David J. Green

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Cohomology of group number 1932 of order 128

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

General information on the group

• The group has 4 minimal generators and exponent 8.
• It is non-abelian.
• It has p-Rank 4.
• Its center has rank 2.
• It has 3 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3 and 4, respectively.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 2.
• The depth coincides with the Duflot bound.
• The Poincaré series is

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

  (t  −  1)4 · (t2  +  1)2 · (t4  +  1)

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

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring generators

The cohomology ring has 14 minimal generators of maximal degree 8:

1. a_1_0, a nilpotent element of degree 1
2. b_1_1, an element of degree 1
3. b_1_2, an element of degree 1
4. b_1_3, an element of degree 1
5. a_3_10, a nilpotent element of degree 3
6. b_3_11, an element of degree 3
7. b_3_12, an element of degree 3
8. c_4_19, a Duflot regular element of degree 4
9. b_5_27, an element of degree 5
10. b_5_28, an element of degree 5
11. b_5_29, an element of degree 5
12. b_7_53, an element of degree 7
13. b_7_54, an element of degree 7
14. c_8_71, a Duflot regular element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 53 minimal relations of maximal degree 14:

1. a_1_0·b_1_2
2. b_1_1·b_1_2 + a_1_0·b_1_3 + a_1_0·b_1_1
3. a_1_0·b_1_3² + a_1_0·b_1_1·b_1_3
4. b_1_1·b_1_3² + b_1_1²·b_1_3 + a_1_0³
5. b_1_2·a_3_10
6. a_1_0·b_3_11
7. b_1_1·b_3_11 + b_1_3·a_3_10 + b_1_1·a_3_10
8. b_1_3·a_3_10 + b_1_1·a_3_10 + a_1_0·b_3_12
9. a_1_0³·b_1_1²
10. b_1_1·b_1_3·b_3_12 + a_1_0²·a_3_10
11. a_3_10·b_3_11
12. b_3_11² + b_1_2·b_1_3²·b_3_11 + b_1_2²·b_1_3·b_3_12 + b_1_2³·b_3_12
       + c_4_19·b_1_2²
13. a_3_10² + a_1_0·b_1_1²·a_3_10 + a_1_0²·b_1_1⁴ + a_1_0²·b_1_1·a_3_10
       + c_4_19·a_1_0²
14. a_3_10·b_3_12 + a_1_0³·a_3_10 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_1
15. b_3_11² + b_1_2·b_5_27 + b_1_2·b_1_3²·b_3_12 + b_1_2·b_1_3²·b_3_11
       + b_1_2²·b_1_3·b_3_12 + b_1_2³·b_3_12 + b_1_2³·b_3_11 + a_3_10·b_3_12
       + a_1_0·b_1_1⁴·b_1_3 + a_1_0·b_1_1⁵
16. b_3_12² + b_1_3³·b_3_12 + b_1_3³·b_3_11 + b_1_2·b_5_28 + b_1_2·b_1_3²·b_3_11
       + b_1_2²·b_1_3·b_3_12 + b_1_2²·b_1_3·b_3_11 + b_1_2³·b_3_11 + a_3_10·b_3_12
       + a_1_0²·b_1_1·a_3_10 + a_1_0³·a_3_10 + c_4_19·b_1_3² + c_4_19·b_1_1²
17. a_1_0·b_5_28 + a_1_0·b_5_27 + a_1_0·b_1_1²·b_3_12 + a_1_0·b_1_1⁴·b_1_3
       + a_1_0·b_1_1⁵
18. b_1_3·b_5_27 + b_1_3³·b_3_12 + b_1_2²·b_1_3·b_3_11 + b_1_1·b_5_28 + b_1_1³·b_3_12
       + a_3_10·b_3_12 + a_1_0·b_1_1²·b_3_12 + a_1_0·b_1_1⁴·b_1_3 + a_1_0·b_1_1⁵
       + a_1_0³·a_3_10 + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_1·b_1_3 + c_4_19·b_1_1²
19. b_3_12² + b_3_11² + b_1_3·b_5_28 + b_1_3³·b_3_12 + b_1_2·b_5_29
       + b_1_2·b_1_3²·b_3_11 + b_1_2²·b_1_3·b_3_12 + b_1_1·b_5_27 + b_1_1⁵·b_1_3 + b_1_1⁶
       + a_3_10·b_3_12 + a_1_0·b_1_1⁴·b_1_3 + a_1_0·b_1_1⁵ + a_1_0²·b_1_1·a_3_10
       + a_1_0³·a_3_10 + c_4_19·b_1_3² + c_4_19·b_1_1·b_1_3
20. b_1_3·b_5_27 + b_1_3³·b_3_12 + b_1_2²·b_1_3·b_3_11 + b_1_1·b_5_27 + b_1_1⁵·b_1_3
       + b_1_1⁶ + a_1_0·b_5_29 + a_1_0·b_5_27 + a_1_0·b_1_1²·b_3_12 + a_1_0·b_1_1⁴·b_1_3
       + a_1_0·b_1_1²·a_3_10 + a_1_0³·a_3_10 + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_1·b_1_3
       + c_4_19·b_1_1²
21. a_1_0·b_1_3·b_5_29 + a_1_0·b_1_1·b_5_27 + a_1_0·b_1_1⁶ + a_1_0·b_1_1³·a_3_10
       + a_1_0²·b_1_1²·a_3_10 + a_1_0³·b_1_1·a_3_10 + c_4_19·a_1_0·b_1_1·b_1_3
       + c_4_19·a_1_0·b_1_1²
22. b_1_1·b_1_3·b_5_29 + b_1_1²·b_5_27 + b_1_1⁷ + b_1_1⁴·a_3_10 + a_1_0·b_1_1·b_5_29
       + a_1_0·b_1_1·b_5_27 + a_1_0·b_1_1⁵·b_1_3 + a_1_0²·b_5_27 + a_1_0²·b_1_1⁵
       + c_4_19·b_1_1²·b_1_3 + c_4_19·b_1_1³ + c_4_19·a_1_0²·b_1_1 + c_4_19·a_1_0³
23. b_3_11·b_5_27 + b_1_3²·b_3_11·b_3_12 + b_1_2³·b_1_3²·b_3_11 + b_1_2⁴·b_1_3·b_3_12
       + b_1_2⁵·b_3_12 + a_1_0·b_1_1⁴·b_3_12 + c_4_19·b_1_2·b_3_11 + c_4_19·b_1_2⁴
       + c_4_19·a_1_0·b_3_12
24. a_3_10·b_5_28 + a_3_10·b_5_27 + a_1_0·b_1_1⁴·b_3_12 + c_4_19·a_1_0·b_1_1²·b_1_3
       + c_4_19·a_1_0·b_1_1³
25. b_3_12·b_5_27 + b_1_3⁵·b_3_12 + b_1_3⁵·b_3_11 + b_1_2²·b_3_11·b_3_12
       + b_1_2²·b_1_3·b_5_29 + b_1_2²·b_1_3³·b_3_12 + b_1_2²·b_1_3³·b_3_11
       + b_1_2³·b_5_29 + b_1_2³·b_5_28 + b_1_2³·b_1_3²·b_3_12 + b_1_2³·b_1_3²·b_3_11
       + b_1_2⁵·b_3_12 + b_1_2⁵·b_3_11 + b_1_1⁵·b_3_12 + a_3_10·b_5_29 + a_3_10·b_5_27
       + b_1_1⁵·a_3_10 + a_1_0·b_1_1⁴·b_3_12 + a_1_0·b_1_1⁴·a_3_10 + a_1_0²·b_1_1⁶
       + a_1_0²·b_1_1³·a_3_10 + c_4_19·b_1_3⁴ + c_4_19·b_1_2·b_3_12 + c_4_19·b_1_2³·b_1_3
       + c_4_19·b_1_2⁴ + c_4_19·b_1_1·b_3_12 + c_4_19·b_1_1³·b_1_3 + c_4_19·a_1_0·b_3_12
       + c_4_19·a_1_0·b_1_1²·b_1_3 + c_4_19·a_1_0·b_1_1³ + c_4_19·a_1_0²·b_1_1²
26. b_3_12·b_5_27 + b_3_11·b_5_29 + b_3_11·b_5_28 + b_1_3·b_7_53 + b_1_3²·b_3_11·b_3_12
       + b_1_3⁵·b_3_12 + b_1_3⁵·b_3_11 + b_1_2·b_1_3⁴·b_3_11 + b_1_2²·b_1_3·b_5_29
       + b_1_2²·b_1_3³·b_3_11 + b_1_2³·b_5_29 + b_1_2³·b_5_28 + b_1_2³·b_1_3²·b_3_12
       + b_1_2³·b_1_3²·b_3_11 + b_1_2⁵·b_3_11 + b_1_1⁵·b_3_12 + b_1_1⁵·a_3_10
       + a_1_0·b_1_1⁴·a_3_10 + a_1_0²·b_1_1·b_5_27 + c_4_19·b_1_3·b_3_12
       + c_4_19·b_1_2·b_3_12 + c_4_19·b_1_2·b_3_11 + c_4_19·b_1_2·b_1_3³
       + c_4_19·b_1_2²·b_1_3² + c_4_19·b_1_2³·b_1_3 + c_4_19·b_1_1·b_3_12
       + c_4_19·b_1_1·a_3_10 + c_4_19·a_1_0·b_1_1²·b_1_3 + c_4_19·a_1_0²·b_1_1²
27. b_3_11·b_5_28 + b_1_2·b_7_53 + b_1_2·b_1_3·b_3_11·b_3_12 + b_1_2·b_1_3⁴·b_3_11
       + b_1_2²·b_3_11·b_3_12 + b_1_2²·b_1_3³·b_3_12 + b_1_2³·b_1_3²·b_3_12
       + b_1_2³·b_1_3²·b_3_11 + b_1_2⁴·b_1_3·b_3_11 + a_1_0·b_1_1⁶·b_1_3 + a_1_0·b_1_1⁷
       + c_4_19·b_1_2·b_3_12 + c_4_19·b_1_2·b_1_3³ + c_4_19·b_1_2⁴ + c_4_19·a_1_0·b_3_12
       + c_4_19·a_1_0·b_1_1²·b_1_3 + c_4_19·a_1_0·b_1_1³
28. a_1_0·b_7_53 + a_1_0·b_1_1⁶·b_1_3 + a_1_0·b_1_1⁷ + a_1_0·b_1_1⁴·a_3_10
       + a_1_0²·b_1_1³·a_3_10 + c_4_19·a_1_0·b_3_12 + c_4_19·a_1_0·a_3_10
       + c_4_19·a_1_0²·b_1_1²
29. b_3_12·b_5_27 + b_1_3⁵·b_3_12 + b_1_3⁵·b_3_11 + b_1_2²·b_3_11·b_3_12
       + b_1_2²·b_1_3·b_5_29 + b_1_2²·b_1_3³·b_3_12 + b_1_2²·b_1_3³·b_3_11
       + b_1_2³·b_5_29 + b_1_2³·b_5_28 + b_1_2³·b_1_3²·b_3_12 + b_1_2³·b_1_3²·b_3_11
       + b_1_2⁵·b_3_12 + b_1_2⁵·b_3_11 + b_1_1·b_7_53 + b_1_1⁵·b_3_12 + b_1_1⁷·b_1_3
       + b_1_1⁸ + b_1_1⁵·a_3_10 + a_1_0·b_1_1⁶·b_1_3 + a_1_0·b_1_1⁷ + a_1_0·b_1_1⁴·a_3_10
       + a_1_0²·b_1_1·b_5_27 + c_4_19·b_1_3⁴ + c_4_19·b_1_2·b_3_12 + c_4_19·b_1_2³·b_1_3
