_6³·b_1_1⁷·b_5_20 + b_2_6⁴·b_1_1⁵·b_5_20 + b_2_6⁴·b_1_1¹⁰
       + b_2_6⁵·b_1_1³·b_5_20 + b_2_6⁵·b_1_1⁸ + b_2_6⁵·b_8_43 + b_2_6⁶·b_1_1·b_5_20
       + b_2_6⁸·b_1_1² + b_2_6⁹ + b_2_5·b_8_43² + b_2_5·b_2_6·b_5_21·b_9_50
       + b_2_5·b_2_6⁸ + b_2_5²·b_5_19·b_9_50 + b_2_5²·b_8_43·b_1_0⁶
       + b_2_5⁴·b_1_0·b_9_50 + b_2_5⁴·b_2_6·b_8_43 + b_2_5⁵·b_1_0³·b_5_19
       + b_2_5⁵·b_1_0⁸ + b_2_5⁶·b_1_0⁶ + b_2_5⁶·b_2_6³ + b_2_5⁷·b_1_0⁴
       + b_2_5⁷·b_2_6² + b_2_5⁸·b_1_0² + b_2_5⁹ + b_8_43·a_10_43 + b_8_43·a_10_36
       + b_2_6⁴·a_10_36 + b_2_5⁴·a_10_43 + a_2_4·b_1_1⁷·b_9_51 + a_2_4·b_1_1¹¹·b_5_20
       + a_2_4·b_2_6·b_5_20·b_9_51 + a_2_4·b_2_6·b_1_1⁹·b_5_20 + a_2_4·b_2_6·b_1_1¹⁴
       + a_2_4·b_2_6²·b_1_1³·b_9_51 + a_2_4·b_2_6³·b_1_1·b_9_51
       + a_2_4·b_2_6⁴·b_1_1³·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁸ + a_2_4·b_2_6⁷·b_1_1²
       + a_2_4·b_2_5⁷·b_2_6 + a_2_4·b_2_5⁸ + a_2_3·b_8_43·b_1_0⁸ + a_2_3·b_2_6⁸
       + a_2_3·b_2_5·b_5_19·b_9_50 + a_2_3·b_2_5·b_1_0¹⁴ + a_2_3·b_2_5·b_8_43·b_1_0⁶
       + a_2_3·b_2_5·b_2_6³·b_8_43 + a_2_3·b_2_5·b_2_6⁷ + a_2_3·b_2_5²·b_1_0³·b_9_50
       + a_2_3·b_2_5²·b_1_0¹² + a_2_3·b_2_5²·b_8_43·b_1_0⁴ + a_2_3·b_2_5³·b_1_0¹⁰
       + a_2_3·b_2_5³·b_8_43·b_1_0² + a_2_3·b_2_5³·b_2_6⁵ + a_2_3·b_2_5⁴·b_8_43
       + a_2_3·b_2_5⁴·b_2_6⁴ + a_2_3·b_2_5⁵·b_1_0·b_5_19 + a_2_3·b_2_5⁵·b_1_0⁶
       + a_2_3·b_2_5⁵·b_2_6³ + a_2_3·b_2_5⁶·b_1_0⁴ + a_2_3·b_2_5⁶·b_2_6²
       + b_2_6·a_10_36·a_1_2·b_5_21 + a_2_3·b_2_5²·b_2_6·a_10_43 + a_2_3·b_2_5³·a_10_43
       + a_2_3·b_2_5⁵·a_1_2·b_5_21 + a_2_3²·b_2_6³·b_8_43 + a_2_3²·b_2_5·b_2_6⁶
       + a_2_3²·b_2_5²·b_2_6·b_8_43 + a_2_3²·b_2_5²·b_2_6⁵ + a_2_3²·b_2_5³·b_2_6⁴
       + a_2_3²·b_2_5⁷ + a_2_3·a_10_43·a_1_2·b_5_21 + a_2_3·b_2_6⁷·a_1_2²
       + a_2_3²·b_2_5·b_2_6·a_10_43 + a_2_3³·b_2_5⁴·b_2_6² + a_2_3³·b_2_5⁵·b_2_6
       + a_2_3³·b_2_5⁶ + c_16_141·b_1_0²
77. b_9_53² + b_9_50² + b_1_1⁹·b_9_51 + b_1_1¹³·b_5_20 + b_8_43²·b_1_0²
       + b_2_6·b_1_1²·b_5_20·b_9_51 + b_2_6·b_1_1¹¹·b_5_20 + b_2_6³·b_1_1⁷·b_5_20
       + b_2_6³·b_1_1¹² + b_2_6⁴·b_1_1·b_9_51 + b_2_6⁶·b_1_1·b_5_20 + b_2_6⁷·b_1_1⁴
       + b_2_6⁸·b_1_1² + b_2_5²·b_8_43·b_1_0·b_5_19 + b_2_5³·b_1_0³·b_9_50
       + b_2_5⁴·b_1_0¹⁰ + b_2_5⁴·b_2_6⁵ + b_2_5⁵·b_1_0³·b_5_19 + b_2_5⁵·b_1_0⁸
       + b_2_5⁶·b_1_0·b_5_19 + b_2_5⁶·b_1_0⁶ + b_2_5⁷·b_1_0⁴ + b_2_5⁷·b_2_6²
       + b_2_5⁸·b_1_0² + b_2_6⁴·a_1_2·b_9_50 + b_2_6⁶·a_1_2·b_5_21 + a_2_4·b_1_1⁷·b_9_51
       + a_2_4·b_1_1¹¹·b_5_20 + a_2_4·b_2_6·b_1_1⁵·b_9_51 + a_2_4·b_2_6·b_1_1⁹·b_5_20
