David J. Green

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Cohomology approximation of group number 59 of order 243

Based on a computation out to degree 20

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 243

General information on the group

• The group has 3 minimal generators and exponent 9.
• It is non-abelian.
• It has p-Rank 3.
• Its center has rank 1.
• It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 3.

Appoximate structure of the cohomology ring

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 243

Ring generators

Out to degree 20, the cohomology ring has 28 minimal generators of maximal degree 20:

1. a_1_0, a nilpotent element of degree 1
2. a_1_1, a nilpotent element of degree 1
3. a_1_2, a nilpotent element of degree 1
4. a_2_2, a nilpotent element of degree 2
5. a_2_3, a nilpotent element of degree 2
6. a_2_4, a nilpotent element of degree 2
7. b_2_5, an element of degree 2
8. a_3_8, a nilpotent element of degree 3
9. a_5_9, a nilpotent element of degree 5
10. a_6_9, a nilpotent element of degree 6
11. b_6_10, an element of degree 6
12. a_7_11, a nilpotent element of degree 7
13. a_7_12, a nilpotent element of degree 7
14. a_7_13, a nilpotent element of degree 7
15. b_8_15, an element of degree 8
16. b_8_16, an element of degree 8
17. b_8_17, an element of degree 8
18. a_9_20, a nilpotent element of degree 9
19. a_9_21, a nilpotent element of degree 9
20. b_10_24, an element of degree 10
21. a_11_25, a nilpotent element of degree 11
22. a_11_26, a nilpotent element of degree 11
23. a_12_22, a nilpotent element of degree 12
24. a_17_34, a nilpotent element of degree 17
25. a_18_27, a nilpotent element of degree 18
26. c_18_37, a Duflot regular element of degree 18
27. a_19_41, a nilpotent element of degree 19
28. a_20_36, a nilpotent element of degree 20

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 243

Ring relations out to degree 20

Note that there will be further "non-obvious" relations at least out to degree 40

There are 14 "obvious" relations:
   a_1_0², a_1_1², a_1_2², a_3_8², a_5_9², a_7_11², a_7_12², a_7_13², a_9_20², a_9_21², a_11_25², a_11_26², a_17_34², a_19_41²

Apart from that, there are 205 minimal relations of maximal degree 20:

1. a_1_0·a_1_1
2. a_2_2·a_1_0
3. a_2_3·a_1_0 − a_2_2·a_1_1
4. a_2_4·a_1_1 + a_2_3·a_1_1 − a_2_2·a_1_1
5. a_2_4·a_1_0 − a_2_3·a_1_1 + a_2_2·a_1_1
6. a_2_2²
7. a_2_2·a_2_3 − a_2_2·a_1_1·a_1_2
8.  − a_2_3² + a_2_2·a_2_4 + a_2_2·a_1_1·a_1_2
9. a_2_3·a_2_4 + a_2_3² + a_2_2·a_1_1·a_1_2
10. a_2_4² + a_2_3² − a_2_3·a_1_1·a_1_2
11. a_1_1·a_3_8 − a_2_3² + a_2_3·a_1_1·a_1_2 + a_2_2·a_1_1·a_1_2
12. a_1_0·a_3_8
13. a_2_2·b_2_5·a_1_1
14. a_2_3·b_2_5·a_1_1 + a_2_2·a_3_8
15. a_2_3·a_3_8 − a_2_3·b_2_5·a_1_1
16. a_2_4·a_3_8 − a_2_3·b_2_5·a_1_1 + a_2_2·a_2_4·a_1_2
17.  − a_2_2·a_2_4·b_2_5 + a_2_2·a_1_2·a_3_8
18. a_1_1·a_5_9
19. a_1_0·a_5_9 − a_2_2·a_2_4·b_2_5
20. b_2_5·a_5_9 − b_2_5²·a_3_8 − b_2_5³·a_1_1 − a_2_4·b_2_5²·a_1_2 − a_2_3·b_2_5²·a_1_2
       − a_2_2·b_2_5²·a_1_2
21. a_2_2·a_5_9 − a_2_2·b_2_5·a_3_8
22. a_2_3·a_5_9 − a_2_2·b_2_5·a_3_8
23. a_2_4·a_5_9 + a_2_2·b_2_5·a_3_8
24. a_6_9·a_1_1
25. a_6_9·a_1_0
26. b_6_10·a_1_0 − b_2_5³·a_1_1
27. a_3_8·a_5_9 + a_2_2·b_2_5·a_1_2·a_3_8
28. a_2_2·a_6_9 + a_2_2·b_2_5·a_1_2·a_3_8
29. a_2_3·a_6_9 + a_2_2·b_2_5·a_1_2·a_3_8
30. a_2_4·a_6_9 + a_2_2·b_2_5·a_1_2·a_3_8
31.  − a_2_3·b_2_5³ + a_2_2·b_6_10 − a_2_2·b_2_5³ − b_2_5³·a_1_1·a_1_2
32. b_2_5·a_6_9 − a_2_4·b_2_5³ + a_2_3·b_6_10 + a_2_3·b_2_5³ + a_2_2·b_2_5³
       + b_2_5³·a_1_1·a_1_2
33. b_2_5·a_6_9 − a_2_3·b_2_5³ + a_2_2·b_2_5³ + a_1_1·a_7_11 + b_6_10·a_1_1·a_1_2
       + b_2_5³·a_1_1·a_1_2 − a_2_2·b_2_5·a_1_2·a_3_8
34.  − a_2_2·b_2_5³ + a_1_0·a_7_11 − a_2_2·b_2_5·a_1_2·a_3_8
35.  − a_2_4·b_6_10 − a_2_4·b_2_5³ + a_2_2·b_2_5³ + a_1_1·a_7_12 − b_6_10·a_1_1·a_1_2
       + b_2_5³·a_1_1·a_1_2 + a_2_2·b_2_5·a_1_2·a_3_8
36. b_2_5·a_6_9 − a_2_3·b_2_5³ − a_2_2·b_2_5³ + a_1_0·a_7_12 + b_2_5³·a_1_1·a_1_2
       − a_2_2·b_2_5·a_1_2·a_3_8
37.  − a_2_4·b_6_10 + a_2_4·b_2_5³ − a_2_3·b_2_5³ + a_2_2·b_2_5³ + a_1_1·a_7_13
       − b_6_10·a_1_1·a_1_2 − b_2_5³·a_1_1·a_1_2 + a_2_2·b_2_5·a_1_2·a_3_8
38. a_2_3·b_2_5³ + a_2_2·b_2_5³ + a_1_0·a_7_13 + a_2_2·b_2_5·a_1_2·a_3_8
39. a_6_9·a_3_8
40.  − b_2_5·b_6_10·a_1_1 − b_2_5³·a_3_8 + b_2_5⁴·a_1_1 − a_2_4·a_7_11 + a_2_3·a_7_12
       + a_2_2·a_7_11 + a_1_1·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_11
41. a_2_4·a_7_12 − a_2_4·a_7_11 + a_2_3·a_7_11 − a_2_2·a_7_12 + a_2_2·a_7_11
       − a_1_1·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_11
42.  − a_2_3·a_7_11 + a_2_2·a_7_12 + a_2_2·a_7_11 + a_1_1·a_1_2·a_7_13 − a_1_1·a_1_2·a_7_12
       + a_1_0·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_11
43.  − b_2_5·b_6_10·a_1_1 − b_2_5³·a_3_8 + b_2_5⁴·a_1_1 + a_2_2·a_7_11 + a_1_0·a_1_2·a_7_13
44. a_2_3·a_7_11 + a_2_2·a_7_13 + a_2_2·a_7_11 − a_1_0·a_1_2·a_7_12 − a_1_0·a_1_2·a_7_11
45. a_2_4·a_7_11 + a_2_3·a_7_13 − a_2_3·a_7_11 − a_1_1·a_1_2·a_7_12 − a_1_0·a_1_2·a_7_12
       − a_1_0·a_1_2·a_7_11
46. b_2_5·b_6_10·a_1_1 + b_2_5³·a_3_8 − b_2_5⁴·a_1_1 + a_2_4·a_7_13 + a_1_1·a_1_2·a_7_12
       − a_1_0·a_1_2·a_7_12 − a_1_0·a_1_2·a_7_11
47. b_8_15·a_1_1 + b_2_5·b_6_10·a_1_1 + b_2_5³·a_3_8 − b_2_5⁴·a_1_1 + a_2_3·a_7_11
       + a_2_2·a_7_11 + a_1_1·a_1_2·a_7_12