       + c_4_19·b_1_2⁴ + c_4_19·b_1_1³·b_1_3 + c_4_19·b_1_1·a_3_10 + c_4_19·a_1_0·b_3_12
       + c_4_19·a_1_0·b_1_1²·b_1_3 + c_4_19·a_1_0²·b_1_1² + c_4_19·a_1_0³·b_1_1
30. b_3_12·b_5_28 + b_3_12·b_5_27 + b_1_3²·b_3_11·b_3_12 + b_1_3⁵·b_3_12 + b_1_3⁵·b_3_11
       + b_1_2·b_7_54 + b_1_2·b_1_3·b_3_11·b_3_12 + b_1_2·b_1_3²·b_5_29
       + b_1_2²·b_3_11·b_3_12 + b_1_2³·b_5_28 + b_1_2³·b_1_3²·b_3_11 + b_1_2⁵·b_3_12
       + b_1_2⁵·b_3_11 + b_1_1⁵·b_3_12 + a_1_0·b_1_1²·b_5_29 + a_1_0·b_1_1²·b_5_27
       + a_1_0·b_1_1⁶·b_1_3 + a_1_0·b_1_1⁴·a_3_10 + a_1_0²·b_1_1³·a_3_10 + c_4_19·b_1_3⁴
       + c_4_19·b_1_2⁴ + c_4_19·b_1_1⁴
31. b_3_12·b_5_27 + b_1_3⁵·b_3_12 + b_1_3⁵·b_3_11 + b_1_2²·b_3_11·b_3_12
       + b_1_2²·b_1_3·b_5_29 + b_1_2²·b_1_3³·b_3_12 + b_1_2²·b_1_3³·b_3_11
       + b_1_2³·b_5_29 + b_1_2³·b_5_28 + b_1_2³·b_1_3²·b_3_12 + b_1_2³·b_1_3²·b_3_11
       + b_1_2⁵·b_3_12 + b_1_2⁵·b_3_11 + b_1_1⁵·b_3_12 + a_1_0·b_7_54 + a_1_0·b_1_1²·b_5_29
       + a_1_0·b_1_1⁶·b_1_3 + a_1_0·b_1_1⁷ + a_1_0²·b_1_1·b_5_27 + a_1_0²·b_1_1⁶
       + c_4_19·b_1_3⁴ + c_4_19·b_1_2·b_3_12 + c_4_19·b_1_2³·b_1_3 + c_4_19·b_1_2⁴
       + c_4_19·b_1_1·b_3_12 + c_4_19·b_1_1³·b_1_3 + c_4_19·a_1_0·b_1_1²·b_1_3
       + c_4_19·a_1_0·a_3_10
32. b_3_12·b_5_29 + b_3_12·b_5_28 + b_1_3·b_7_54 + b_1_3³·b_5_29
       + b_1_2·b_1_3·b_3_11·b_3_12 + b_1_2·b_1_3²·b_5_29 + b_1_2²·b_3_11·b_3_12
       + b_1_2²·b_1_3·b_5_29 + b_1_2²·b_1_3³·b_3_11 + b_1_2³·b_5_29
       + b_1_2³·b_1_3²·b_3_12 + b_1_2³·b_1_3²·b_3_11 + b_1_2⁴·b_1_3·b_3_11
       + b_1_2⁵·b_3_12 + b_1_1·b_7_54 + b_1_1³·b_5_29 + b_1_1⁵·b_3_12 + b_1_1⁷·b_1_3
       + b_1_1⁸ + a_1_0·b_1_1²·b_5_29 + a_1_0·b_1_1²·b_5_27 + a_1_0·b_1_1⁴·b_3_12
       + a_1_0·b_1_1⁶·b_1_3 + a_1_0·b_1_1⁴·a_3_10 + a_1_0²·b_1_1³·a_3_10
       + c_4_19·b_1_3·b_3_12 + c_4_19·b_1_2·b_3_12 + c_4_19·b_1_2·b_1_3³ + c_4_19·b_1_2⁴
       + c_4_19·b_1_1·b_3_12 + c_4_19·a_1_0·b_3_12 + c_4_19·a_1_0³·b_1_1
33. b_1_1·b_1_3·b_7_54 + b_1_1⁴·b_5_27 + b_1_1⁹ + b_1_1⁶·a_3_10 + a_1_0·b_1_1³·b_5_29
       + a_1_0·b_1_1⁷·b_1_3 + a_1_0·b_1_1⁸ + a_1_0·a_3_10·b_5_27 + a_1_0²·b_1_1²·b_5_27
       + a_1_0²·b_1_1⁷ + c_4_19·b_1_1⁵ + c_4_19·b_1_1²·a_3_10
       + c_4_19·a_1_0·b_1_1·b_3_12 + c_4_19·a_1_0·b_1_1³·b_1_3 + c_4_19·a_1_0·b_1_1⁴
       + c_4_19·a_1_0·b_1_1·a_3_10
34. a_3_10·b_7_53 + a_1_0·b_1_1⁶·b_3_12 + a_1_0·b_1_1⁶·a_3_10 + a_1_0²·b_1_1⁸
       + a_1_0²·a_3_10·b_5_27 + c_4_19²·a_1_0·b_1_3 + c_4_19²·a_1_0·b_1_1
       + c_4_19²·a_1_0²
35. b_3_11·b_7_53 + b_1_2·b_1_3²·b_7_53 + b_1_2²·b_1_3·b_7_54
       + b_1_2²·b_1_3²·b_3_11·b_3_12 + b_1_2²·b_1_3³·b_5_29 + b_1_2²·b_1_3⁵·b_3_12
       + b_1_2²·b_1_3⁵·b_3_11 + b_1_2³·b_7_54 + b_1_2³·b_1_3·b_3_11·b_3_12
       + b_1_2³·b_1_3⁴·b_3_12 + b_1_2³·b_1_3⁴·b_3_11 + b_1_2⁴·b_1_3·b_5_29
       + b_1_2⁴·b_1_3³·b_3_12 + b_1_2⁴·b_1_3³·b_3_11 + b_1_2⁶·b_1_3·b_3_11
       + b_1_2⁷·b_3_12 + a_1_0·b_1_1⁶·b_3_12 + c_4_19·b_3_11·b_3_12 + c_4_19·b_1_3³·b_3_11
       + c_4_19·b_1_2·b_5_28 + c_4_19·b_1_2·b_1_3²·b_3_12 + c_4_19·b_1_2·b_1_3⁵
       + c_4_19·b_1_2³·b_3_11 + c_4_19·b_1_2⁵·b_1_3 + c_4_19·b_1_2⁶
       + c_4_19·a_1_0·b_1_1²·b_3_12 + c_4_19·a_1_0³·a_3_10 + c_4_19²·a_1_0·b_1_3
       + c_4_19²·a_1_0·b_1_1
36. b_5_27·b_5_28 + b_5_27² + b_1_3⁴·b_3_11·b_3_12 + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11
       + b_1_2·b_1_3²·b_7_54 + b_1_2·b_1_3³·b_3_11·b_3_12 + b_1_2·b_1_3⁴·b_5_29
       + b_1_2³·b_7_53 + b_1_2³·b_1_3·b_3_11·b_3_12 + b_1_2³·b_1_3⁴·b_3_11
       + b_1_2⁴·b_3_11·b_3_12 + b_1_2⁴·b_1_3·b_5_29 + b_1_2⁴·b_1_3³·b_3_12
       + b_1_2⁵·b_5_29 + b_1_2⁵·b_5_28 + b_1_2⁵·b_1_3²·b_3_12 + b_1_2⁵·b_1_3²·b_3_11
       + b_1_2⁶·b_1_3·b_3_12 + b_1_2⁶·b_1_3·b_3_11 + b_1_2⁷·b_3_11 + b_1_1⁷·b_3_12
       + b_1_1⁹·b_1_3 + b_1_1¹⁰ + a_1_0·b_1_1²·b_7_54 + a_1_0·b_1_1⁴·b_5_29
       + a_1_0·b_1_1⁶·b_3_12 + a_1_0²·b_1_1³·b_5_27 + a_1_0²·b_1_1⁸
       + a_1_0²·a_3_10·b_5_27 + c_4_19·b_1_3⁶ + c_4_19·b_1_2·b_5_28
       + c_4_19·b_1_2·b_1_3²·b_3_12 + c_4_19·b_1_2³·b_3_12 + c_4_19·b_1_2³·b_1_3³
       + c_4_19·b_1_2⁴·b_1_3² + c_4_19·b_1_2⁵·b_1_3 + c_4_19·b_1_2⁶
       + c_4_19·b_1_1³·b_3_12 + c_4_19·b_1_1⁶ + c_4_19·a_1_0·b_5_29 + c_4_19·a_1_0·b_5_27
       + c_4_19·a_1_0²·b_1_1·a_3_10 + c_4_19²·b_1_2²
37. b_5_28² + b_5_27² + b_3_12·b_7_54 + b_3_11·b_7_53 + b_1_3³·b_7_53 + b_1_3⁷·b_3_12
       + b_1_3⁷·b_3_11 + b_1_2·b_1_3²·b_7_53 + b_1_2·b_1_3³·b_3_11·b_3_12
       + b_1_2²·b_1_3²·b_3_11·b_3_12 + b_1_2²·b_1_3³·b_5_29 + b_1_2²·b_1_3⁵·b_3_12
       + b_1_2³·b_7_53 + b_1_2³·b_1_3·b_3_11·b_3_12 + b_1_2³·b_1_3²·b_5_29
       + b_1_2³·b_1_3⁴·b_3_12 + b_1_2⁴·b_1_3·b_5_29 + b_1_2⁴·b_1_3³·b_3_11
       + b_1_2⁵·b_5_29 + b_1_2⁵·b_5_28 + b_1_2⁵·b_1_3²·b_3_11 + b_1_2⁶·b_1_3·b_3_12
       + b_1_2⁶·b_1_3·b_3_11 + b_1_2⁷·b_3_11 + b_1_1³·b_7_54 + b_1_1⁵·b_5_29
       + b_1_1⁷·a_3_10 + a_1_0·b_1_1⁴·b_5_29 + a_1_0·b_1_1⁸·b_1_3 + a_1_0·b_1_1⁹
       + a_1_0·b_1_1·a_3_10·b_5_27 + a_1_0²·b_1_1³·b_5_27 + a_1_0²·b_1_1⁵·a_3_10
       + c_4_19·b_3_11·b_3_12 + c_4_19·b_1_3·b_5_29 + c_4_19·b_1_3³·b_3_11
       + c_4_19·b_1_2·b_5_29 + c_4_19·b_1_2·b_5_28 + c_4_19·b_1_2·b_1_3²·b_3_12
       + c_4_19·b_1_2·b_1_3²·b_3_11 + c_4_19·b_1_2²·b_1_3·b_3_11 + c_4_19·b_1_2²·b_1_3⁴
       + c_4_19·b_1_2³·b_3_11 + c_4_19·b_1_2³·b_1_3³ + c_4_19·b_1_2⁴·b_1_3²
       + c_4_19·b_1_2⁵·b_1_3 + c_4_19·b_1_2⁶ + c_4_19·b_1_1·b_5_29 + c_4_19·b_1_1³·b_3_12
       + c_4_19·b_1_1⁶ + c_4_19·a_1_0·b_5_29 + c_4_19·a_1_0·b_5_27
       + c_4_19·a_1_0²·b_1_1·a_3_10 + c_4_19²·b_1_3² + c_4_19²·b_1_2·b_1_3
       + c_4_19²·b_1_1·b_1_3 + c_4_19²·a_1_0·b_1_3 + c_4_19²·a_1_0·b_1_1
38. b_5_27·b_5_28 + b_5_27² + b_3_12·b_7_53 + b_3_11·b_7_54 + b_1_3³·b_7_53
       + b_1_3⁴·b_3_11·b_3_12 + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11 + b_1_2·b_1_3²·b_7_54
       + b_1_2·b_1_3⁴·b_5_29 + b_1_2·b_1_3⁶·b_3_11 + b_1_2²·b_1_3·b_7_53
       + b_1_2²·b_1_3⁵·b_3_11 + b_1_2³·b_7_53 + b_1_2³·b_1_3⁴·b_3_12 + b_1_2⁵·b_5_29
       + b_1_2⁵·b_5_28 + b_1_2⁵·b_1_3²·b_3_11 + b_1_2⁶·b_1_3·b_3_11 + b_1_2⁷·b_3_11
       + b_1_1⁹·b_1_3 + b_1_1¹⁰ + b_1_1⁷·a_3_10 + a_1_0·b_1_1⁶·b_3_12 + a_1_0·b_1_1⁸·b_1_3
       + a_1_0·b_1_1⁹ + a_1_0·b_1_1⁶·a_3_10 + a_1_0²·b_1_1³·b_5_27
       + a_1_0²·a_3_10·b_5_27 + a_1_0²·b_1_1⁵·a_3_10 + c_4_19·b_3_11·b_3_12
       + c_4_19·b_1_3³·b_3_12 + c_4_19·b_1_2·b_1_3²·b_3_11 + c_4_19·b_1_2·b_1_3⁵
       + c_4_19·b_1_2²·b_1_3·b_3_12 + c_4_19·b_1_2²·b_1_3·b_3_11 + c_4_19·b_1_2²·b_1_3⁴
       + c_4_19·b_1_2³·b_1_3³ + c_4_19·b_1_2⁵·b_1_3 + c_4_19·b_1_2⁶
       + c_4_19·b_1_1³·b_3_12 + c_4_19·b_1_1⁵·b_1_3 + c_4_19·b_1_1⁶
       + c_4_19·b_1_1³·a_3_10 + c_4_19·a_1_0·b_5_29 + c_4_19·a_1_0·b_5_27
       + c_4_19·a_1_0·b_1_1²·b_3_12 + c_4_19·a_1_0·b_1_1²·a_3_10 + c_4_19·a_1_0²·b_1_1⁴