       + a_2_4·b_2_6·b_1_1¹⁴ + a_2_4·b_2_6²·b_1_1³·b_9_51 + a_2_4·b_2_6³·b_1_1·b_9_51
       + a_2_4·b_2_6⁴·b_1_1³·b_5_20 + a_2_4·b_2_6⁶·b_1_1⁴ + a_2_4·b_2_5⁷·b_2_6
       + a_2_4·b_2_5⁸ + a_2_3·b_2_6⁴·b_8_43 + a_2_3·b_2_5²·b_8_43·b_1_0⁴
       + a_2_3·b_2_5³·b_1_0·b_9_50 + a_2_3·b_2_5³·b_1_0¹⁰
       + a_2_3·b_2_5³·b_8_43·b_1_0² + a_2_3·b_2_5³·b_2_6⁵ + a_2_3·b_2_5⁴·b_2_6⁴
       + a_2_3·b_2_5⁶·b_1_0⁴ + a_2_3·b_2_5⁷·b_2_6 + a_2_3·b_2_5⁸ + b_2_6⁸·a_1_2²
       + a_2_3·b_2_5⁵·a_1_2·b_5_21 + a_2_3²·b_2_6³·b_8_43 + a_2_3²·b_2_5·b_2_6²·b_8_43
       + a_2_3²·b_2_5·b_2_6⁶ + a_2_3²·b_2_5²·b_2_6·b_8_43 + a_2_3²·b_2_5²·b_2_6⁵
       + a_2_3²·b_2_5³·b_8_43 + a_2_3²·b_2_5³·b_2_6⁴ + a_2_3²·b_2_5⁴·b_2_6³
       + a_2_3²·b_2_5⁵·b_2_6² + a_2_3²·b_2_5⁶·b_2_6 + b_2_6⁵·a_1_2³·b_5_21
       + a_2_3·b_2_6⁷·a_1_2² + a_2_3³·b_2_5²·b_8_43 + a_2_3³·b_2_5⁶
       + c_16_141·b_1_1²
78. b_9_53² + b_9_51² + b_9_50² + b_2_6⁴·b_1_1·b_9_51 + b_2_6⁴·b_1_1¹⁰
       + b_2_6⁵·b_1_1³·b_5_20 + b_2_6⁶·b_1_1·b_5_20 + b_2_6⁸·b_1_1²
       + b_2_5²·b_8_43·b_1_0·b_5_19 + b_2_5³·b_1_0³·b_9_50 + b_2_5³·b_2_6⁶
       + b_2_5⁴·b_1_0·b_9_50 + b_2_5⁵·b_1_0³·b_5_19 + b_2_5⁵·b_1_0⁸ + b_2_5⁵·b_2_6⁴
       + b_2_5⁶·b_1_0⁶ + b_2_5⁶·b_2_6³ + b_2_5⁷·b_1_0⁴ + b_2_5⁷·b_2_6²
       + b_2_5⁸·b_1_0² + b_2_5⁸·b_2_6 + b_2_5⁹ + b_2_6⁴·a_1_2·b_9_50
       + b_2_6⁶·a_1_2·b_5_21 + b_2_5⁶·a_1_2·b_5_21 + a_2_4·b_2_6⁴·b_1_1³·b_5_20
       + a_2_4·b_2_6⁵·b_1_1⁶ + a_2_4·b_2_5⁷·b_2_6 + a_2_3·b_2_6⁴·b_8_43
       + a_2_3·b_2_5·b_2_6³·b_8_43 + a_2_3·b_2_5·b_2_6⁷ + a_2_3·b_2_5²·b_8_43·b_1_0⁴
       + a_2_3·b_2_5²·b_2_6²·b_8_43 + a_2_3·b_2_5²·b_2_6⁶ + a_2_3·b_2_5³·b_1_0·b_9_50
       + a_2_3·b_2_5³·b_1_0¹⁰ + a_2_3·b_2_5³·b_8_43·b_1_0²
       + a_2_3·b_2_5⁴·b_1_0³·b_5_19 + a_2_3·b_2_5⁴·b_1_0⁸ + a_2_3·b_2_5⁵·b_1_0·b_5_19
       + a_2_3·b_2_5⁵·b_2_6³ + a_2_3·b_2_5⁸ + b_2_6·a_10_36·a_1_2·b_5_21
       + b_2_6⁸·a_1_2² + a_2_3·b_2_5³·a_10_43 + a_2_3²·b_2_5²·b_2_6·b_8_43
       + a_2_3²·b_2_5⁴·b_2_6³ + a_2_3²·b_2_5⁵·b_2_6² + a_2_3²·b_2_5⁷
       + a_2_3·b_2_6⁷·a_1_2² + a_2_3²·b_2_5²·a_10_43 + a_2_3²·b_2_5⁴·a_1_2·b_5_21
       + a_2_3³·b_2_5²·b_8_43 + a_2_3³·b_2_5⁴·b_2_6² + a_2_3³·b_2_5⁶
       + c_16_141·a_1_2²
79. a_10_43·b_9_51 + a_10_43·b_9_50 + a_10_36·b_9_53 + a_10_36·b_9_51
       + b_2_6²·a_10_36·b_5_21 + b_2_5²·a_10_43·b_5_21 + b_2_5²·a_10_36·b_5_19
       + a_2_4·b_1_1³·b_5_20·b_9_51 + a_2_4·b_1_1⁸·b_9_51 + a_2_4·b_2_6·b_1_1¹⁰·b_5_20
       + a_2_4·b_2_6⁴·b_1_1⁴·b_5_20 + a_2_4·b_2_6⁵·b_1_1²·b_5_20