48. b_8_15·a_1_0 + a_2_2·a_7_11 + a_1_0·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_11
49. b_8_16·a_1_1 − b_2_5⁴·a_1_1 + a_2_4·a_7_11 + a_2_2·a_7_12 + a_2_2·a_7_11
       + a_1_0·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_11
50. b_8_16·a_1_0 + b_2_5³·a_3_8 − b_2_5⁴·a_1_1 + a_2_3·a_7_11 − a_1_0·a_1_2·a_7_12
       + a_1_0·a_1_2·a_7_11
51. b_8_17·a_1_1 + b_6_10·a_3_8 − b_2_5⁴·a_1_1 + a_2_2·a_7_12 − a_2_2·a_7_11
       + a_1_0·a_1_2·a_7_12 + a_1_0·a_1_2·a_7_11
52. b_8_17·a_1_0 − b_2_5·b_6_10·a_1_1 + b_2_5³·a_3_8 + a_2_2·a_7_11 − a_1_0·a_1_2·a_7_12
53. a_3_8·a_7_11 − b_6_10·a_1_2·a_3_8 + b_2_5·a_1_1·a_7_12 − b_2_5³·a_1_2·a_3_8
       − b_2_5⁴·a_1_1·a_1_2 − a_2_2·a_1_2·a_7_11
54. a_2_2·b_8_15 + b_2_5·a_1_0·a_7_13 + b_2_5·a_1_0·a_7_12 + b_2_5·a_1_0·a_7_11
       − b_2_5³·a_1_2·a_3_8 + b_2_5⁴·a_1_1·a_1_2 + a_2_2·a_1_2·a_7_12
55. a_2_3·b_8_15 − a_3_8·a_7_11 + b_6_10·a_1_2·a_3_8 + b_2_5·a_1_1·a_7_13
       + b_2_5·a_1_0·a_7_12 + b_2_5·a_1_0·a_7_11 − b_2_5³·a_1_2·a_3_8 + b_2_5⁴·a_1_1·a_1_2
       + a_2_3·a_1_2·a_7_12
56. a_2_4·b_8_15 − a_3_8·a_7_13 + a_3_8·a_7_12 + b_2_5·a_1_0·a_7_13 + b_2_5·a_1_0·a_7_12
       + b_2_5·a_1_0·a_7_11 + b_2_5³·a_1_2·a_3_8 + b_2_5⁴·a_1_1·a_1_2 + a_2_3·a_1_2·a_7_12
       − a_2_2·a_1_2·a_7_12 − a_2_2·a_1_2·a_7_11
57. a_2_2·b_8_16 + a_3_8·a_7_11 − b_6_10·a_1_2·a_3_8 − b_2_5·a_1_0·a_7_12
       − b_2_5·a_1_0·a_7_11 + b_2_5⁴·a_1_1·a_1_2 + a_2_2·a_1_2·a_7_12 − a_2_2·a_1_2·a_7_11
58. a_2_3·b_8_16 − a_3_8·a_7_13 + a_3_8·a_7_12 + a_3_8·a_7_11 − b_6_10·a_1_2·a_3_8
       + b_2_5·a_1_1·a_7_13 − b_2_5·a_1_0·a_7_13 + b_2_5⁴·a_1_1·a_1_2 + a_2_3·a_1_2·a_7_12
       + a_2_2·a_1_2·a_7_11
59. a_2_4·b_8_16 + a_3_8·a_7_13 − a_3_8·a_7_12 − b_2_5·a_1_1·a_7_13 + b_2_5·a_1_0·a_7_13
       + b_2_5·a_1_0·a_7_12 + b_2_5·a_1_0·a_7_11 − a_2_3·a_1_2·a_7_12 + a_2_2·a_1_2·a_7_11
60. a_2_2·b_8_17 + a_3_8·a_7_11 − b_6_10·a_1_2·a_3_8 + b_2_5·a_1_1·a_7_13
       + b_2_5·a_1_0·a_7_13 + b_2_5·a_1_0·a_7_12 + b_2_5·a_1_0·a_7_11 + a_2_2·a_1_2·a_7_12
       + a_2_2·a_1_2·a_7_11
61. a_2_3·b_8_17 − b_2_5·a_1_0·a_7_13 − b_2_5·a_1_0·a_7_12 − b_2_5·a_1_0·a_7_11
       + a_2_3·a_1_2·a_7_12 − a_2_2·a_1_2·a_7_12 − a_2_2·a_1_2·a_7_11
62. a_2_4·b_8_17 + a_3_8·a_7_13 + b_6_10·a_1_2·a_3_8 − b_2_5·a_1_0·a_7_13
       − b_2_5³·a_1_2·a_3_8 − b_2_5⁴·a_1_1·a_1_2 − a_2_2·a_1_2·a_7_12
63.  − a_3_8·a_7_13 + a_3_8·a_7_12 + a_3_8·a_7_11 + a_1_1·a_9_20 − b_2_5·a_1_1·a_7_13
       − b_2_5·a_1_0·a_7_13 + b_2_5·a_1_0·a_7_12 + b_2_5·a_1_0·a_7_11 + b_2_5³·a_1_2·a_3_8
       − b_2_5⁴·a_1_1·a_1_2 − a_2_3·a_1_2·a_7_12 + a_2_2·a_1_2·a_7_11
64. a_1_0·a_9_20 + b_2_5·a_1_1·a_7_13 + b_2_5·a_1_0·a_7_13 + b_2_5·a_1_0·a_7_12
       − b_2_5·a_1_0·a_7_11 + b_2_5⁴·a_1_1·a_1_2 − a_2_3·a_1_2·a_7_12 + a_2_2·a_1_2·a_7_12
       + a_2_2·a_1_2·a_7_11
65. a_3_8·a_7_12 + a_1_1·a_9_21 − b_2_5·a_1_1·a_7_13 + b_2_5·a_1_0·a_7_13
       − b_2_5·a_1_0·a_7_12 − b_2_5·a_1_0·a_7_11 + b_2_5⁴·a_1_1·a_1_2 + a_2_2·a_1_2·a_7_12
       + a_2_2·a_1_2·a_7_11
66.  − a_3_8·a_7_11 + a_1_0·a_9_21 + b_6_10·a_1_2·a_3_8 − b_2_5·a_1_0·a_7_13
       + b_2_5·a_1_0·a_7_11 + b_2_5³·a_1_2·a_3_8 + b_2_5⁴·a_1_1·a_1_2
67. a_6_9·a_5_9