       + c_4_19·a_1_0²·b_1_1·a_3_10 + c_4_19²·b_1_3² + c_4_19²·b_1_2²
       + c_4_19²·b_1_1²
39. b_5_27·b_5_28 + b_5_27² + b_1_3⁴·b_3_11·b_3_12 + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11
       + b_1_2·b_1_3²·b_7_54 + b_1_2·b_1_3³·b_3_11·b_3_12 + b_1_2·b_1_3⁴·b_5_29
       + b_1_2³·b_7_53 + b_1_2³·b_1_3·b_3_11·b_3_12 + b_1_2³·b_1_3⁴·b_3_11
       + b_1_2⁴·b_3_11·b_3_12 + b_1_2⁴·b_1_3·b_5_29 + b_1_2⁴·b_1_3³·b_3_12
       + b_1_2⁵·b_5_29 + b_1_2⁵·b_5_28 + b_1_2⁵·b_1_3²·b_3_12 + b_1_2⁵·b_1_3²·b_3_11
       + b_1_2⁶·b_1_3·b_3_12 + b_1_2⁶·b_1_3·b_3_11 + b_1_2⁷·b_3_11 + b_1_1⁷·b_3_12
       + b_1_1⁹·b_1_3 + b_1_1¹⁰ + a_3_10·b_7_54 + b_1_1²·a_3_10·b_5_27 + b_1_1⁷·a_3_10
       + a_1_0·b_1_1⁶·b_3_12 + a_1_0·b_1_1⁸·b_1_3 + a_1_0·b_1_1⁹
       + a_1_0·b_1_1·a_3_10·b_5_27 + a_1_0²·b_1_1⁸ + a_1_0²·b_1_1⁵·a_3_10
       + c_4_19·b_1_3⁶ + c_4_19·b_1_2·b_5_28 + c_4_19·b_1_2·b_1_3²·b_3_12
       + c_4_19·b_1_2³·b_3_12 + c_4_19·b_1_2³·b_1_3³ + c_4_19·b_1_2⁴·b_1_3²
       + c_4_19·b_1_2⁵·b_1_3 + c_4_19·b_1_2⁶ + c_4_19·b_1_1³·b_3_12 + c_4_19·b_1_1⁶
       + c_4_19·b_1_1³·a_3_10 + c_4_19·a_1_0·b_1_1²·b_3_12 + c_4_19·a_1_0·b_1_1⁴·b_1_3
       + c_4_19·a_1_0·b_1_1⁵ + c_4_19·a_1_0·b_1_1²·a_3_10 + c_4_19·a_1_0²·b_1_1·a_3_10
       + c_4_19·a_1_0³·a_3_10 + c_4_19²·b_1_2² + c_4_19²·a_1_0·b_1_3
       + c_4_19²·a_1_0·b_1_1 + c_4_19²·a_1_0²
40. b_5_28·b_5_29 + b_5_28² + b_5_27·b_5_28 + b_5_27² + b_3_11·b_7_53 + b_1_3³·b_7_53
       + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11 + b_1_2·b_1_3⁶·b_3_12 + b_1_2²·b_1_3·b_7_53
       + b_1_2²·b_1_3³·b_5_29 + b_1_2²·b_1_3⁵·b_3_12 + b_1_2³·b_1_3·b_3_11·b_3_12
       + b_1_2³·b_1_3⁴·b_3_11 + b_1_2⁴·b_1_3³·b_3_12 + b_1_2⁵·b_5_29
       + b_1_2⁵·b_1_3²·b_3_12 + b_1_1³·b_7_54 + b_1_1⁵·b_5_29 + b_1_1⁵·b_5_27
       + b_1_1⁹·b_1_3 + b_1_1¹⁰ + b_1_1²·a_3_10·b_5_27 + b_1_1⁷·a_3_10
       + a_1_0·b_1_1⁴·b_5_29 + a_1_0·b_1_1⁸·b_1_3 + a_1_0·b_1_1⁹ + c_8_71·b_1_2·b_1_3
       + c_4_19·b_3_11·b_3_12 + c_4_19·b_1_3³·b_3_12 + c_4_19·b_1_3³·b_3_11
       + c_4_19·b_1_2·b_5_28 + c_4_19·b_1_2·b_1_3⁵ + c_4_19·b_1_2²·b_1_3·b_3_11
       + c_4_19·b_1_2²·b_1_3⁴ + c_4_19·b_1_2³·b_3_12 + c_4_19·b_1_2³·b_3_11
       + c_4_19·b_1_2⁴·b_1_3² + c_4_19·b_1_1·b_5_29 + c_4_19·b_1_1·b_5_27
       + c_4_19·b_1_1³·b_3_12 + c_4_19·b_1_1⁵·b_1_3 + c_4_19·b_1_1⁶
       + c_4_19·b_1_1³·a_3_10 + c_4_19·a_1_0·b_5_29 + c_4_19·a_1_0·b_5_27
       + c_4_19·a_1_0·b_1_1⁴·b_1_3 + c_4_19·a_1_0·b_1_1⁵ + c_4_19·a_1_0·b_1_1²·a_3_10
       + c_4_19·a_1_0³·a_3_10 + c_4_19²·b_1_2² + c_4_19²·a_1_0·b_1_3
       + c_4_19²·a_1_0·b_1_1
41. b_5_28² + b_5_27² + b_3_11·b_7_53 + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11
       + b_1_2·b_1_3²·b_7_53 + b_1_2·b_1_3⁶·b_3_11 + b_1_2²·b_1_3²·b_3_11·b_3_12
       + b_1_2²·b_1_3³·b_5_29 + b_1_2²·b_1_3⁵·b_3_11 + b_1_2³·b_7_54
       + b_1_2⁴·b_1_3³·b_3_12 + b_1_2⁵·b_5_29 + b_1_2⁵·b_1_3²·b_3_12
       + b_1_2⁵·b_1_3²·b_3_11 + b_1_2⁶·b_1_3·b_3_12 + b_1_2⁶·b_1_3·b_3_11 + b_1_2⁷·b_3_12
       + b_1_2⁷·b_3_11 + b_1_1⁹·b_1_3 + b_1_1¹⁰ + a_1_0²·b_1_1⁵·a_3_10 + c_8_71·b_1_2²
       + c_4_19·b_3_11·b_3_12 + c_4_19·b_1_3³·b_3_11 + c_4_19·b_1_3⁶ + c_4_19·b_1_2·b_5_28
       + c_4_19·b_1_2·b_1_3²·b_3_12 + c_4_19·b_1_2·b_1_3⁵ + c_4_19·b_1_2²·b_1_3·b_3_12
       + c_4_19·b_1_2²·b_1_3⁴ + c_4_19·b_1_2³·b_1_3³ + c_4_19·b_1_2⁶ + c_4_19·b_1_1⁶
       + c_4_19·a_1_0·b_1_1²·b_3_12 + c_4_19·a_1_0³·a_3_10 + c_4_19²·b_1_2²
       + c_4_19²·a_1_0·b_1_3 + c_4_19²·a_1_0·b_1_1
42. b_5_27² + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11 + b_1_2²·b_1_3³·b_5_29
       + b_1_2²·b_1_3⁵·b_3_12 + b_1_2²·b_1_3⁵·b_3_11 + b_1_2³·b_1_3²·b_5_29
       + b_1_2³·b_1_3⁴·b_3_12 + b_1_2⁴·b_1_3·b_5_29 + b_1_2⁵·b_5_29 + b_1_2⁵·b_5_28
       + b_1_2⁶·b_1_3·b_3_12 + b_1_2⁷·b_3_11 + b_1_1⁹·b_1_3 + b_1_1¹⁰
       + a_1_0·b_1_1⁴·b_5_27 + a_1_0·b_1_1⁹ + a_1_0²·b_1_1⁸ + a_1_0²·a_3_10·b_5_27
       + c_4_19·b_1_3⁶ + c_4_19·b_1_2³·b_1_3³ + c_4_19·b_1_2⁴·b_1_3²
       + c_4_19·b_1_2⁵·b_1_3 + c_4_19·a_1_0·b_1_1⁵ + c_8_71·a_1_0²
       + c_4_19·a_1_0²·b_1_1·a_3_10 + c_4_19²·b_1_2² + c_4_19²·b_1_1²
       + c_4_19²·a_1_0²
43. b_5_27·b_5_29 + b_5_27² + b_1_3³·b_7_54 + b_1_3⁴·b_3_11·b_3_12 + b_1_3⁵·b_5_29
       + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11 + b_1_2·b_1_3²·b_7_54 + b_1_2²·b_1_3·b_7_53
       + b_1_2²·b_1_3³·b_5_29 + b_1_2²·b_1_3⁵·b_3_11 + b_1_2³·b_7_53
       + b_1_2³·b_1_3·b_3_11·b_3_12 + b_1_2³·b_1_3²·b_5_29 + b_1_2³·b_1_3⁴·b_3_12
       + b_1_2³·b_1_3⁴·b_3_11 + b_1_2⁴·b_1_3·b_5_29 + b_1_2⁴·b_1_3³·b_3_11
       + b_1_2⁵·b_5_29 + b_1_2⁵·b_5_28 + b_1_2⁵·b_1_3²·b_3_11 + b_1_2⁶·b_1_3·b_3_12
       + b_1_2⁶·b_1_3·b_3_11 + b_1_2⁷·b_3_12 + b_1_2⁷·b_3_11 + b_1_1⁵·b_5_29 + b_1_1¹⁰
       + b_1_1²·a_3_10·b_5_27 + b_1_1⁷·a_3_10 + a_1_0·b_1_1⁴·b_5_27 + a_1_0·b_1_1⁹
       + a_1_0·b_1_1⁶·a_3_10 + a_1_0²·b_1_1⁸ + a_1_0²·a_3_10·b_5_27
       + c_4_19·b_1_3³·b_3_12 + c_4_19·b_1_3⁶ + c_4_19·b_1_2·b_5_29 + c_4_19·b_1_2·b_1_3⁵
       + c_4_19·b_1_2²·b_1_3·b_3_12 + c_4_19·b_1_2²·b_1_3⁴ + c_4_19·b_1_2³·b_3_12
       + c_4_19·b_1_2³·b_3_11 + c_4_19·b_1_2⁴·b_1_3² + c_4_19·b_1_2⁵·b_1_3
       + c_4_19·b_1_1·b_5_29 + c_4_19·b_1_1·b_5_27 + c_4_19·b_1_1⁶ + c_8_71·a_1_0·b_1_3
       + c_8_71·a_1_0·b_1_1 + c_4_19·a_1_0·b_5_29 + c_4_19·a_1_0·b_5_27
       + c_4_19·a_1_0·b_1_1⁴·b_1_3 + c_4_19·a_1_0·b_1_1²·a_3_10
       + c_4_19·a_1_0²·b_1_1·a_3_10 + c_4_19·a_1_0³·a_3_10 + c_4_19²·b_1_2²
       + c_4_19²·a_1_0·b_1_3 + c_4_19²·a_1_0·b_1_1
44. b_5_29² + b_5_28² + b_1_3³·b_7_54 + b_1_3⁵·b_5_29 + b_1_3⁷·b_3_12 + b_1_3⁷·b_3_11
       + b_1_2·b_1_3³·b_3_11·b_3_12 + b_1_2·b_1_3⁴·b_5_29 + b_1_2·b_1_3⁶·b_3_12
       + b_1_2³·b_1_3⁴·b_3_11 + b_1_2⁴·b_1_3³·b_3_12 + b_1_2⁵·b_5_28
       + b_1_2⁵·b_1_3²·b_3_12 + b_1_2⁵·b_1_3²·b_3_11 + b_1_2⁶·b_1_3·b_3_11
       + b_1_2⁷·b_3_12 + b_1_2⁷·b_3_11 + b_1_1³·b_7_54 + b_1_1⁵·b_5_27 + b_1_1⁷·b_3_12
       + b_1_1⁷·a_3_10 + a_1_0·b_1_1⁴·b_5_29 + a_1_0·b_1_1⁴·b_5_27 + a_1_0·b_1_1⁸·b_1_3
       + a_1_0·b_1_1⁶·a_3_10 + a_1_0²·b_1_1³·b_5_27 + a_1_0²·b_1_1⁵·a_3_10
       + c_8_71·b_1_3² + c_8_71·b_1_1² + c_4_19·b_1_3³·b_3_12
       + c_4_19·b_1_2·b_1_3²·b_3_11 + c_4_19·b_1_2²·b_1_3⁴ + c_4_19·b_1_2⁶
       + c_4_19·a_1_0·b_1_1²·b_3_12 + c_4_19·a_1_0²·b_1_1·a_3_10 + c_4_19²·b_1_2²
45. b_5_27·b_7_53 + b_1_3²·b_3_11·b_7_54 + b_1_3⁵·b_7_53 + b_1_2·b_1_3⁵·b_3_11·b_3_12
       + b_1_2·b_1_3⁸·b_3_11 + b_1_2²·b_1_3³·b_7_53 + b_1_2²·b_1_3⁷·b_3_11
       + b_1_2³·b_1_3²·b_7_53 + b_1_2³·b_1_3³·b_3_11·b_3_12 + b_1_2³·b_1_3⁶·b_3_12
       + b_1_2³·b_1_3⁶·b_3_11 + b_1_2⁴·b_1_3·b_7_54 + b_1_2⁴·b_1_3⁵·b_3_11
       + b_1_2⁵·b_7_54 + b_1_2⁵·b_1_3·b_3_11·b_3_12 + b_1_2⁵·b_1_3⁴·b_3_11