       + a_2_4·b_2_6⁶·b_1_1⁵ + a_2_3·b_8_43·b_9_50 + a_2_3·b_8_43²·b_1_0
       + a_2_3·b_2_6⁶·b_5_21 + a_2_3·b_2_5·b_8_43·b_1_0²·b_5_19
       + a_2_3·b_2_5·b_2_6⁵·b_5_21 + a_2_3·b_2_5·b_2_6⁵·b_5_20
       + a_2_3·b_2_5²·b_2_6⁴·b_5_20 + a_2_3·b_2_5³·b_1_0¹¹
       + a_2_3·b_2_5³·b_2_6³·b_5_20 + a_2_3·b_2_5⁴·b_1_0⁹ + a_2_3·b_2_5⁴·b_8_43·b_1_0
       + a_2_3·b_2_5⁴·b_2_6²·b_5_21 + a_2_3·b_2_5⁴·b_2_6²·b_5_20
       + a_2_3·b_2_5⁵·b_1_0⁷ + a_2_3·b_2_5⁵·b_2_6·b_5_20 + a_2_3·b_2_5⁷·b_1_0³
       + a_2_3·b_2_5⁸·b_1_0 + b_2_6⁴·a_10_43·a_1_2 + b_2_6⁶·a_1_2²·b_5_21
       + b_2_5⁴·a_10_43·a_1_2 + a_2_3²·b_2_5·b_2_6⁴·b_5_20 + a_2_3²·b_2_5⁴·b_2_6·b_5_20
       + a_2_3²·b_2_5⁵·b_5_21 + a_2_3²·b_2_5⁵·b_5_20 + b_2_6·a_10_43·a_1_2²·b_5_21
       + b_2_6⁸·a_1_2³ + a_2_3·b_2_6³·a_10_43·a_1_2 + a_2_3·b_2_5³·a_10_43·a_1_2
       + a_2_3²·a_10_43·b_5_19 + a_2_3²·b_2_5⁷·a_1_2 + a_2_3³·b_2_5³·b_2_6·b_5_21
       + a_2_3³·b_2_5⁴·b_5_21 + b_2_6³·a_10_43·a_1_2³
80. a_10_43·b_9_53 + a_10_43·b_9_50 + b_2_6²·a_10_43·b_5_21 + b_2_6²·a_10_43·b_5_20
       + b_2_6²·a_10_36·b_5_20 + b_2_5²·a_10_43·b_5_20 + a_2_4·b_2_6³·b_1_1²·b_9_51
       + a_2_4·b_2_6³·b_1_1⁶·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁴·b_5_20
       + a_2_4·b_2_6⁴·b_1_1⁹ + a_2_4·b_2_6⁵·b_1_1⁷ + a_2_4·b_2_6⁶·b_1_1⁵
       + a_2_3·b_8_43·b_9_50 + a_2_3·b_8_43²·b_1_0 + a_2_3·b_2_6⁶·b_5_21
       + a_2_3·b_2_5·b_1_0·b_5_19·b_9_50 + a_2_3·b_2_5·b_2_6⁵·b_5_21
       + a_2_3·b_2_5·b_2_6⁵·b_5_20 + a_2_3·b_2_5²·b_8_43·b_1_0⁵
       + a_2_3·b_2_5²·b_2_6⁴·b_5_21 + a_2_3·b_2_5³·b_1_0²·b_9_50
       + a_2_3·b_2_5³·b_8_43·b_1_0³ + a_2_3·b_2_5³·b_2_6³·b_5_21
       + a_2_3·b_2_5³·b_2_6³·b_5_20 + a_2_3·b_2_5⁴·b_9_50 + a_2_3·b_2_5⁴·b_1_0⁹
       + a_2_3·b_2_5⁴·b_2_6²·b_5_21 + a_2_3·b_2_5⁵·b_1_0⁷ + a_2_3·b_2_5⁵·b_2_6·b_5_21
       + a_2_3·b_2_5⁶·b_5_20 + a_2_3·b_2_5⁶·b_1_0⁵ + b_2_6⁴·a_10_36·a_1_2
       + b_2_6⁶·a_1_2²·b_5_21 + b_2_5⁴·a_10_43·a_1_2 + a_2_3·b_2_5⁸·a_1_2
       + a_2_3²·b_2_5²·b_2_6³·b_5_21 + a_2_3²·b_2_5³·b_2_6²·b_5_21
       + a_2_3²·b_2_5³·b_2_6²·b_5_20 + a_2_3²·b_2_5⁵·b_5_21 + a_2_3²·b_2_5⁵·b_5_19
       + b_2_6·a_10_43·a_1_2²·b_5_21 + b_2_6⁸·a_1_2³ + a_2_3·b_2_6³·a_10_43·a_1_2
       + a_2_3·b_2_5³·a_10_43·a_1_2 + a_2_3²·a_10_43·b_5_21 + a_2_3²·a_10_43·b_5_20
       + a_2_3³·b_2_5²·b_2_6²·b_5_21 + a_2_3³·b_2_5⁴·b_5_21 + a_2_3³·b_2_5⁴·b_5_19
       + b_2_6³·a_10_43·a_1_2³
81. a_10_36·b_9_53 + a_10_36·b_9_51 + a_10_36·b_9_50 + b_2_6²·a_10_36·b_5_20