68.  − b_2_5·b_6_10·a_3_8 − b_2_5⁴·a_3_8 + a_2_2·b_2_5·a_7_12 − a_2_2·b_2_5·a_7_11
       − b_2_5·a_1_0·a_1_2·a_7_12 − b_2_5·a_1_0·a_1_2·a_7_11
69. b_8_17·a_3_8 − b_8_16·a_3_8 + b_8_15·a_3_8 + b_6_10·a_5_9 + b_2_5·b_6_10·a_3_8
       + b_2_5⁴·a_3_8 − b_2_5⁵·a_1_1 + b_2_5·a_1_1·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_13
70. b_8_16·a_3_8 − b_8_15·a_3_8 + b_2_5·b_6_10·a_3_8 − a_2_3·b_2_5·a_7_12
       + a_1_1·a_1_2·a_9_20 + b_2_5·a_1_1·a_1_2·a_7_13 − b_2_5·a_1_1·a_1_2·a_7_12
       − b_2_5·a_1_0·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_12 − b_2_5·a_1_0·a_1_2·a_7_11
71.  − b_8_16·a_3_8 + b_8_15·a_3_8 + b_2_5⁴·a_3_8 + a_2_2·a_9_20 − a_2_2·b_2_5·a_7_11
       − b_2_5·a_1_1·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_13
72.  − b_8_16·a_3_8 + b_8_15·a_3_8 + b_2_5⁴·a_3_8 + a_2_3·a_9_20 + a_2_2·b_2_5·a_7_11
73. b_8_16·a_3_8 + b_8_15·a_3_8 + b_2_5·b_6_10·a_3_8 + a_2_4·a_9_20 + a_2_2·b_2_5·a_7_11
       − b_2_5·a_1_1·a_1_2·a_7_12 + b_2_5·a_1_0·a_1_2·a_7_13 + b_2_5·a_1_0·a_1_2·a_7_12
       + b_2_5·a_1_0·a_1_2·a_7_11
74.  − b_8_15·a_3_8 + b_2_5·b_6_10·a_3_8 + b_2_5⁴·a_3_8 + a_2_3·b_2_5·a_7_12
       + a_1_1·a_1_2·a_9_21 + b_2_5·a_1_0·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_12
       − b_2_5·a_1_0·a_1_2·a_7_11
75. b_2_5·b_6_10·a_3_8 + b_2_5⁴·a_3_8 + a_2_3·b_2_5·a_7_12 + a_2_2·a_9_21
       + a_2_2·b_2_5·a_7_11 + b_2_5·a_1_1·a_1_2·a_7_13 − b_2_5·a_1_1·a_1_2·a_7_12
       − b_2_5·a_1_0·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_12 − b_2_5·a_1_0·a_1_2·a_7_11
76. a_2_3·a_9_21 + a_2_2·b_2_5·a_7_11 + b_2_5·a_1_1·a_1_2·a_7_13
       + b_2_5·a_1_1·a_1_2·a_7_12 + b_2_5·a_1_0·a_1_2·a_7_13
77.  − b_8_16·a_3_8 − b_8_15·a_3_8 − b_2_5·b_6_10·a_3_8 + a_2_4·a_9_21 + a_2_2·b_2_5·a_7_11
       + b_2_5·a_1_1·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_12
       − b_2_5·a_1_0·a_1_2·a_7_11
78. b_10_24·a_1_1 − b_6_10·a_5_9 + b_2_5⁴·a_3_8 − b_2_5⁵·a_1_1 − a_2_3·b_2_5·a_7_12
       + a_2_2·b_2_5·a_7_11 − b_2_5·a_1_1·a_1_2·a_7_13 + b_2_5·a_1_0·a_1_2·a_7_13
       − b_2_5·a_1_0·a_1_2·a_7_12 − b_2_5·a_1_0·a_1_2·a_7_11
79. b_10_24·a_1_0 + b_2_5·b_6_10·a_3_8 + b_2_5⁵·a_1_1 + a_2_3·b_2_5·a_7_12
       − b_2_5·a_1_0·a_1_2·a_7_13 − b_2_5·a_1_0·a_1_2·a_7_12 − b_2_5·a_1_0·a_1_2·a_7_11
80. a_6_9²
81. a_6_9·b_6_10 − a_5_9·a_7_12 − a_5_9·a_7_11 − b_2_5²·a_1_1·a_7_12 + b_2_5⁴·a_1_2·a_3_8
       − b_2_5⁵·a_1_1·a_1_2 + a_2_2·b_2_5·a_1_2·a_7_12 + a_2_2·b_2_5·a_1_2·a_7_11
82. a_5_9·a_7_11 + a_3_8·a_9_20 − b_2_5²·a_1_1·a_7_13 + b_2_5²·a_1_0·a_7_13
       − b_2_5²·a_1_0·a_7_12 − b_2_5²·a_1_0·a_7_11 − b_2_5⁴·a_1_2·a_3_8
       + b_2_5⁵·a_1_1·a_1_2
83.  − a_6_9·b_6_10 − a_5_9·a_7_13 − a_5_9·a_7_12 + b_6_10·a_1_2·a_5_9 + b_2_5·a_1_1·a_9_20
       − b_2_5²·a_1_1·a_7_13 + b_2_5²·a_1_0·a_7_13 + b_2_5⁴·a_1_2·a_3_8
       + b_2_5⁵·a_1_1·a_1_2
84. a_6_9·b_6_10 − a_5_9·a_7_12 + a_5_9·a_7_11 + b_6_10·a_1_2·a_5_9 + b_2_5²·a_1_1·a_7_12
       − b_2_5²·a_1_0·a_7_13 − b_2_5⁵·a_1_1·a_1_2 + a_2_2·a_1_2·a_9_20
       + a_2_2·b_2_5·a_1_2·a_7_11
85.  − a_5_9·a_7_13 − a_5_9·a_7_12 + a_3_8·a_9_21 − b_2_5²·a_1_1·a_7_13