       + b_1_2⁶·b_1_3·b_5_29 + b_1_2⁶·b_1_3³·b_3_11 + b_1_2⁸·b_1_3·b_3_11 + b_1_2⁹·b_3_12
       + b_1_1¹¹·b_1_3 + b_1_1¹² + b_1_1⁴·a_3_10·b_5_27 + b_1_1⁹·a_3_10
       + a_1_0·b_1_1⁴·b_7_54 + a_1_0·b_1_1⁶·b_5_27 + a_1_0·b_1_1¹⁰·b_1_3
       + a_1_0·b_1_1³·a_3_10·b_5_27 + a_1_0²·b_1_1¹⁰ + a_1_0²·b_1_1⁷·a_3_10
       + c_4_19·b_1_3²·b_3_11·b_3_12 + c_4_19·b_1_3⁵·b_3_12 + c_4_19·b_1_3⁸
       + c_4_19·b_1_2·b_7_53 + c_4_19·b_1_2·b_1_3⁴·b_3_12 + c_4_19·b_1_2·b_1_3⁷
       + c_4_19·b_1_2²·b_3_11·b_3_12 + c_4_19·b_1_2²·b_1_3·b_5_29
       + c_4_19·b_1_2²·b_1_3³·b_3_12 + c_4_19·b_1_2²·b_1_3⁶ + c_4_19·b_1_2³·b_5_29
       + c_4_19·b_1_2³·b_1_3²·b_3_12 + c_4_19·b_1_2³·b_1_3⁵ + c_4_19·b_1_2⁴·b_1_3⁴
       + c_4_19·b_1_2⁵·b_3_12 + c_4_19·b_1_2⁷·b_1_3 + c_4_19·b_1_2⁸
       + c_4_19·b_1_1⁵·b_3_12 + c_4_19·b_1_1⁸ + c_4_19·a_3_10·b_5_27
       + c_4_19·b_1_1⁵·a_3_10 + c_4_19·a_1_0·b_1_1²·b_5_27 + c_4_19·a_1_0·b_1_1⁶·b_1_3
       + c_4_19·a_1_0·b_1_1⁷ + c_4_19·a_1_0·b_1_1⁴·a_3_10 + c_4_19·a_1_0²·b_1_1·b_5_27
       + c_4_19²·b_1_3⁴ + c_4_19²·b_1_2³·b_1_3 + c_4_19²·b_1_2⁴
       + c_4_19²·b_1_1·b_3_12 + c_4_19²·b_1_1³·b_1_3 + c_4_19²·a_1_0·b_3_12
       + c_4_19²·a_1_0·b_1_1²·b_1_3 + c_4_19²·a_1_0·b_1_1³ + c_4_19²·a_1_0²·b_1_1²
       + c_4_19²·a_1_0³·b_1_1
46. b_5_28·b_7_54 + b_5_27·b_7_54 + b_5_27·b_7_53 + b_1_2·b_1_3·b_3_11·b_7_54
       + b_1_2·b_1_3⁵·b_3_11·b_3_12 + b_1_2²·b_3_11·b_7_54 + b_1_2²·b_1_3³·b_7_53
       + b_1_2²·b_1_3⁴·b_3_11·b_3_12 + b_1_2²·b_1_3⁷·b_3_12 + b_1_2²·b_1_3⁷·b_3_11
       + b_1_2³·b_1_3²·b_7_54 + b_1_2³·b_1_3⁴·b_5_29 + b_1_2³·b_1_3⁶·b_3_11
       + b_1_2⁴·b_1_3·b_7_54 + b_1_2⁴·b_1_3·b_7_53 + b_1_2⁴·b_1_3²·b_3_11·b_3_12
       + b_1_2⁴·b_1_3⁵·b_3_12 + b_1_2⁴·b_1_3⁵·b_3_11 + b_1_2⁵·b_7_54 + b_1_2⁵·b_7_53
       + b_1_2⁵·b_1_3²·b_5_29 + b_1_2⁵·b_1_3⁴·b_3_12 + b_1_2⁶·b_3_11·b_3_12
       + b_1_2⁶·b_1_3³·b_3_12 + b_1_2⁶·b_1_3³·b_3_11 + b_1_2⁷·b_5_28
       + b_1_2⁷·b_1_3²·b_3_12 + b_1_2⁷·b_1_3²·b_3_11 + b_1_2⁸·b_1_3·b_3_11
       + b_1_2⁹·b_3_12 + b_1_1⁷·b_5_29 + b_1_1⁷·b_5_27 + b_1_1¹² + b_1_1⁴·a_3_10·b_5_27
       + b_1_1⁹·a_3_10 + a_1_0·b_1_1⁶·b_5_29 + a_1_0·b_1_1⁶·b_5_27 + a_1_0·b_1_1⁸·b_3_12
       + a_1_0·b_1_1¹¹ + a_1_0·b_1_1³·a_3_10·b_5_27 + a_1_0²·b_1_1⁵·b_5_27
       + a_1_0²·b_1_1¹⁰ + c_8_71·b_1_2·b_3_12 + c_8_71·b_1_2·b_1_3³
       + c_8_71·b_1_2²·b_1_3² + c_8_71·b_1_2³·b_1_3 + c_8_71·b_1_2⁴
       + c_4_19·b_1_3²·b_3_11·b_3_12 + c_4_19·b_1_3³·b_5_29 + c_4_19·b_1_3⁵·b_3_12
       + c_4_19·b_1_2·b_7_53 + c_4_19·b_1_2·b_1_3²·b_5_29 + c_4_19·b_1_2·b_1_3⁴·b_3_12
       + c_4_19·b_1_2·b_1_3⁷ + c_4_19·b_1_2²·b_1_3⁶ + c_4_19·b_1_2³·b_5_28
       + c_4_19·b_1_2³·b_1_3²·b_3_11 + c_4_19·b_1_2⁵·b_3_11 + c_4_19·b_1_2⁶·b_1_3²
       + c_4_19·b_1_1³·b_5_29 + c_8_71·a_1_0·b_1_1²·b_1_3 + c_8_71·a_1_0·b_1_1³
       + c_4_19·a_3_10·b_5_27 + c_4_19·a_1_0·b_1_1²·b_5_27 + c_4_19·a_1_0·b_1_1⁴·b_3_12
       + c_4_19·a_1_0·b_1_1⁶·b_1_3 + c_4_19·a_1_0·b_1_1⁷ + c_4_19·a_1_0²·b_1_1·b_5_27
       + c_4_19²·b_1_2·b_3_12 + c_4_19²·b_1_2·b_1_3³ + c_4_19²·b_1_2⁴
       + c_4_19²·b_1_1·b_3_12 + c_4_19²·a_1_0·b_3_12 + c_4_19²·a_1_0·b_1_1²·b_1_3
       + c_4_19²·a_1_0·b_1_1³ + c_4_19²·a_1_0²·b_1_1² + c_4_19²·a_1_0³·b_1_1
47. b_5_27·b_7_54 + b_1_3⁵·b_7_53 + b_1_2·b_1_3⁵·b_3_11·b_3_12 + b_1_2·b_1_3⁸·b_3_11
       + b_1_2²·b_3_11·b_7_54 + b_1_2²·b_1_3⁷·b_3_12 + b_1_2²·b_1_3⁷·b_3_11
       + b_1_2³·b_1_3²·b_7_54 + b_1_2³·b_1_3²·b_7_53 + b_1_2³·b_1_3³·b_3_11·b_3_12
       + b_1_2³·b_1_3⁴·b_5_29 + b_1_2³·b_1_3⁶·b_3_12 + b_1_2⁴·b_1_3³·b_5_29
       + b_1_2⁴·b_1_3⁵·b_3_12 + b_1_2⁴·b_1_3⁵·b_3_11 + b_1_2⁵·b_1_3⁴·b_3_12
       + b_1_2⁵·b_1_3⁴·b_3_11 + b_1_2⁶·b_1_3·b_5_29 + b_1_2⁷·b_5_29 + b_1_2⁷·b_5_28
       + b_1_2⁹·b_3_12 + b_1_2⁹·b_3_11 + b_1_1⁵·b_7_54 + b_1_1¹¹·b_1_3
       + b_1_1⁴·a_3_10·b_5_27 + a_1_0·b_1_1⁴·b_7_54 + a_1_0·b_1_1¹⁰·b_1_3
       + a_1_0·b_1_1⁸·a_3_10 + a_1_0²·b_1_1⁵·b_5_27 + a_1_0²·b_1_1²·a_3_10·b_5_27
       + c_8_71·b_1_2²·b_1_3² + c_4_19·b_1_3³·b_5_29 + c_4_19·b_1_3⁸
       + c_4_19·b_1_2·b_7_54 + c_4_19·b_1_2·b_1_3²·b_5_29 + c_4_19·b_1_2·b_1_3⁴·b_3_11
       + c_4_19·b_1_2·b_1_3⁷ + c_4_19·b_1_2²·b_1_3³·b_3_12
       + c_4_19·b_1_2²·b_1_3³·b_3_11 + c_4_19·b_1_2³·b_1_3²·b_3_11
       + c_4_19·b_1_2⁴·b_1_3⁴ + c_4_19·b_1_2⁵·b_1_3³ + c_4_19·b_1_2⁷·b_1_3
       + c_4_19·b_1_2⁸ + c_4_19·b_1_1·b_7_54 + c_4_19·b_1_1³·b_5_27 + c_4_19·b_1_1⁸
       + c_8_71·a_1_0·b_3_12 + c_8_71·a_1_0·b_1_1²·b_1_3 + c_8_71·a_1_0·b_1_1³
       + c_4_19·a_3_10·b_5_27 + c_4_19·a_1_0·b_1_1²·b_5_27 + c_4_19·a_1_0·b_1_1⁴·b_3_12
       + c_4_19·a_1_0·b_1_1⁶·b_1_3 + c_8_71·a_1_0²·b_1_1² + c_4_19·a_1_0·b_1_1⁴·a_3_10
       + c_4_19·a_1_0²·b_1_1⁶ + c_8_71·a_1_0³·b_1_1 + c_4_19·a_1_0²·b_1_1³·a_3_10
       + c_4_19²·b_1_3⁴ + c_4_19²·b_1_2·b_1_3³ + c_4_19²·b_1_2²·b_1_3²
       + c_4_19²·b_1_1⁴ + c_4_19²·b_1_1·a_3_10 + c_4_19²·a_1_0·b_3_12
       + c_4_19²·a_1_0·b_1_1³ + c_4_19²·a_1_0²·b_1_1² + c_4_19²·a_1_0³·b_1_1
48. b_5_29·b_7_54 + b_5_28·b_7_54 + b_1_3⁶·b_3_11·b_3_12 + b_1_2·b_1_3·b_3_11·b_7_54
       + b_1_2·b_1_3⁴·b_7_53 + b_1_2·b_1_3⁵·b_3_11·b_3_12 + b_1_2·b_1_3⁸·b_3_11
       + b_1_2²·b_3_11·b_7_54 + b_1_2²·b_1_3³·b_7_53 + b_1_2²·b_1_3⁴·b_3_11·b_3_12
       + b_1_2²·b_1_3⁷·b_3_11 + b_1_2³·b_1_3²·b_7_53 + b_1_2³·b_1_3⁴·b_5_29
       + b_1_2³·b_1_3⁶·b_3_12 + b_1_2³·b_1_3⁶·b_3_11 + b_1_2⁴·b_1_3·b_7_54
       + b_1_2⁴·b_1_3⁵·b_3_11 + b_1_2⁵·b_7_54 + b_1_2⁵·b_7_53 + b_1_2⁵·b_1_3⁴·b_3_12
       + b_1_2⁵·b_1_3⁴·b_3_11 + b_1_2⁶·b_1_3³·b_3_12 + b_1_2⁶·b_1_3³·b_3_11
       + b_1_2⁷·b_5_29 + b_1_2⁷·b_1_3²·b_3_12 + b_1_2⁷·b_1_3²·b_3_11
       + b_1_2⁸·b_1_3·b_3_12 + b_1_2⁹·b_3_11 + b_1_1⁷·b_5_27 + b_1_1⁹·b_3_12 + b_1_1¹²
       + b_1_1⁴·a_3_10·b_5_27 + a_1_0·b_1_1⁶·b_5_29 + a_1_0·b_1_1⁸·b_3_12
       + a_1_0·b_1_1¹⁰·b_1_3 + a_1_0·b_1_1¹¹ + a_1_0·b_1_1³·a_3_10·b_5_27
       + a_1_0·b_1_1⁸·a_3_10 + a_1_0²·b_1_1⁵·b_5_27 + a_1_0²·b_1_1¹⁰
       + a_1_0²·b_1_1²·a_3_10·b_5_27 + c_8_71·b_1_3·b_3_12 + c_8_71·b_1_3⁴
       + c_8_71·b_1_2²·b_1_3² + c_8_71·b_1_2⁴ + c_8_71·b_1_1·b_3_12 + c_8_71·b_1_1⁴
       + c_4_19·b_1_3·b_7_54 + c_4_19·b_1_3⁵·b_3_11 + c_4_19·b_1_3⁸ + c_4_19·b_1_2·b_7_54
       + c_4_19·b_1_2·b_1_3·b_3_11·b_3_12 + c_4_19·b_1_2·b_1_3⁴·b_3_11
       + c_4_19·b_1_2·b_1_3⁷ + c_4_19·b_1_2²·b_1_3·b_5_29 + c_4_19·b_1_2²·b_1_3³·b_3_12
       + c_4_19·b_1_2²·b_1_3⁶ + c_4_19·b_1_2³·b_5_28 + c_4_19·b_1_2³·b_1_3²·b_3_12
       + c_4_19·b_1_2³·b_1_3²·b_3_11 + c_4_19·b_1_2³·b_1_3⁵
       + c_4_19·b_1_2⁴·b_1_3·b_3_12 + c_4_19·b_1_2⁴·b_1_3⁴ + c_4_19·b_1_2⁵·b_3_12
       + c_4_19·b_1_2⁷·b_1_3 + c_4_19·b_1_2⁸ + c_4_19·b_1_1·b_7_54 + c_4_19·b_1_1³·b_5_29
       + c_4_19·b_1_1³·b_5_27 + c_4_19·b_1_1⁷·b_1_3 + c_8_71·a_1_0·b_1_1²·b_1_3