       + b_2_5²·a_10_36·b_5_19 + a_2_4·b_2_6²·b_1_1⁴·b_9_51
       + a_2_4·b_2_6²·b_1_1⁸·b_5_20 + a_2_4·b_2_6⁴·b_1_1⁹ + a_2_3·b_2_6⁶·b_5_20
       + a_2_3·b_2_5·b_1_0·b_5_19·b_9_50 + a_2_3·b_2_5·b_8_43·b_1_0²·b_5_19
       + a_2_3·b_2_5·b_2_6⁵·b_5_21 + a_2_3·b_2_5·b_2_6⁵·b_5_20
       + a_2_3·b_2_5²·b_8_43·b_1_0⁵ + a_2_3·b_2_5²·b_2_6⁴·b_5_21
       + a_2_3·b_2_5²·b_2_6⁴·b_5_20 + a_2_3·b_2_5³·b_8_43·b_1_0³
       + a_2_3·b_2_5³·b_2_6³·b_5_20 + a_2_3·b_2_5⁴·b_9_50 + a_2_3·b_2_5⁴·b_8_43·b_1_0
       + a_2_3·b_2_5⁴·b_2_6²·b_5_20 + a_2_3·b_2_5⁵·b_1_0⁷ + a_2_3·b_2_5⁵·b_2_6·b_5_20
       + a_2_3·b_2_5⁶·b_1_0⁵ + b_2_6⁴·a_10_36·a_1_2 + b_2_6⁶·a_1_2²·b_5_21
       + a_2_3·b_2_6·a_10_43·b_5_21 + a_2_3·b_2_6⁸·a_1_2 + a_2_3·b_2_5·a_10_43·b_5_20
       + a_2_3·b_2_5·a_10_43·b_5_19 + a_2_3·b_2_5⁸·a_1_2 + a_2_3²·b_2_6⁵·b_5_21
       + a_2_3²·b_2_5·b_2_6⁴·b_5_21 + a_2_3²·b_2_5²·b_2_6³·b_5_20
       + a_2_3²·b_2_5³·b_2_6²·b_5_20 + a_2_3²·b_2_5⁴·b_2_6·b_5_21
       + a_2_3²·b_2_5⁵·b_5_21 + a_2_3²·b_2_5⁵·b_5_20 + a_2_3²·b_2_5⁵·b_5_19
       + b_2_6⁸·a_1_2³ + a_2_3·b_2_6³·a_10_43·a_1_2 + a_2_3²·a_10_43·b_5_21
       + a_2_3²·a_10_43·b_5_19 + a_2_3²·b_2_5⁷·a_1_2 + a_2_3³·b_2_5²·b_2_6²·b_5_21
       + a_2_3³·b_2_5³·b_2_6·b_5_21 + b_2_6³·a_10_43·a_1_2³ + c_16_141·a_1_2³
82. a_10_36·b_9_53 + a_10_36·b_9_51 + b_2_6²·a_10_36·b_5_21 + b_2_6²·a_10_36·b_5_20
       + b_2_5²·a_10_36·b_5_19 + a_2_4·b_1_1³·b_5_20·b_9_51 + a_2_4·b_1_1⁸·b_9_51
       + a_2_4·b_2_6·b_1_1¹⁰·b_5_20 + a_2_4·b_2_6²·b_1_1⁴·b_9_51
       + a_2_4·b_2_6²·b_1_1⁸·b_5_20 + a_2_4·b_2_6³·b_1_1²·b_9_51
       + a_2_4·b_2_6³·b_1_1⁶·b_5_20 + a_2_4·b_2_6⁵·b_1_1⁷ + a_2_3·b_8_43·b_9_50
       + a_2_3·b_8_43·b_1_0⁹ + a_2_3·b_8_43²·b_1_0 + a_2_3·b_2_6⁶·b_5_21
       + a_2_3·b_2_6⁶·b_5_20 + a_2_3·b_2_5·b_8_43·b_1_0²·b_5_19
       + a_2_3·b_2_5·b_2_6⁵·b_5_21 + a_2_3·b_2_5²·b_2_6⁴·b_5_21
       + a_2_3·b_2_5²·b_2_6⁴·b_5_20 + a_2_3·b_2_5³·b_1_0¹¹
       + a_2_3·b_2_5³·b_2_6³·b_5_21 + a_2_3·b_2_5³·b_2_6³·b_5_20 + a_2_3·b_2_5⁴·b_9_50
       + a_2_3·b_2_5⁴·b_2_6²·b_5_20 + a_2_3·b_2_5⁵·b_1_0²·b_5_19
       + a_2_3·b_2_5⁵·b_2_6·b_5_21 + a_2_3·b_2_5⁵·b_2_6·b_5_20 + a_2_3·b_2_5⁶·b_1_0⁵
       + a_2_3·b_2_5⁷·b_1_0³ + a_2_3·b_2_5⁸·b_1_0 + b_2_6⁴·a_10_43·a_1_2
       + b_2_6⁶·a_1_2²·b_5_21 + b_2_5⁴·a_10_43·a_1_2 + a_2_3·b_2_6·a_10_43·b_5_21
       + a_2_3·b_2_6·a_10_43·b_5_20 + a_2_3·b_2_6⁸·a_1_2 + a_2_3·b_2_5·a_10_43·b_5_20
       + a_2_3·b_2_5·a_10_43·b_5_19 + a_2_3²·b_2_6⁵·b_5_20
       + a_2_3²·b_2_5²·b_2_6³·b_5_20 + a_2_3²·b_2_5⁴·b_2_6·b_5_21