       + b_2_5²·a_1_1·a_7_12 + b_2_5²·a_1_0·a_7_13 − b_2_5²·a_1_0·a_7_12
       − b_2_5²·a_1_0·a_7_11 − b_2_5⁵·a_1_1·a_1_2 − a_2_2·b_2_5·a_1_2·a_7_11
86. a_6_9·b_6_10 − a_5_9·a_7_12 − a_5_9·a_7_11 + b_2_5·a_1_1·a_9_21 − b_2_5²·a_1_1·a_7_13
       + b_2_5²·a_1_1·a_7_12 − b_2_5²·a_1_0·a_7_13 − b_2_5⁴·a_1_2·a_3_8
       − b_2_5⁵·a_1_1·a_1_2
87. a_2_2·b_10_24 − a_5_9·a_7_13 + a_5_9·a_7_12 − a_5_9·a_7_11 + b_6_10·a_1_2·a_5_9
       + b_2_5²·a_1_1·a_7_12 − b_2_5²·a_1_0·a_7_13 − b_2_5⁴·a_1_2·a_3_8
       + b_2_5⁵·a_1_1·a_1_2 + a_2_2·b_2_5·a_1_2·a_7_11
88. a_2_3·b_10_24 − a_5_9·a_7_13 + a_5_9·a_7_12 − a_5_9·a_7_11 + b_6_10·a_1_2·a_5_9
       + b_2_5²·a_1_1·a_7_13 + b_2_5²·a_1_0·a_7_12 + b_2_5²·a_1_0·a_7_11
       + b_2_5⁵·a_1_1·a_1_2
89.  − a_6_9·b_6_10 + a_2_4·b_10_24 + a_5_9·a_7_13 − a_5_9·a_7_12 + b_2_5²·a_1_1·a_7_13
       − b_2_5²·a_1_1·a_7_12 − b_2_5²·a_1_0·a_7_13 + b_2_5²·a_1_0·a_7_12
       + b_2_5²·a_1_0·a_7_11 − b_2_5⁵·a_1_1·a_1_2 − a_2_2·b_2_5·a_1_2·a_7_11
90. a_5_9·a_7_13 − a_5_9·a_7_12 + a_5_9·a_7_11 + a_1_1·a_11_25 − b_2_5²·a_1_1·a_7_13
       − b_2_5²·a_1_1·a_7_12 + b_2_5²·a_1_0·a_7_13 − b_2_5²·a_1_0·a_7_12
       − b_2_5²·a_1_0·a_7_11 − b_2_5⁴·a_1_2·a_3_8 + b_2_5⁵·a_1_1·a_1_2
       + a_2_2·b_2_5·a_1_2·a_7_11
91. a_1_0·a_11_25 − b_2_5²·a_1_1·a_7_13 + b_2_5²·a_1_1·a_7_12 + b_2_5²·a_1_0·a_7_12
       + b_2_5²·a_1_0·a_7_11 − b_2_5⁴·a_1_2·a_3_8 + b_2_5⁵·a_1_1·a_1_2
       − a_2_2·b_2_5·a_1_2·a_7_11
92.  − a_6_9·b_6_10 − a_5_9·a_7_13 + a_5_9·a_7_12 + a_5_9·a_7_11 + a_1_1·a_11_26
       + b_2_5²·a_1_1·a_7_13 + b_2_5²·a_1_1·a_7_12 − b_2_5²·a_1_0·a_7_13
       + a_2_2·b_2_5·a_1_2·a_7_11
93.  − a_6_9·b_6_10 − a_5_9·a_7_13 − a_5_9·a_7_12 − a_5_9·a_7_11 + a_1_0·a_11_26
       − b_6_10·a_1_2·a_5_9 − b_2_5²·a_1_1·a_7_13 + b_2_5²·a_1_1·a_7_12
       − b_2_5²·a_1_0·a_7_13 − b_2_5²·a_1_0·a_7_12 + b_2_5⁵·a_1_1·a_1_2
94.  − b_6_10·a_7_11 − b_6_10²·a_1_2 − b_6_10²·a_1_1 + b_2_5³·a_7_12 + b_2_5³·a_7_11
       + b_2_5⁶·a_1_1 − a_6_9·a_7_12 + a_6_9·a_7_11 − a_2_2·b_2_5²·a_7_12
       + a_2_2·b_2_5²·a_7_11 + b_2_5²·a_1_1·a_1_2·a_7_13 − b_2_5²·a_1_1·a_1_2·a_7_12
       + b_2_5²·a_1_0·a_1_2·a_7_11
95.  − a_6_9·a_7_12 − a_6_9·a_7_11 − a_2_2·b_2_5²·a_7_12 − a_2_2·b_2_5²·a_7_11
       − b_2_5²·a_1_1·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_13
       − b_2_5²·a_1_0·a_1_2·a_7_12 − b_2_5²·a_1_0·a_1_2·a_7_11
96. a_6_9·a_7_13 + a_6_9·a_7_12 − a_6_9·a_7_11 − b_2_5²·a_1_1·a_1_2·a_7_12
       − b_2_5²·a_1_0·a_1_2·a_7_12 − b_2_5²·a_1_0·a_1_2·a_7_11
97. b_8_16·a_5_9 − b_8_15·a_5_9 + b_6_10·a_7_11 + b_6_10²·a_1_2 + b_6_10²·a_1_1
       − b_2_5³·a_7_12 − b_2_5³·a_7_11 − b_2_5⁵·a_3_8 + b_2_5⁶·a_1_1 − a_6_9·a_7_12
       − a_2_2·b_2_5²·a_7_12 + b_2_5²·a_1_1·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_12
98.  − b_8_17·a_5_9 + b_8_15·a_5_9 + b_6_10²·a_1_1 + b_2_5⁵·a_3_8 + a_6_9·a_7_11
       + a_2_2·b_2_5²·a_7_12 − a_2_2·b_2_5²·a_7_11 + b_2_5·a_1_1·a_1_2·a_9_20
       + b_2_5²·a_1_1·a_1_2·a_7_12
99.  − b_8_15·a_5_9 − b_6_10·a_7_11 − b_6_10²·a_1_2 − b_6_10²·a_1_1 + b_2_5³·a_7_12
       + b_2_5³·a_7_11 + b_2_5⁶·a_1_1 − a_6_9·a_7_12 + a_2_2·b_2_5·a_9_20