       + c_8_71·a_1_0·b_1_1³ + c_4_19·b_1_1⁵·a_3_10 + c_4_19·a_1_0·b_7_54
       + c_4_19·a_1_0·b_1_1²·b_5_29 + c_4_19·a_1_0·b_1_1⁴·b_3_12
       + c_4_19·a_1_0·b_1_1⁶·b_1_3 + c_4_19·a_1_0·b_1_1⁷ + c_4_19·a_1_0²·b_1_1⁶
       + c_4_19·a_1_0²·b_1_1³·a_3_10 + c_4_19²·b_1_3·b_3_12 + c_4_19²·b_1_2²·b_1_3²
       + c_4_19²·b_1_1·b_3_12 + c_4_19²·a_1_0·b_1_1²·b_1_3 + c_4_19²·a_1_0·a_3_10
       + c_4_19²·a_1_0³·b_1_1
49. b_5_29·b_7_53 + b_5_28·b_7_53 + b_5_27·b_7_54 + b_1_3⁵·b_7_53 + b_1_3⁶·b_3_11·b_3_12
       + b_1_2·b_1_3⁴·b_7_53 + b_1_2·b_1_3⁵·b_3_11·b_3_12 + b_1_2²·b_1_3³·b_7_54
       + b_1_2²·b_1_3⁵·b_5_29 + b_1_2³·b_1_3²·b_7_54 + b_1_2³·b_1_3²·b_7_53
       + b_1_2³·b_1_3³·b_3_11·b_3_12 + b_1_2³·b_1_3⁶·b_3_12 + b_1_2³·b_1_3⁶·b_3_11
       + b_1_2⁴·b_1_3·b_7_53 + b_1_2⁴·b_1_3⁵·b_3_12 + b_1_2⁴·b_1_3⁵·b_3_11
       + b_1_2⁵·b_7_54 + b_1_2⁵·b_1_3⁴·b_3_12 + b_1_2⁶·b_3_11·b_3_12
       + b_1_2⁶·b_1_3·b_5_29 + b_1_2⁶·b_1_3³·b_3_11 + b_1_2⁷·b_5_29 + b_1_2⁷·b_5_28
       + b_1_2⁷·b_1_3²·b_3_12 + b_1_2⁷·b_1_3²·b_3_11 + b_1_2⁸·b_1_3·b_3_12
       + b_1_2⁸·b_1_3·b_3_11 + b_1_2⁹·b_3_11 + b_1_1⁵·b_7_54 + b_1_1⁷·b_5_29
       + b_1_1⁷·b_5_27 + b_1_1⁹·b_3_12 + b_1_1¹¹·b_1_3 + b_1_1¹² + b_1_1⁴·a_3_10·b_5_27
       + a_1_0·b_1_1⁶·b_5_29 + a_1_0·b_1_1¹¹ + a_1_0²·b_1_1¹⁰
       + a_1_0²·b_1_1²·a_3_10·b_5_27 + c_8_71·b_1_3·b_3_11 + c_8_71·b_1_2²·b_1_3²
       + c_4_19·b_1_3·b_7_54 + c_4_19·b_1_3³·b_5_29 + c_4_19·b_1_3⁵·b_3_11 + c_4_19·b_1_3⁸
       + c_4_19·b_1_2·b_7_54 + c_4_19·b_1_2·b_7_53 + c_4_19·b_1_2·b_1_3·b_3_11·b_3_12
       + c_4_19·b_1_2·b_1_3⁴·b_3_12 + c_4_19·b_1_2·b_1_3⁴·b_3_11
       + c_4_19·b_1_2²·b_1_3³·b_3_12 + c_4_19·b_1_2³·b_1_3²·b_3_12
       + c_4_19·b_1_2⁵·b_3_12 + c_4_19·b_1_2⁵·b_3_11 + c_4_19·b_1_2⁵·b_1_3³
       + c_4_19·b_1_1³·b_5_29 + c_4_19·b_1_1⁵·b_3_12 + c_4_19·b_1_1⁷·b_1_3
       + c_4_19·b_1_1⁸ + c_8_71·a_1_0·b_1_1²·b_1_3 + c_8_71·a_1_0·b_1_1³
       + c_4_19·a_3_10·b_5_27 + c_4_19·a_1_0·b_7_54 + c_4_19·a_1_0·b_1_1⁶·b_1_3
       + c_4_19·a_1_0·b_1_1⁷ + c_8_71·a_1_0²·b_1_1² + c_4_19·a_1_0²·b_1_1⁶
       + c_8_71·a_1_0³·b_1_1 + c_4_19·a_1_0²·b_1_1³·a_3_10 + c_4_19²·b_1_3·b_3_12
       + c_4_19²·b_1_3⁴ + c_4_19²·b_1_2·b_1_3³ + c_4_19²·b_1_2²·b_1_3²
       + c_4_19²·b_1_1·b_3_12 + c_4_19²·b_1_1³·b_1_3 + c_4_19²·b_1_1·a_3_10
       + c_4_19²·a_1_0·b_3_12 + c_4_19²·a_1_0·a_3_10 + c_4_19²·a_1_0²·b_1_1²
       + c_4_19²·a_1_0³·b_1_1
50. b_5_28·b_7_53 + b_1_2·b_1_3⁴·b_7_53 + b_1_2·b_1_3⁵·b_3_11·b_3_12
       + b_1_2²·b_3_11·b_7_54 + b_1_2²·b_1_3³·b_7_54 + b_1_2²·b_1_3³·b_7_53
       + b_1_2²·b_1_3⁴·b_3_11·b_3_12 + b_1_2²·b_1_3⁵·b_5_29 + b_1_2²·b_1_3⁷·b_3_12
       + b_1_2³·b_1_3²·b_7_54 + b_1_2³·b_1_3³·b_3_11·b_3_12 + b_1_2³·b_1_3⁶·b_3_12
       + b_1_2⁴·b_1_3²·b_3_11·b_3_12 + b_1_2⁴·b_1_3³·b_5_29 + b_1_2⁴·b_1_3⁵·b_3_12
       + b_1_2⁵·b_1_3·b_3_11·b_3_12 + b_1_2⁵·b_1_3²·b_5_29 + b_1_2⁵·b_1_3⁴·b_3_11
       + b_1_2⁶·b_3_11·b_3_12 + b_1_2⁶·b_1_3³·b_3_11 + b_1_2⁷·b_1_3²·b_3_11
       + b_1_2⁹·b_3_12 + b_1_1⁹·b_3_12 + b_1_1⁴·a_3_10·b_5_27 + a_1_0·b_1_1⁸·b_3_12
       + a_1_0·b_1_1¹⁰·b_1_3 + a_1_0·b_1_1¹¹ + a_1_0·b_1_1³·a_3_10·b_5_27
       + a_1_0²·b_1_1⁷·a_3_10 + c_8_71·b_1_2·b_3_11 + c_4_19·b_1_3²·b_3_11·b_3_12
       + c_4_19·b_1_3⁵·b_3_11 + c_4_19·b_1_2·b_7_54 + c_4_19·b_1_2·b_1_3·b_3_11·b_3_12
       + c_4_19·b_1_2·b_1_3⁴·b_3_12 + c_4_19·b_1_2·b_1_3⁴·b_3_11 + c_4_19·b_1_2·b_1_3⁷
       + c_4_19·b_1_2²·b_3_11·b_3_12 + c_4_19·b_1_2²·b_1_3³·b_3_12
       + c_4_19·b_1_2²·b_1_3⁶ + c_4_19·b_1_2³·b_1_3²·b_3_11 + c_4_19·b_1_2³·b_1_3⁵
       + c_4_19·b_1_2⁴·b_1_3·b_3_12 + c_4_19·b_1_2⁴·b_1_3·b_3_11 + c_4_19·b_1_2⁴·b_1_3⁴
       + c_4_19·b_1_2⁵·b_1_3³ + c_4_19·b_1_2⁶·b_1_3² + c_4_19·b_1_2⁷·b_1_3
       + c_4_19·b_1_2⁸ + c_4_19·b_1_1⁷·b_1_3 + c_4_19·b_1_1⁸ + c_4_19·a_3_10·b_5_27
       + c_4_19·a_1_0·b_1_1²·b_5_27 + c_4_19·a_1_0²·b_1_1·b_5_27 + c_4_19·a_1_0²·b_1_1⁶
       + c_4_19·a_1_0²·b_1_1³·a_3_10 + c_4_19²·b_1_2·b_3_12 + c_4_19²·b_1_2²·b_1_3²
       + c_4_19²·b_1_1·b_3_12 + c_4_19²·b_1_1³·b_1_3 + c_4_19²·b_1_1⁴
       + c_4_19²·a_1_0·b_3_12 + c_4_19²·a_1_0²·b_1_1² + c_4_19²·a_1_0³·b_1_1
51. b_7_53·b_7_54 + b_7_53² + b_1_2²·b_1_3²·b_3_11·b_7_54 + b_1_2²·b_1_3⁵·b_7_53
       + b_1_2³·b_1_3⁴·b_7_54 + b_1_2³·b_1_3⁶·b_5_29 + b_1_2³·b_1_3⁸·b_3_11
       + b_1_2⁴·b_3_11·b_7_54 + b_1_2⁴·b_1_3³·b_7_54 + b_1_2⁴·b_1_3³·b_7_53
       + b_1_2⁴·b_1_3⁷·b_3_12 + b_1_2⁴·b_1_3⁷·b_3_11 + b_1_2⁵·b_1_3²·b_7_53
       + b_1_2⁵·b_1_3³·b_3_11·b_3_12 + b_1_2⁵·b_1_3⁶·b_3_11 + b_1_2⁶·b_1_3⁵·b_3_12
       + b_1_2⁷·b_1_3·b_3_11·b_3_12 + b_1_2⁷·b_1_3⁴·b_3_12 + b_1_2⁷·b_1_3⁴·b_3_11
       + b_1_2⁸·b_1_3·b_5_29 + b_1_2⁹·b_5_29 + b_1_2¹⁰·b_1_3·b_3_11 + b_1_2¹¹·b_3_12
       + b_1_1⁷·b_7_54 + b_1_1⁹·b_5_27 + b_1_1¹³·b_1_3 + b_1_1⁶·a_3_10·b_5_27
       + a_1_0·b_1_1⁶·b_7_54 + a_1_0·b_1_1⁸·b_5_29 + a_1_0·b_1_1⁸·b_5_27
       + a_1_0·b_1_1¹²·b_1_3 + a_1_0·b_1_1⁵·a_3_10·b_5_27 + a_1_0·b_1_1¹⁰·a_3_10
       + a_1_0²·b_1_1⁷·b_5_27 + a_1_0²·b_1_1⁹·a_3_10 + c_8_71·b_3_11·b_3_12
       + c_8_71·b_1_3³·b_3_11 + c_8_71·b_1_2·b_1_3²·b_3_11 + c_8_71·b_1_2²·b_1_3·b_3_12
       + c_8_71·b_1_2³·b_3_12 + c_4_19·b_3_11·b_7_54 + c_4_19·b_1_3³·b_7_54
       + c_4_19·b_1_3⁷·b_3_11 + c_4_19·b_1_2·b_1_3²·b_7_54
       + c_4_19·b_1_2·b_1_3³·b_3_11·b_3_12 + c_4_19·b_1_2·b_1_3⁶·b_3_11
       + c_4_19·b_1_2²·b_1_3·b_7_53 + c_4_19·b_1_2²·b_1_3⁵·b_3_12
       + c_4_19·b_1_2²·b_1_3⁸ + c_4_19·b_1_2³·b_1_3·b_3_11·b_3_12
       + c_4_19·b_1_2³·b_1_3⁷ + c_4_19·b_1_2⁴·b_3_11·b_3_12
       + c_4_19·b_1_2⁴·b_1_3·b_5_29 + c_4_19·b_1_2⁴·b_1_3³·b_3_11
       + c_4_19·b_1_2⁴·b_1_3⁶ + c_4_19·b_1_2⁵·b_1_3²·b_3_12
       + c_4_19·b_1_2⁵·b_1_3²·b_3_11 + c_4_19·b_1_2⁵·b_1_3⁵
       + c_4_19·b_1_2⁶·b_1_3·b_3_12 + c_4_19·b_1_2⁶·b_1_3·b_3_11 + c_4_19·b_1_2⁶·b_1_3⁴
       + c_4_19·b_1_2⁷·b_3_11 + c_4_19·b_1_2⁷·b_1_3³ + c_4_19·b_1_2¹⁰
       + c_4_19·b_1_1³·b_7_54 + c_4_19·b_1_1⁵·b_5_29 + c_4_19·b_1_1⁵·b_5_27
       + c_4_19·b_1_1⁹·b_1_3 + c_4_19·b_1_1¹⁰ + c_8_71·a_1_0·b_1_1²·b_3_12
       + c_4_19·b_1_1²·a_3_10·b_5_27 + c_4_19·a_1_0·b_1_1⁴·b_5_27
       + c_4_19·a_1_0·b_1_1⁶·b_3_12 + c_4_19·a_1_0·b_1_1·a_3_10·b_5_27
       + c_4_19·a_1_0²·a_3_10·b_5_27 + c_4_19·a_1_0²·b_1_1⁵·a_3_10
       + c_4_19²·b_3_11·b_3_12 + c_4_19²·b_1_3·b_5_29 + c_4_19²·b_1_3⁶
       + c_4_19²·b_1_2·b_5_29 + c_4_19²·b_1_2·b_5_28 + c_4_19²·b_1_2²·b_1_3⁴
       + c_4_19²·b_1_2³·b_1_3³ + c_4_19²·b_1_2⁴·b_1_3² + c_4_19²·b_1_2⁵·b_1_3
       + c_4_19²·b_1_1·b_5_29 + c_4_19²·b_1_1³·b_3_12 + c_4_19²·b_1_1⁶
       + c_4_19²·b_1_1³·a_3_10 + c_4_19²·a_1_0·b_1_1²·b_3_12
       + c_4_19²·a_1_0·b_1_1⁴·b_1_3 + c_4_19²·a_1_0·b_1_1²·a_3_10
       + c_4_19²·a_1_0²·b_1_1·a_3_10 + c_4_19³·b_1_2·b_1_3 + c_4_19³·b_1_2²