       + a_2_3²·b_2_5⁴·b_2_6·b_5_20 + a_2_3²·b_2_5⁵·b_5_21 + a_2_3²·b_2_5⁵·b_5_19
       + b_2_6·a_10_43·a_1_2²·b_5_21 + a_2_3·b_2_5³·a_10_43·a_1_2 + a_2_3²·a_10_43·b_5_21
       + a_2_3²·a_10_43·b_5_20 + a_2_3²·a_10_43·b_5_19 + a_2_3²·b_2_5⁷·a_1_2
       + a_2_3³·b_2_5³·b_2_6·b_5_21 + a_2_3³·b_2_5⁴·b_5_19 + a_2_3·c_16_141·b_1_0
83. a_10_43·b_9_50 + a_10_36·b_9_50 + b_2_6²·a_10_43·b_5_21 + b_2_6²·a_10_43·b_5_20
       + b_2_5·b_2_6·a_10_43·b_5_21 + a_2_4·b_1_1³·b_5_20·b_9_51 + a_2_4·b_1_1⁸·b_9_51
       + a_2_4·b_2_6·b_1_1¹⁰·b_5_20 + a_2_4·b_2_6²·b_1_1⁴·b_9_51
       + a_2_4·b_2_6²·b_1_1⁸·b_5_20 + a_2_4·b_2_6³·b_1_1²·b_9_51
       + a_2_4·b_2_6³·b_1_1⁶·b_5_20 + a_2_4·b_2_6⁴·b_9_51 + a_2_4·b_2_6⁴·b_1_1⁹
       + a_2_4·b_2_6⁵·b_1_1²·b_5_20 + a_2_4·b_2_6⁶·b_5_20 + a_2_4·b_2_6⁸·b_1_1
       + a_2_3·b_2_6⁶·b_5_20 + a_2_3·b_2_5·b_1_0·b_5_19·b_9_50
       + a_2_3·b_2_5·b_8_43·b_1_0²·b_5_19 + a_2_3·b_2_5·b_2_6⁵·b_5_21
       + a_2_3·b_2_5·b_2_6⁵·b_5_20 + a_2_3·b_2_5²·b_8_43·b_5_19
       + a_2_3·b_2_5²·b_2_6⁴·b_5_21 + a_2_3·b_2_5²·b_2_6⁴·b_5_20
       + a_2_3·b_2_5³·b_1_0²·b_9_50 + a_2_3·b_2_5³·b_1_0¹¹
       + a_2_3·b_2_5³·b_8_43·b_1_0³ + a_2_3·b_2_5³·b_2_6³·b_5_21
       + a_2_3·b_2_5³·b_2_6³·b_5_20 + a_2_3·b_2_5⁴·b_9_50 + a_2_3·b_2_5⁴·b_8_43·b_1_0
       + a_2_3·b_2_5⁴·b_2_6²·b_5_21 + a_2_3·b_2_5⁵·b_1_0²·b_5_19 + a_2_3·b_2_5⁶·b_5_21
       + a_2_3·b_2_5⁶·b_5_20 + a_2_3·b_2_5⁶·b_1_0⁵ + a_2_3·b_2_5⁷·b_1_0³
       + a_2_3·b_2_6·a_10_43·b_5_20 + a_2_3·b_2_6⁸·a_1_2 + a_2_3·b_2_5·a_10_43·b_5_21
       + a_2_3·b_2_5·a_10_43·b_5_20 + a_2_3·b_2_5·a_10_43·b_5_19 + a_2_3·b_2_5⁸·a_1_2
       + a_2_3²·b_2_6⁵·b_5_21 + a_2_3²·b_2_5³·b_2_6²·b_5_21
       + a_2_3²·b_2_5³·b_2_6²·b_5_20 + a_2_3²·b_2_5⁴·b_2_6·b_5_21
       + a_2_3²·b_2_5⁴·b_2_6·b_5_20 + a_2_3²·b_2_5⁵·b_5_19
       + b_2_6·a_10_43·a_1_2²·b_5_21 + a_2_3²·a_10_43·b_5_21 + a_2_3²·a_10_43·b_5_20
       + a_2_3³·b_2_5²·b_2_6²·b_5_21 + a_2_3³·b_2_5³·b_2_6·b_5_21
       + a_2_3·c_16_141·a_1_2
84. a_10_36·b_9_53 + a_10_36·b_9_50 + b_2_6²·a_10_36·b_5_21 + b_2_6²·a_10_36·b_5_20
       + a_2_4·b_1_1³·b_5_20·b_9_51 + a_2_4·b_1_1⁸·b_9_51 + a_2_4·b_1_1¹²·b_5_20
       + a_2_4·b_2_6·b_1_1·b_5_20·b_9_51 + a_2_4·b_2_6·b_1_1¹⁰·b_5_20
       + a_2_4·b_2_6²·b_1_1⁸·b_5_20 + a_2_4·b_2_6³·b_1_1⁶·b_5_20
       + a_2_4·b_2_6³·b_1_1¹¹ + a_2_4·b_2_6⁵·b_1_1²·b_5_20 + a_2_4·b_2_6⁷·b_1_1³
       + a_2_3·b_8_43·b_9_50 + a_2_3·b_8_43²·b_1_0 + a_2_3·b_2_6⁶·b_5_21
       + a_2_3·b_2_6⁶·b_5_20 + a_2_3·b_2_5·b_1_0·b_5_19·b_9_50