       + a_2_2·b_2_5²·a_7_11 + b_2_5²·a_1_0·a_1_2·a_7_12 − b_2_5²·a_1_0·a_1_2·a_7_11
100. b_10_24·a_3_8 − b_8_17·a_5_9 − b_8_15·a_5_9 + b_6_10·a_7_11 + b_6_10²·a_1_2
        − b_2_5³·a_7_12 − b_2_5³·a_7_11 − b_2_5⁵·a_3_8 + b_2_5⁶·a_1_1 + a_2_2·b_2_5²·a_7_12
        − b_2_5²·a_1_0·a_1_2·a_7_11
101.  − b_8_17·a_5_9 + b_8_15·a_5_9 + b_6_10²·a_1_1 + b_2_5·a_11_25 − b_2_5·b_10_24·a_1_2
        − b_2_5²·a_9_21 + b_2_5²·a_9_20 − b_2_5²·b_8_16·a_1_2 + b_2_5³·a_7_13
        + b_2_5³·a_7_12 + b_2_5³·a_7_11 + b_2_5³·b_6_10·a_1_2 + b_2_5⁶·a_1_1 + a_6_9·a_7_12
        − a_6_9·a_7_11 + a_2_2·b_2_5²·a_7_12 + b_2_5²·a_1_1·a_1_2·a_7_12
        − b_2_5²·a_1_0·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_11
102.  − b_8_17·a_5_9 + b_6_10·a_7_11 + b_6_10²·a_1_2 − b_6_10²·a_1_1 − b_2_5³·a_7_12
        − b_2_5³·a_7_11 + b_2_5⁵·a_3_8 − b_2_5⁶·a_1_1 + a_6_9·a_7_11 + a_2_2·a_11_25
        + a_2_2·b_2_5²·a_7_12 − a_2_2·b_2_5²·a_7_11 − b_2_5²·a_1_0·a_1_2·a_7_12
        + b_2_5²·a_1_0·a_1_2·a_7_11
103.  − b_8_17·a_5_9 − b_8_15·a_5_9 + b_6_10·a_7_11 + b_6_10²·a_1_2 − b_6_10²·a_1_1
        − b_2_5³·a_7_12 − b_2_5³·a_7_11 + b_2_5⁵·a_3_8 − b_2_5⁶·a_1_1 + a_2_3·a_11_25
        + a_2_2·b_2_5²·a_7_12 + b_2_5²·a_1_1·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_12
104. b_8_17·a_5_9 + b_6_10·a_7_11 + b_6_10²·a_1_2 − b_2_5³·a_7_12 − b_2_5³·a_7_11
        − b_2_5⁵·a_3_8 − b_2_5⁶·a_1_1 + a_6_9·a_7_12 + a_2_4·a_11_25 − a_2_2·b_2_5²·a_7_12
        − b_2_5²·a_1_1·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_12
105.  − b_8_17·a_5_9 + b_8_15·a_5_9 − b_6_10·a_7_11 − b_6_10²·a_1_2 + b_2_5³·a_7_12
        + b_2_5³·a_7_11 + b_2_5⁵·a_3_8 + b_2_5⁶·a_1_1 − a_6_9·a_7_11 + a_2_2·b_2_5²·a_7_12
        + a_1_1·a_1_2·a_11_26 − b_2_5²·a_1_0·a_1_2·a_7_12
106. b_8_15·a_5_9 − a_6_9·a_7_12 + a_2_2·a_11_26 − a_2_2·b_2_5²·a_7_11
        − b_2_5²·a_1_1·a_1_2·a_7_12 − b_2_5²·a_1_0·a_1_2·a_7_12
        − b_2_5²·a_1_0·a_1_2·a_7_11
107. b_8_17·a_5_9 − b_8_15·a_5_9 − b_6_10²·a_1_1 − b_2_5⁵·a_3_8 + a_6_9·a_7_12
        + a_2_3·a_11_26 − a_2_2·b_2_5²·a_7_12 − a_2_2·b_2_5²·a_7_11
        − b_2_5²·a_1_1·a_1_2·a_7_12
108.  − b_8_17·a_5_9 + b_6_10·a_7_11 + b_6_10²·a_1_2 − b_6_10²·a_1_1 − b_2_5³·a_7_12
        − b_2_5³·a_7_11 + b_2_5⁵·a_3_8 − b_2_5⁶·a_1_1 − a_6_9·a_7_11 + a_2_4·a_11_26
        − a_2_2·b_2_5²·a_7_12 − b_2_5²·a_1_0·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_11
109. b_6_10·a_7_11 + b_6_10²·a_1_2 + b_6_10²·a_1_1 − b_2_5³·a_7_12 − b_2_5³·a_7_11
        − b_2_5⁶·a_1_1 + a_12_22·a_1_1 + b_2_5²·a_1_1·a_1_2·a_7_12
        − b_2_5²·a_1_0·a_1_2·a_7_12 + b_2_5²·a_1_0·a_1_2·a_7_11
110.  − b_8_17·a_5_9 + b_8_15·a_5_9 − b_6_10·a_7_11 − b_6_10²·a_1_2 + b_2_5³·a_7_12
        + b_2_5³·a_7_11 + b_2_5⁵·a_3_8 + b_2_5⁶·a_1_1 + a_12_22·a_1_0 − a_6_9·a_7_12
        − a_6_9·a_7_11 + b_2_5²·a_1_1·a_1_2·a_7_12 − b_2_5²·a_1_0·a_1_2·a_7_12
111. a_6_9·b_8_15 − a_7_11·a_7_12 − b_6_10·a_1_2·a_7_12 − b_6_10·a_1_1·a_7_12
        − b_2_5³·a_1_2·a_7_12 − b_2_5³·a_1_2·a_7_11 − b_2_5³·a_1_1·a_7_12
        + b_2_5⁵·a_1_2·a_3_8 − b_2_5⁶·a_1_1·a_1_2 − a_2_2·b_2_5²·a_1_2·a_7_11