       + c_4_19³·b_1_1·b_1_3 + c_4_19³·b_1_1²
52. b_7_53·b_7_54 + b_1_2·b_1_3³·b_3_11·b_7_54 + b_1_2·b_1_3⁶·b_7_53
       + b_1_2·b_1_3⁷·b_3_11·b_3_12 + b_1_2²·b_1_3²·b_3_11·b_7_54
       + b_1_2²·b_1_3⁵·b_7_54 + b_1_2²·b_1_3⁷·b_5_29 + b_1_2³·b_1_3⁴·b_7_53
       + b_1_2³·b_1_3⁶·b_5_29 + b_1_2³·b_1_3⁸·b_3_12 + b_1_2⁴·b_3_11·b_7_54
       + b_1_2⁴·b_1_3³·b_7_54 + b_1_2⁴·b_1_3³·b_7_53 + b_1_2⁴·b_1_3⁴·b_3_11·b_3_12
       + b_1_2⁴·b_1_3⁷·b_3_12 + b_1_2⁵·b_1_3²·b_7_54 + b_1_2⁵·b_1_3²·b_7_53
       + b_1_2⁵·b_1_3⁶·b_3_11 + b_1_2⁶·b_1_3·b_7_54 + b_1_2⁶·b_1_3²·b_3_11·b_3_12
       + b_1_2⁶·b_1_3³·b_5_29 + b_1_2⁶·b_1_3⁵·b_3_12 + b_1_2⁶·b_1_3⁵·b_3_11
       + b_1_2⁷·b_1_3²·b_5_29 + b_1_2⁸·b_3_11·b_3_12 + b_1_2⁸·b_1_3·b_5_29
       + b_1_2⁸·b_1_3³·b_3_12 + b_1_2⁸·b_1_3³·b_3_11 + b_1_2⁹·b_5_29
       + b_1_2⁹·b_1_3²·b_3_12 + b_1_2⁹·b_1_3²·b_3_11 + b_1_2¹¹·b_3_12 + b_1_1⁷·b_7_54
       + b_1_1⁹·b_5_27 + b_1_1¹⁴ + b_1_1⁶·a_3_10·b_5_27 + a_1_0·b_1_1⁶·b_7_54
       + a_1_0·b_1_1⁸·b_5_29 + a_1_0·b_1_1⁸·b_5_27 + a_1_0·b_1_1¹²·b_1_3
       + a_1_0·b_1_1⁵·a_3_10·b_5_27 + a_1_0²·b_1_1⁷·b_5_27 + a_1_0²·b_1_1¹²
       + c_8_71·b_3_11·b_3_12 + c_8_71·b_1_3³·b_3_11 + c_8_71·b_1_2⁴·b_1_3²
       + c_8_71·b_1_2⁵·b_1_3 + c_4_19·b_3_11·b_7_54 + c_4_19·b_1_3³·b_7_54
       + c_4_19·b_1_3⁷·b_3_11 + c_4_19·b_1_2·b_1_3²·b_7_54 + c_4_19·b_1_2·b_1_3⁶·b_3_12
       + c_4_19·b_1_2·b_1_3⁹ + c_4_19·b_1_2²·b_1_3·b_7_54 + c_4_19·b_1_2²·b_1_3·b_7_53
       + c_4_19·b_1_2²·b_1_3⁸ + c_4_19·b_1_2³·b_1_3·b_3_11·b_3_12
       + c_4_19·b_1_2³·b_1_3²·b_5_29 + c_4_19·b_1_2³·b_1_3⁴·b_3_12
       + c_4_19·b_1_2³·b_1_3⁷ + c_4_19·b_1_2⁴·b_1_3⁶ + c_4_19·b_1_2⁵·b_5_29
       + c_4_19·b_1_2⁵·b_5_28 + c_4_19·b_1_2⁵·b_1_3²·b_3_12
       + c_4_19·b_1_2⁵·b_1_3²·b_3_11 + c_4_19·b_1_2⁶·b_1_3·b_3_11
       + c_4_19·b_1_2⁶·b_1_3⁴ + c_4_19·b_1_2⁷·b_3_12 + c_4_19·b_1_2⁷·b_3_11
       + c_4_19·b_1_2¹⁰ + c_4_19·b_1_1³·b_7_54 + c_4_19·b_1_1⁵·b_5_29
       + c_4_19·b_1_1⁵·b_5_27 + c_4_19·b_1_1⁹·b_1_3 + c_4_19·b_1_1¹⁰
       + c_8_71·a_1_0·b_1_1²·b_3_12 + c_4_19·b_1_1²·a_3_10·b_5_27
       + c_4_19·a_1_0·b_1_1⁴·b_5_27 + c_4_19·a_1_0·b_1_1⁶·b_3_12
       + c_4_19·a_1_0·b_1_1·a_3_10·b_5_27 + c_4_19·a_1_0²·b_1_1⁸
       + c_4_19·a_1_0²·a_3_10·b_5_27 + c_4_19·a_1_0²·b_1_1⁵·a_3_10
       + c_4_19·c_8_71·b_1_2² + c_4_19²·b_3_11·b_3_12 + c_4_19²·b_1_3·b_5_29
       + c_4_19²·b_1_3³·b_3_12 + c_4_19²·b_1_3³·b_3_11 + c_4_19²·b_1_2·b_5_29
       + c_4_19²·b_1_2·b_1_3²·b_3_11 + c_4_19²·b_1_2²·b_1_3·b_3_11
       + c_4_19²·b_1_2²·b_1_3⁴ + c_4_19²·b_1_1·b_5_29 + c_4_19²·b_1_1³·b_3_12
       + c_4_19²·b_1_1⁵·b_1_3 + c_4_19²·b_1_1⁶ + c_4_19²·b_1_1³·a_3_10
       + c_4_19²·a_1_0·b_1_1²·b_3_12 + c_4_19²·a_1_0·b_1_1⁴·b_1_3
       + c_4_19²·a_1_0²·b_1_1·a_3_10 + c_4_19³·b_1_3² + c_4_19³·b_1_2·b_1_3
       + c_4_19³·b_1_2² + c_4_19³·b_1_1·b_1_3 + c_4_19³·a_1_0·b_1_3
       + c_4_19³·a_1_0·b_1_1 + c_4_19³·a_1_0²
53. b_7_54² + b_7_53·b_7_54 + b_7_53² + b_1_3⁴·b_3_11·b_7_54
       + b_1_2·b_1_3⁷·b_3_11·b_3_12 + b_1_2²·b_1_3²·b_3_11·b_7_54
       + b_1_2²·b_1_3⁵·b_7_53 + b_1_2²·b_1_3⁹·b_3_12 + b_1_2²·b_1_3⁹·b_3_11
       + b_1_2³·b_1_3⁴·b_7_53 + b_1_2³·b_1_3⁵·b_3_11·b_3_12 + b_1_2³·b_1_3⁶·b_5_29
       + b_1_2⁴·b_3_11·b_7_54 + b_1_2⁴·b_1_3³·b_7_54 + b_1_2⁵·b_1_3³·b_3_11·b_3_12
       + b_1_2⁵·b_1_3⁴·b_5_29 + b_1_2⁵·b_1_3⁶·b_3_11 + b_1_2⁶·b_1_3·b_7_54
       + b_1_2⁶·b_1_3·b_7_53 + b_1_2⁶·b_1_3⁵·b_3_11 + b_1_2⁷·b_7_53
       + b_1_2⁷·b_1_3⁴·b_3_11 + b_1_2⁸·b_3_11·b_3_12 + b_1_2⁸·b_1_3³·b_3_11
       + b_1_2⁹·b_5_29 + b_1_2⁹·b_5_28 + b_1_2¹⁰·b_1_3·b_3_12 + b_1_2¹¹·b_3_11
       + b_1_1¹¹·b_3_12 + b_1_1¹⁴ + b_1_1⁶·a_3_10·b_5_27 + b_1_1¹¹·a_3_10
       + a_1_0·b_1_1⁸·b_5_29 + a_1_0·b_1_1¹⁰·b_3_12 + a_1_0·b_1_1¹²·b_1_3 + a_1_0·b_1_1¹³
       + a_1_0²·b_1_1⁷·b_5_27 + a_1_0²·b_1_1¹² + c_8_71·b_3_11·b_3_12
       + c_8_71·b_1_3³·b_3_12 + c_8_71·b_1_3⁶ + c_8_71·b_1_2·b_5_28
       + c_8_71·b_1_2²·b_1_3·b_3_12 + c_8_71·b_1_2²·b_1_3·b_3_11 + c_8_71·b_1_2²·b_1_3⁴
       + c_8_71·b_1_2³·b_3_12 + c_8_71·b_1_2³·b_3_11 + c_8_71·b_1_2⁴·b_1_3²
       + c_8_71·b_1_2⁵·b_1_3 + c_8_71·b_1_1⁶ + c_4_19·b_3_11·b_7_54
       + c_4_19·b_1_3⁴·b_3_11·b_3_12 + c_4_19·b_1_3⁷·b_3_12 + c_4_19·b_1_3⁷·b_3_11
       + c_4_19·b_1_3¹⁰ + c_4_19·b_1_2·b_1_3²·b_7_54 + c_4_19·b_1_2·b_1_3³·b_3_11·b_3_12
       + c_4_19·b_1_2·b_1_3⁶·b_3_11 + c_4_19·b_1_2²·b_1_3·b_7_53
       + c_4_19·b_1_2²·b_1_3³·b_5_29 + c_4_19·b_1_2²·b_1_3⁵·b_3_12
       + c_4_19·b_1_2²·b_1_3⁵·b_3_11 + c_4_19·b_1_2²·b_1_3⁸ + c_4_19·b_1_2³·b_7_53
       + c_4_19·b_1_2³·b_1_3²·b_5_29 + c_4_19·b_1_2³·b_1_3⁴·b_3_12
       + c_4_19·b_1_2³·b_1_3⁴·b_3_11 + c_4_19·b_1_2³·b_1_3⁷
       + c_4_19·b_1_2⁴·b_1_3³·b_3_11 + c_4_19·b_1_2⁵·b_1_3²·b_3_12
       + c_4_19·b_1_2⁵·b_1_3⁵ + c_4_19·b_1_2⁶·b_1_3·b_3_12 + c_4_19·b_1_2⁶·b_1_3·b_3_11
       + c_4_19·b_1_2⁷·b_3_11 + c_4_19·b_1_2⁷·b_1_3³ + c_4_19·b_1_2¹⁰
       + c_4_19·b_1_1⁵·b_5_29 + c_4_19·b_1_1⁵·b_5_27 + c_4_19·b_1_1⁷·b_3_12
       + c_4_19·b_1_1⁹·b_1_3 + c_8_71·a_1_0·b_1_1²·b_3_12 + c_4_19·b_1_1²·a_3_10·b_5_27
       + c_4_19·b_1_1⁷·a_3_10 + c_4_19·a_1_0·b_1_1⁴·b_5_29 + c_4_19·a_1_0·b_1_1⁶·b_3_12
       + c_4_19·a_1_0·b_1_1⁸·b_1_3 + c_8_71·a_1_0²·b_1_1⁴
       + c_4_19·a_1_0·b_1_1·a_3_10·b_5_27 + c_4_19·a_1_0·b_1_1⁶·a_3_10
       + c_8_71·a_1_0²·b_1_1·a_3_10 + c_4_19·a_1_0²·a_3_10·b_5_27 + c_4_19·c_8_71·b_1_3²
       + c_4_19·c_8_71·b_1_1² + c_4_19²·b_3_11·b_3_12 + c_4_19²·b_1_3·b_5_29
       + c_4_19²·b_1_3³·b_3_11 + c_4_19²·b_1_3⁶ + c_4_19²·b_1_2·b_5_29
       + c_4_19²·b_1_2·b_1_3⁵ + c_4_19²·b_1_2²·b_1_3·b_3_12
       + c_4_19²·b_1_2²·b_1_3·b_3_11 + c_4_19²·b_1_2²·b_1_3⁴ + c_4_19²·b_1_2³·b_3_12
       + c_4_19²·b_1_2³·b_3_11 + c_4_19²·b_1_2⁴·b_1_3² + c_4_19²·b_1_2⁵·b_1_3
       + c_4_19²·b_1_2⁶ + c_4_19²·b_1_1·b_5_29 + c_4_19²·b_1_1³·b_3_12
       + c_4_19²·b_1_1⁶ + c_4_19·c_8_71·a_1_0·b_1_3 + c_4_19·c_8_71·a_1_0·b_1_1
       + c_4_19²·b_1_1³·a_3_10 + c_4_19²·a_1_0·b_1_1⁵ + c_4_19²·a_1_0²·b_1_1⁴
       + c_4_19³·b_1_3² + c_4_19³·b_1_2·b_1_3 + c_4_19³·b_1_2² + c_4_19³·b_1_1·b_1_3
       + c_4_19³·a_1_0·b_1_3 + c_4_19³·a_1_0·b_1_1 + c_4_19³·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 14.
• The completion test was perfect: It applied in the last degree in which a generator or relation was found.
• The following is a filter regular homogeneous system of parameters:
  1. c_4_19, a Duflot regular element of degree 4
  2. c_8_71, a Duflot regular element of degree 8
  3. b_1_3² + b_1_2·b_1_3 + b_1_2² + b_1_1·b_1_3 + b_1_1², an element of degree 2
  4. b_1_3², an element of degree 2
• The Raw Filter Degree Type of that HSOP is [-1, -1, 7, 10, 12].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 2