       + a_2_3·b_2_5·b_8_43·b_1_0²·b_5_19 + a_2_3·b_2_5·b_8_43·b_1_0⁷
       + a_2_3·b_2_5·b_2_6⁵·b_5_21 + a_2_3·b_2_5²·b_8_43·b_5_19
       + a_2_3·b_2_5²·b_2_6⁴·b_5_20 + a_2_3·b_2_5³·b_1_0¹¹
       + a_2_3·b_2_5³·b_8_43·b_1_0³ + a_2_3·b_2_5³·b_2_6³·b_5_20
       + a_2_3·b_2_5⁴·b_8_43·b_1_0 + a_2_3·b_2_5⁴·b_2_6²·b_5_20
       + a_2_3·b_2_5⁵·b_2_6·b_5_21 + a_2_3·b_2_5⁵·b_2_6·b_5_20 + a_2_3·b_2_5⁶·b_5_21
       + a_2_3·b_2_5⁶·b_1_0⁵ + a_2_3·b_2_5⁸·b_1_0 + b_2_6⁴·a_10_43·a_1_2
       + b_2_6⁴·a_10_36·a_1_2 + b_2_6⁶·a_1_2²·b_5_21 + a_2_3·b_2_6·a_10_43·b_5_21
       + a_2_3·b_2_6·a_10_43·b_5_20 + a_2_3·b_2_6⁸·a_1_2 + a_2_3·b_2_5·a_10_43·b_5_21
       + a_2_3·b_2_5·a_10_43·b_5_20 + a_2_3·b_2_5⁸·a_1_2 + a_2_3²·b_2_6⁵·b_5_21
       + a_2_3²·b_2_6⁵·b_5_20 + a_2_3²·b_2_5²·b_2_6³·b_5_21
       + a_2_3²·b_2_5²·b_2_6³·b_5_20 + a_2_3²·b_2_5⁴·b_2_6·b_5_20
       + a_2_3³·b_2_5³·b_2_6·b_5_21 + a_2_3³·b_2_5⁴·b_5_21 + a_2_3³·b_2_5⁴·b_5_19
       + a_2_4·c_16_141·b_1_1
85. a_10_36² + a_2_3²·b_2_6⁸ + a_2_3²·b_2_5²·b_2_6⁶ + a_2_3²·b_2_5⁴·b_2_6⁴
       + a_2_3²·b_2_5⁶·b_2_6² + a_2_3²·b_2_5⁷·b_2_6 + b_2_6⁶·a_1_2³·b_5_21
       + a_2_3·b_2_6⁸·a_1_2² + a_2_3³·b_2_5³·b_8_43 + a_2_3³·b_2_5⁷
86. a_10_36·a_10_43 + b_2_5²·a_10_43·a_1_2·b_5_21 + a_2_3·b_2_6⁴·a_10_43
       + a_2_3·b_2_5·b_2_6³·a_10_43 + a_2_3·b_2_5⁴·a_10_43 + b_2_6⁶·a_1_2³·b_5_21
       + a_2_3·b_2_6⁸·a_1_2² + a_2_3²·b_2_5·b_2_6²·a_10_43 + a_2_3²·b_2_5³·a_10_43
       + a_2_3²·b_2_5⁵·a_1_2·b_5_21 + a_2_3³·b_2_5³·b_8_43 + a_2_3³·b_2_5⁶·b_2_6
       + a_2_3·c_16_141·a_1_2²
87. a_10_43² + a_2_3·b_2_6⁴·a_10_43 + a_2_3·b_2_6⁶·a_1_2·b_5_21
       + a_2_3·b_2_5²·b_2_6²·a_10_43 + a_2_3·b_2_5⁶·a_1_2·b_5_21 + a_2_3²·b_2_6⁸
       + a_2_3²·b_2_5·b_2_6³·b_8_43 + a_2_3²·b_2_5²·b_2_6²·b_8_43
       + a_2_3²·b_2_5²·b_2_6⁶ + a_2_3²·b_2_5⁴·b_8_43 + a_2_3²·b_2_5⁴·b_2_6⁴
       + a_2_3²·b_2_5⁶·b_2_6² + b_2_6⁴·a_10_43·a_1_2²
       + a_2_3·b_2_6·a_10_43·a_1_2·b_5_21 + a_2_3²·b_2_5·b_2_6²·a_10_43
       + a_2_3²·b_2_5⁵·a_1_2·b_5_21 + a_2_3³·b_2_5³·b_8_43 + a_2_3³·b_2_5⁵·b_2_6²
       + a_2_3³·b_2_5⁷ + a_2_3²·c_16_141

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_141, a Duflot regular element of degree 16
  2. b_1_1⁴ + b_1_0⁴ + b_2_6² + b_2_5·b_2_6 + b_2_5², an element of degree 4
  3. b_2_6²·b_1_1² + b_2_5·b_2_6² + b_2_5²·b_1_0² + b_2_5²·b_2_6, an element of degree 6
• The Raw Filter Degree Type of that HSOP is [-1, 12, 15, 23].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].