112. b_6_10·b_8_15 − b_2_5·b_6_10² + b_2_5³·b_8_17 − b_2_5³·b_8_16 + b_2_5³·b_8_15
        + b_2_5⁴·b_6_10 + b_6_10·a_1_2·a_7_12 + b_6_10²·a_1_1·a_1_2 − b_2_5³·a_1_2·a_7_11
        − b_2_5³·a_1_0·a_7_12 − b_2_5⁵·a_1_2·a_3_8 − a_2_2·b_2_5²·a_1_2·a_7_12
113. a_6_9·b_8_17 − a_6_9·b_8_16 − b_6_10·a_1_1·a_7_12 + b_6_10²·a_1_1·a_1_2
        + b_2_5³·a_1_1·a_7_12 − b_2_5⁶·a_1_1·a_1_2 + a_2_2·b_2_5²·a_1_2·a_7_12
        − a_2_2·b_2_5²·a_1_2·a_7_11
114. a_6_9·b_8_16 + a_7_11·a_7_12 + a_5_9·a_9_20 + b_6_10·a_1_2·a_7_12 + b_6_10·a_1_1·a_7_12
        + b_6_10²·a_1_1·a_1_2 + b_2_5³·a_1_2·a_7_12 + b_2_5³·a_1_2·a_7_11
        − b_2_5³·a_1_0·a_7_12 − b_2_5³·a_1_0·a_7_11 − a_2_2·b_2_5²·a_1_2·a_7_12
        + a_2_2·b_2_5²·a_1_2·a_7_11
115.  − a_6_9·b_8_16 − a_7_11·a_7_12 − b_6_10·a_1_2·a_7_12 − b_6_10·a_1_1·a_7_12
        + b_2_5²·a_1_1·a_9_20 − b_2_5³·a_1_2·a_7_12 − b_2_5³·a_1_2·a_7_11
        + b_2_5³·a_1_0·a_7_12 + b_2_5³·a_1_0·a_7_11 + b_2_5⁵·a_1_2·a_3_8
        + b_2_5⁶·a_1_1·a_1_2 + a_2_2·b_2_5²·a_1_2·a_7_11
116. a_7_11·a_7_12 + b_6_10·a_1_2·a_7_12 + b_6_10·a_1_1·a_7_12 + b_2_5³·a_1_2·a_7_12
        + b_2_5³·a_1_2·a_7_11 + b_2_5³·a_1_1·a_7_12 − b_2_5⁵·a_1_2·a_3_8
        + b_2_5⁶·a_1_1·a_1_2 + a_2_2·b_2_5·a_1_2·a_9_20 − a_2_2·b_2_5²·a_1_2·a_7_12
        + a_2_2·b_2_5²·a_1_2·a_7_11
117. a_6_9·b_8_16 + a_5_9·a_9_21 − b_6_10·a_1_1·a_7_12 − b_2_5³·a_1_1·a_7_12
        + b_2_5³·a_1_0·a_7_12 + b_2_5³·a_1_0·a_7_11 + b_2_5⁵·a_1_2·a_3_8
        + b_2_5⁶·a_1_1·a_1_2 − a_2_2·b_2_5²·a_1_2·a_7_12
118.  − b_6_10·b_8_16 − b_6_10·b_8_15 + b_2_5·b_6_10² + b_2_5²·b_10_24 + b_2_5³·b_8_15
        + b_2_5⁴·b_6_10 − a_7_11·a_7_13 − a_7_11·a_7_12 + b_6_10·a_1_2·a_7_13
        + b_6_10·a_1_2·a_7_12 − b_6_10·a_1_1·a_7_12 − b_2_5³·a_1_2·a_7_13
        + b_2_5³·a_1_2·a_7_12 + b_2_5³·a_1_2·a_7_11 + b_2_5³·a_1_0·a_7_12
        + b_2_5⁶·a_1_1·a_1_2 − a_2_2·b_2_5²·a_1_2·a_7_12
119. a_6_9·b_8_16 − a_7_11·a_7_12 + a_3_8·a_11_25 − b_6_10·a_1_2·a_7_12 − b_6_10·a_1_1·a_7_12
        + b_6_10²·a_1_1·a_1_2 − b_2_5³·a_1_2·a_7_12 − b_2_5³·a_1_2·a_7_11
        − b_2_5³·a_1_1·a_7_12 − b_2_5³·a_1_0·a_7_12 − b_2_5³·a_1_0·a_7_11
        + b_2_5⁵·a_1_2·a_3_8 − b_2_5⁶·a_1_1·a_1_2 + a_2_2·b_2_5²·a_1_2·a_7_12
120.  − a_6_9·b_8_16 − a_7_11·a_7_12 + a_3_8·a_11_26 − b_6_10·a_1_2·a_7_12
        − b_2_5³·a_1_2·a_7_12 − b_2_5³·a_1_2·a_7_11 − b_2_5³·a_1_1·a_7_12
        + b_2_5³·a_1_0·a_7_12 + b_2_5³·a_1_0·a_7_11 − a_2_2·b_2_5²·a_1_2·a_7_11
121.  − a_6_9·b_8_16 + b_2_5·a_12_22 + a_7_11·a_7_13 + b_6_10·a_1_2·a_7_13
        + b_6_10·a_1_1·a_7_12 − b_2_5·a_1_2·a_11_26 + b_2_5²·a_1_2·a_9_20
        + b_2_5³·a_1_2·a_7_13 − b_2_5³·a_1_2·a_7_12 − b_2_5³·a_1_2·a_7_11
        − b_2_5³·a_1_1·a_7_12 + b_2_5³·a_1_0·a_7_12 + b_2_5³·a_1_0·a_7_11
        + b_2_5⁵·a_1_2·a_3_8 − b_2_5⁶·a_1_1·a_1_2 + a_2_2·b_2_5²·a_1_2·a_7_12
122.  − a_7_11·a_7_12 − b_6_10·a_1_2·a_7_12 − b_6_10·a_1_1·a_7_12 − b_2_5³·a_1_2·a_7_12
        − b_2_5³·a_1_2·a_7_11 − b_2_5³·a_1_1·a_7_12 + b_2_5⁵·a_1_2·a_3_8
        − b_2_5⁶·a_1_1·a_1_2 + a_2_2·a_12_22 + a_2_2·b_2_5²·a_1_2·a_7_12
        + a_2_2·b_2_5²·a_1_2·a_7_11