1. a_1_0 → 0, an element of degree 1
2. b_1_1 → 0, an element of degree 1
3. b_1_2 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_10 → 0, an element of degree 3
6. b_3_11 → 0, an element of degree 3
7. b_3_12 → 0, an element of degree 3
8. c_4_19 → c_1_0⁴, an element of degree 4
9. b_5_27 → 0, an element of degree 5
10. b_5_28 → 0, an element of degree 5
11. b_5_29 → 0, an element of degree 5
12. b_7_53 → 0, an element of degree 7
13. b_7_54 → 0, an element of degree 7
14. c_8_71 → c_1_1⁸ + c_1_0⁸, an element of degree 8

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

1. a_1_0 → 0, an element of degree 1
2. b_1_1 → c_1_2, an element of degree 1
3. b_1_2 → 0, an element of degree 1
4. b_1_3 → c_1_2, an element of degree 1
5. a_3_10 → 0, an element of degree 3
6. b_3_11 → 0, an element of degree 3
7. b_3_12 → 0, an element of degree 3
8. c_4_19 → c_1_0²·c_1_2² + c_1_0⁴, an element of degree 4
9. b_5_27 → c_1_0·c_1_2⁴ + c_1_0⁴·c_1_2, an element of degree 5
10. b_5_28 → c_1_0·c_1_2⁴ + c_1_0⁴·c_1_2, an element of degree 5
11. b_5_29 → c_1_2⁵ + c_1_0·c_1_2⁴ + c_1_0⁴·c_1_2, an element of degree 5
12. b_7_53 → 0, an element of degree 7
13. b_7_54 → c_1_2⁷ + c_1_0·c_1_2⁶ + c_1_0²·c_1_2⁵, an element of degree 7
14. c_8_71 → c_1_2⁸ + c_1_1⁴·c_1_2⁴ + c_1_1⁸ + c_1_0⁴·c_1_2⁴ + c_1_0⁸, an element of degree 8