• We found that there exists some filter regular HSOP formed by the first term of the above HSOP, together with 2 elements of degree 2.

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_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. a_2_3 → 0, an element of degree 2
5. a_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. b_5_21 → 0, an element of degree 5
11. b_8_43 → 0, an element of degree 8
12. b_9_50 → 0, an element of degree 9
13. b_9_51 → 0, an element of degree 9
14. b_9_53 → 0, an element of degree 9
15. a_10_36 → 0, an element of degree 10
16. a_10_43 → 0, an element of degree 10
17. c_16_141 → c_1_0¹⁶, an element of degree 16

Restriction map to a maximal el. ab. subgp. of rank 3

1. a_1_2 → 0, an element of degree 1
2. b_1_0 → c_1_1, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. a_2_3 → 0, an element of degree 2
5. a_2_4 → 0, an element of degree 2
6. b_2_5 → c_1_2² + c_1_1·c_1_2, an element of degree 2
7. b_2_6 → 0, an element of degree 2
8. b_5_19 → c_1_2⁵ + c_1_1·c_1_2⁴ + c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0²·c_1_1³
      + c_1_0⁴·c_1_1, an element of degree 5
9. b_5_20 → c_1_1·c_1_2⁴ + c_1_1³·c_1_2², an element of degree 5
10. b_5_21 → c_1_2⁵ + c_1_1²·c_1_2³ + c_1_0²·c_1_1³ + c_1_0⁴·c_1_1, an element of degree 5
11. b_8_43 → c_1_2⁸ + c_1_1·c_1_2⁷ + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2⁴ + c_1_1⁶·c_1_2²
       + c_1_1⁷·c_1_2 + c_1_0²·c_1_1⁴·c_1_2² + c_1_0²·c_1_1⁵·c_1_2 + c_1_0²·c_1_1⁶
       + c_1_0⁴·c_1_1²·c_1_2² + c_1_0⁴·c_1_1³·c_1_2 + c_1_0⁴·c_1_1⁴, an element of degree 8
12. b_9_50 → c_1_1·c_1_2⁸ + c_1_1³·c_1_2⁶ + c_1_1⁴·c_1_2⁵ + 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
13. b_9_51 → c_1_2⁹ + c_1_1·c_1_2⁸ + c_1_1²·c_1_2⁷ + c_1_1⁸·c_1_2 + c_1_0²·c_1_1³·c_1_2⁴
       + c_1_0²·c_1_1⁶·c_1_2 + c_1_0²·c_1_1⁷ + c_1_0⁴·c_1_1·c_1_2⁴
       + c_1_0⁴·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1⁵, an element of degree 9
14. b_9_53 → c_1_1⁴·c_1_2⁵ + c_1_1⁶·c_1_2³ + 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_0²·c_1_1⁷
       + c_1_0⁴·c_1_1·c_1_2⁴ + c_1_0⁴·c_1_1³·c_1_2² + c_1_0⁸·c_1_1, an element of degree 9
15. a_10_36 → 0, an element of degree 10
16. a_10_43 → 0, an element of degree 10
17. c_16_141 → c_1_1·c_1_2¹⁵ + c_1_1⁸·c_1_2⁸ + c_1_1¹¹·c_1_2⁵ + c_1_1¹⁵·c_1_2
       + c_1_0²·c_1_1³·c_1_2¹¹ + c_1_0²·c_1_1⁵·c_1_2⁹ + c_1_0²·c_1_1⁷·c_1_2⁷
       + c_1_0²·c_1_1⁸·c_1_2⁶ + c_1_0²·c_1_1¹¹·c_1_2³ + c_1_0²·c_1_1¹³·c_1_2
       + c_1_0²·c_1_1¹⁴ + c_1_0⁴·c_1_1·c_1_2¹¹ + c_1_0⁴·c_1_1³·c_1_2⁹
       + c_1_0⁴·c_1_1⁴·c_1_2⁸ + c_1_0⁴·c_1_1⁶·c_1_2⁶ + c_1_0⁴·c_1_1⁸·c_1_2⁴
       + c_1_0⁴·c_1_1¹⁰·c_1_2² + c_1_0⁶·c_1_1⁸·c_1_2² + c_1_0⁶·c_1_1⁹·c_1_2
       + c_1_0⁸·c_1_2⁸ + c_1_0⁸·c_1_1·c_1_2⁷ + c_1_0⁸·c_1_1⁴·c_1_2⁴
       + c_1_0⁸·c_1_1⁵·c_1_2³ + c_1_0¹⁰·c_1_1⁴·c_1_2² + c_1_0¹⁰·c_1_1⁵·c_1_2
       + c_1_0¹²·c_1_1²·c_1_2² + c_1_0¹²·c_1_1³·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_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → c_1_1, an element of degree 1
4. a_2_3 → 0, an element of degree 2
5. a_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_1³·c_1_2², an element of degree 5
9. b_5_20 → c_1_0²·c_1_1³ + c_1_0⁴·c_1_1, an element of degree 5
10. b_5_21 → 0, an element of degree 5
11. b_8_43 → c_1_2⁸ + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2⁵ + c_1_1⁵·c_1_2³
       + c_1_0²·c_1_1⁴·c_1_2² + c_1_0²·c_1_1⁵·c_1_2 + c_1_0⁴·c_1_1²·c_1_2²
       + c_1_0⁴·c_1_1³·c_1_2, an element of degree 8
12. b_9_50 → 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_1⁷ + c_1_0⁴·c_1_1⁵, an element of degree 9
13. b_9_51 → c_1_1·c_1_2⁸ + c_1_1⁵·c_1_2⁴ + c_1_0²·c_1_1³·c_1_2⁴ + c_1_0²·c_1_1⁶·c_1_2
       + c_1_0⁴·c_1_1·c_1_2⁴ + c_1_0⁴·c_1_1⁴·c_1_2 + c_1_0⁴·c_1_1⁵ + c_1_0⁸·c_1_1, an element of degree 9
14. b_9_53 → c_1_1·c_1_2⁸ + 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_0²·c_1_1⁵·c_1_2²
       + c_1_0²·c_1_1⁶·c_1_2 + c_1_0²·c_1_1⁷ + c_1_0⁴·c_1_1³·c_1_2²
       + c_1_0⁴·c_1_1⁴·c_1_2 + c_1_0⁸·c_1_1, an element of degree 9
15. a_10_36 → 0, an element of degree 10
16. a_10_43 → 0, an element of degree 10
17. c_16_141 → c_1_2¹⁶ + c_1_1²·c_1_2¹⁴ + c_1_1³·c_1_2¹³ + c_1_1⁴·c_1_2¹²
       + c_1_1⁵·c_1_2¹¹ + c_1_1⁶·c_1_2¹⁰ + c_1_1⁷·c_1_2⁹ + c_1_1⁹·c_1_2⁷
       + c_1_1¹⁰·c_1_2⁶ + 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_0²·c_1_1¹⁴ + c_1_0⁴·c_1_1⁴·c_1_2⁸
       + c_1_0⁴·c_1_1¹⁰·c_1_2² + c_1_0⁶·c_1_1⁸·c_1_2² + c_1_0⁶·c_1_1⁹·c_1_2
       + c_1_0⁸·c_1_2⁸ + c_1_0⁸·c_1_1²·c_1_2⁶ + c_1_0⁸·c_1_1³·c_1_2⁵
       + c_1_0⁸·c_1_1⁵·c_1_2³ + c_1_0⁸·c_1_1⁶·c_1_2² + c_1_0⁸·c_1_1⁷·c_1_2
       + c_1_0¹⁰·c_1_1⁴·c_1_2² + c_1_0¹⁰·c_1_1⁵·c_1_2 + c_1_0¹²·c_1_1²·c_1_2²
       + c_1_0¹²·c_1_1³·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_2 → 0, an element of degree 1
2. b_1_0 → 0, an element of degree 1
3. b_1_1 → 0, an element of degree 1
4. a_2_3 → 0, an element of degree 2
5. a_2_4 → 0, an element of degree 2
6. b_2_5 → c_1_2², an element of degree 2
7. b_2_6 → c_1_1², an element of degree 2
8. b_5_19 → c_1_2⁵ + c_1_1²·c_1_2³, 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. b_5_21 → c_1_2⁵ + c_1_1·c_1_2⁴ + c_1_1²·c_1_2³ + c_1_1⁴·c_1_2, an element of degree 5
11. b_8_43 → c_1_2⁸ + c_1_1·c_1_2⁷ + c_1_1³·c_1_2⁵ + c_1_1⁴·c_1_2⁴ + c_1_1⁸, an element of degree 8
12. b_9_50 → c_1_1²·c_1_2⁷ + c_1_1³·c_1_2⁶ + c_1_1⁵·c_1_2⁴ + c_1_1⁶·c_1_2³, an element of degree 9
13. b_9_51 → c_1_2⁹ + c_1_1·c_1_2⁸ + c_1_1³·c_1_2⁶ + c_1_1⁴·c_1_2⁵ + c_1_1⁵·c_1_2⁴
       + c_1_1⁶·c_1_2³, an element of degree 9
14. b_9_53 → c_1_1³·c_1_2⁶ + c_1_1⁶·c_1_2³, an element of degree 9
15. a_10_36 → 0, an element of degree 10
16. a_10_43 → 0, an element of degree 10
17. c_16_141 → 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_1¹¹·c_1_2⁵ + 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

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128