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

1. a_1_0 → 0, an element of degree 1
2. b_1_1 → c_1_2, an element of degree 1
3. b_1_2 → 0, an element of degree 1
4. b_1_3 → 0, an element of degree 1
5. a_3_10 → 0, an element of degree 3
6. b_3_11 → 0, an element of degree 3
7. b_3_12 → c_1_0·c_1_2² + c_1_0²·c_1_2, an element of degree 3
8. c_4_19 → c_1_0²·c_1_2² + c_1_0⁴, an element of degree 4
9. b_5_27 → c_1_2⁵ + c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
10. b_5_28 → c_1_0·c_1_2⁴ + c_1_0⁴·c_1_2, an element of degree 5
11. b_5_29 → c_1_2⁵ + c_1_1²·c_1_2³ + c_1_1⁴·c_1_2, an element of degree 5
12. b_7_53 → c_1_2⁷ + c_1_0³·c_1_2⁴ + c_1_0⁴·c_1_2³ + c_1_0⁵·c_1_2² + c_1_0⁶·c_1_2, an element of degree 7
13. b_7_54 → c_1_1²·c_1_2⁵ + c_1_1⁴·c_1_2³ + c_1_0·c_1_1²·c_1_2⁴ + c_1_0·c_1_1⁴·c_1_2²
       + c_1_0²·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2³ + c_1_0²·c_1_1⁴·c_1_2
       + c_1_0⁴·c_1_2³, an element of degree 7
14. c_8_71 → c_1_1²·c_1_2⁶ + c_1_1⁸ + c_1_0·c_1_2⁷ + c_1_0·c_1_1²·c_1_2⁵
       + c_1_0·c_1_1⁴·c_1_2³ + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_2²
       + c_1_0⁸, an element of degree 8

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

1. a_1_0 → 0, an element of degree 1
2. b_1_1 → 0, an element of degree 1
3. b_1_2 → c_1_2, an element of degree 1
4. b_1_3 → c_1_3, an element of degree 1
5. a_3_10 → 0, an element of degree 3
6. b_3_11 → c_1_0·c_1_2² + c_1_0²·c_1_2, an element of degree 3
7. b_3_12 → c_1_1·c_1_2² + c_1_1²·c_1_2 + c_1_0·c_1_3² + c_1_0·c_1_2² + c_1_0²·c_1_3
      + c_1_0²·c_1_2, an element of degree 3
8. c_4_19 → c_1_1·c_1_2²·c_1_3 + c_1_1·c_1_2³ + c_1_1²·c_1_2·c_1_3 + c_1_1²·c_1_2²
      + c_1_0·c_1_3³ + c_1_0·c_1_2²·c_1_3 + c_1_0·c_1_2³ + c_1_0⁴, an element of degree 4
9. b_5_27 → c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2³·c_1_3 + c_1_1·c_1_2⁴ + c_1_1²·c_1_2·c_1_3²
      + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³ + c_1_0·c_1_3⁴ + c_1_0·c_1_2·c_1_3³
      + c_1_0·c_1_2²·c_1_3² + c_1_0·c_1_2³·c_1_3 + c_1_0²·c_1_3³
      + c_1_0²·c_1_2·c_1_3² + c_1_0²·c_1_2³ + c_1_0⁴·c_1_2, an element of degree 5
10. b_5_28 → c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2³·c_1_3 + c_1_1²·c_1_2·c_1_3²
       + c_1_1²·c_1_2²·c_1_3 + c_1_1²·c_1_2³ + c_1_1⁴·c_1_2 + c_1_0·c_1_2⁴
       + c_1_0⁴·c_1_2, an element of degree 5
11. b_5_29 → c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2³·c_1_3 + c_1_1²·c_1_3³ + c_1_1²·c_1_2³
       + c_1_1⁴·c_1_3 + c_1_1⁴·c_1_2 + c_1_0·c_1_2·c_1_3³ + c_1_0²·c_1_3³
       + c_1_0²·c_1_2²·c_1_3 + c_1_0⁴·c_1_3, an element of degree 5
12. b_7_53 → c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3² + c_1_1·c_1_2⁵·c_1_3 + c_1_1·c_1_2⁶
       + c_1_1²·c_1_2·c_1_3⁴ + c_1_1²·c_1_2³·c_1_3² + c_1_1⁴·c_1_2²·c_1_3
       + c_1_1⁴·c_1_2³ + c_1_0·c_1_3⁶ + c_1_0·c_1_2·c_1_3⁵ + c_1_0·c_1_2²·c_1_3⁴
       + c_1_0·c_1_2³·c_1_3³ + c_1_0·c_1_2⁶ + c_1_0·c_1_1·c_1_2⁵
       + c_1_0·c_1_1⁴·c_1_2² + c_1_0²·c_1_3⁵ + c_1_0²·c_1_2²·c_1_3³
       + c_1_0²·c_1_2⁴·c_1_3 + c_1_0²·c_1_2⁵ + c_1_0²·c_1_1²·c_1_2³
       + c_1_0²·c_1_1⁴·c_1_2 + c_1_0³·c_1_3⁴ + c_1_0³·c_1_2²·c_1_3²
       + c_1_0³·c_1_2³·c_1_3 + c_1_0⁴·c_1_3³ + c_1_0⁴·c_1_2·c_1_3²
       + c_1_0⁴·c_1_1·c_1_2² + c_1_0⁴·c_1_1²·c_1_2 + c_1_0⁵·c_1_3² + c_1_0⁶·c_1_3, an element of degree 7
13. b_7_54 → c_1_1·c_1_2·c_1_3⁵ + c_1_1·c_1_2²·c_1_3⁴ + c_1_1·c_1_2³·c_1_3³
       + c_1_1·c_1_2⁴·c_1_3² + c_1_1²·c_1_3⁵ + c_1_1²·c_1_2·c_1_3⁴ + c_1_1³·c_1_2⁴
       + c_1_1⁴·c_1_3³ + c_1_1⁴·c_1_2·c_1_3² + c_1_1⁴·c_1_2³ + c_1_1⁵·c_1_2²
       + c_1_1⁶·c_1_2 + c_1_0·c_1_2²·c_1_3⁴ + c_1_0·c_1_2³·c_1_3³ + c_1_0·c_1_2⁵·c_1_3
       + c_1_0·c_1_1·c_1_2·c_1_3⁴ + c_1_0·c_1_1·c_1_2²·c_1_3³
       + c_1_0·c_1_1·c_1_2³·c_1_3² + c_1_0·c_1_1·c_1_2⁵ + c_1_0·c_1_1²·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2·c_1_3³ + c_1_0·c_1_1⁴·c_1_3² + c_1_0·c_1_1⁴·c_1_2²
       + c_1_0²·c_1_2·c_1_3⁴ + c_1_0²·c_1_2³·c_1_3² + c_1_0²·c_1_2⁴·c_1_3
       + c_1_0²·c_1_1·c_1_2·c_1_3³ + c_1_0²·c_1_1·c_1_2⁴ + c_1_0²·c_1_1²·c_1_3³
       + c_1_0²·c_1_1²·c_1_2²·c_1_3 + c_1_0²·c_1_1⁴·c_1_3 + c_1_0²·c_1_1⁴·c_1_2
       + c_1_0³·c_1_2·c_1_3³ + c_1_0³·c_1_2³·c_1_3 + c_1_0⁴·c_1_2·c_1_3²
       + c_1_0⁴·c_1_2²·c_1_3, an element of degree 7
14. c_8_71 → c_1_1·c_1_2²·c_1_3⁵ + c_1_1·c_1_2³·c_1_3⁴ + c_1_1·c_1_2⁴·c_1_3³
       + c_1_1·c_1_2⁵·c_1_3² + c_1_1·c_1_2⁶·c_1_3 + c_1_1²·c_1_2·c_1_3⁵
       + c_1_1²·c_1_2⁶ + c_1_1³·c_1_2⁴·c_1_3 + c_1_1⁴·c_1_3⁴ + c_1_1⁴·c_1_2·c_1_3³
       + c_1_1⁴·c_1_2²·c_1_3² + c_1_1⁵·c_1_2²·c_1_3 + c_1_1⁶·c_1_2·c_1_3 + c_1_1⁸
       + c_1_0·c_1_3⁷ + c_1_0·c_1_2²·c_1_3⁵ + c_1_0·c_1_2⁷ + c_1_0·c_1_1·c_1_2·c_1_3⁵
       + c_1_0·c_1_1·c_1_2²·c_1_3⁴ + c_1_0·c_1_1·c_1_2⁵·c_1_3 + c_1_0·c_1_1·c_1_2⁶
       + c_1_0·c_1_1²·c_1_3⁵ + c_1_0·c_1_1²·c_1_2·c_1_3⁴
       + c_1_0·c_1_1²·c_1_2²·c_1_3³ + c_1_0·c_1_1²·c_1_2⁵ + c_1_0·c_1_1⁴·c_1_3³
       + c_1_0·c_1_1⁴·c_1_2²·c_1_3 + c_1_0²·c_1_3⁶ + c_1_0²·c_1_2·c_1_3⁵
       + c_1_0²·c_1_2³·c_1_3³ + c_1_0²·c_1_2⁵·c_1_3 + c_1_0²·c_1_1·c_1_2·c_1_3⁴
       + c_1_0²·c_1_1·c_1_2²·c_1_3³ + c_1_0²·c_1_1·c_1_2⁵ + c_1_0²·c_1_1²·c_1_3⁴
       + c_1_0²·c_1_1²·c_1_2·c_1_3³ + c_1_0²·c_1_1²·c_1_2²·c_1_3²
       + c_1_0²·c_1_1²·c_1_2³·c_1_3 + c_1_0²·c_1_1²·c_1_2⁴ + c_1_0²·c_1_1⁴·c_1_3²
       + c_1_0²·c_1_1⁴·c_1_2·c_1_3 + c_1_0³·c_1_3⁵ + c_1_0³·c_1_2²·c_1_3³
       + c_1_0³·c_1_2⁵ + c_1_0⁴·c_1_2²·c_1_3² + c_1_0⁴·c_1_2³·c_1_3
       + c_1_0⁴·c_1_2⁴ + c_1_0⁴·c_1_1·c_1_2²·c_1_3 + c_1_0⁴·c_1_1²·c_1_2·c_1_3
       + c_1_0⁵·c_1_3³ + c_1_0⁵·c_1_2²·c_1_3 + c_1_0⁵·c_1_2³ + c_1_0⁶·c_1_3²
       + c_1_0⁶·c_1_2·c_1_3 + c_1_0⁶·c_1_2² + c_1_0⁸, an element of degree 8

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128