123.  − a_7_11·a_7_12 − b_6_10·a_1_2·a_7_12 − b_6_10·a_1_1·a_7_12 − b_2_5³·a_1_2·a_7_12
        − b_2_5³·a_1_2·a_7_11 − b_2_5³·a_1_1·a_7_12 + b_2_5⁵·a_1_2·a_3_8
        − b_2_5⁶·a_1_1·a_1_2 + a_2_3·a_12_22 − a_2_2·b_2_5²·a_1_2·a_7_11
124. a_7_11·a_7_12 + b_6_10·a_1_2·a_7_12 + b_6_10·a_1_1·a_7_12 + b_2_5³·a_1_2·a_7_12
        + b_2_5³·a_1_2·a_7_11 + b_2_5³·a_1_1·a_7_12 − b_2_5⁵·a_1_2·a_3_8
        + b_2_5⁶·a_1_1·a_1_2 + a_2_4·a_12_22 − a_2_2·b_2_5²·a_1_2·a_7_12
        + a_2_2·b_2_5²·a_1_2·a_7_11
125.  − b_8_16·a_7_11 − b_8_15·a_7_13 + b_2_5·b_6_10·a_7_12 − b_2_5³·b_8_17·a_1_2
        + b_2_5³·b_8_16·a_1_2 − b_2_5³·b_8_15·a_1_2 + b_2_5⁴·a_7_12 + b_2_5⁴·a_7_11
        + b_2_5⁴·b_6_10·a_1_2 − a_1_2·a_7_12·a_7_13 + a_1_2·a_7_11·a_7_13
        + b_2_5²·a_1_1·a_1_2·a_9_20 − b_2_5³·a_1_1·a_1_2·a_7_12
        + b_2_5³·a_1_0·a_1_2·a_7_11
126. b_8_17·a_7_11 + b_8_16·a_7_11 − b_8_15·a_7_12 − b_8_15·a_7_11 + b_6_10·b_8_17·a_1_2
        − b_6_10²·a_3_8 + b_2_5·b_6_10·a_7_13 − b_2_5·b_6_10²·a_1_2 + b_2_5³·a_9_20
        + b_2_5³·b_8_17·a_1_2 − b_2_5³·b_8_16·a_1_2 − b_2_5³·b_8_15·a_1_2 + b_2_5⁴·a_7_13
        − b_2_5⁴·a_7_12 + b_2_5⁷·a_1_1 − b_6_10·a_1_1·a_1_2·a_7_12
        + b_2_5³·a_1_1·a_1_2·a_7_12 + b_2_5³·a_1_0·a_1_2·a_7_12
        − b_2_5³·a_1_0·a_1_2·a_7_11
127.  − b_8_17·a_7_13 + b_8_17·a_7_12 − b_8_16·a_7_11 − b_8_15·a_7_12 + b_8_15·a_7_11
        + b_6_10·a_9_20 + b_6_10·b_8_17·a_1_2 − b_2_5·b_6_10·a_7_12 + b_2_5⁴·b_6_10·a_1_2
        + b_2_5⁷·a_1_1 − a_1_2·a_7_12·a_7_13 − a_1_2·a_7_11·a_7_13 − b_6_10·a_1_1·a_1_2·a_7_12
        − b_2_5³·a_1_1·a_1_2·a_7_12 + b_2_5³·a_1_0·a_1_2·a_7_12
        − b_2_5³·a_1_0·a_1_2·a_7_11
128. a_6_9·a_9_20 − b_6_10·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_0·a_1_2·a_7_12
        − b_2_5³·a_1_0·a_1_2·a_7_11
129.  − b_8_17·a_7_11 − b_8_16·a_7_11 − b_8_15·a_7_13 − b_8_15·a_7_11 − b_6_10·b_8_17·a_1_2
        + b_6_10²·a_3_8 + b_2_5·b_6_10·a_7_12 − b_2_5·b_6_10²·a_1_2 + b_2_5³·a_9_21
        − b_2_5³·b_8_17·a_1_2 + b_2_5³·b_8_15·a_1_2 − b_2_5⁴·a_7_13 − b_2_5⁴·a_7_12
        + b_2_5⁴·b_6_10·a_1_2 + b_2_5⁷·a_1_1 − a_1_2·a_7_12·a_7_13 − a_1_2·a_7_11·a_7_13
        − b_6_10·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_1·a_1_2·a_7_12
130.  − b_8_17·a_7_13 + b_8_17·a_7_11 − b_8_16·a_7_13 − b_8_16·a_7_12 − b_8_16·a_7_11
        + b_8_15·a_7_12 − b_8_15·a_7_11 + b_6_10·a_9_21 + b_6_10·b_8_17·a_1_2
        + b_2_5·b_6_10·a_7_13 − b_2_5·b_6_10²·a_1_2 + b_2_5⁴·a_7_12 + b_2_5⁴·a_7_11
        + b_2_5⁴·b_6_10·a_1_2 + b_2_5⁶·a_3_8 + b_2_5⁷·a_1_1 − a_1_2·a_7_12·a_7_13
        + b_6_10·a_1_1·a_1_2·a_7_12 + b_2_5³·a_1_0·a_1_2·a_7_12
131. b_8_16·a_7_11 + b_8_15·a_7_13 − b_2_5·b_6_10·a_7_12 + b_2_5³·b_8_17·a_1_2
        − b_2_5³·b_8_16·a_1_2 + b_2_5³·b_8_15·a_1_2 − b_2_5⁴·a_7_12 − b_2_5⁴·a_7_11
        − b_2_5⁴·b_6_10·a_1_2 + a_6_9·a_9_21 + a_1_2·a_7_12·a_7_13 − a_1_2·a_7_11·a_7_13
        + b_6_10·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_0·a_1_2·a_7_11
132. b_10_24·a_5_9 − b_8_16·a_7_11 − b_8_15·a_7_13 + b_6_10²·a_3_8 + b_2_5·b_6_10·a_7_12
        − b_2_5³·b_8_17·a_1_2 + b_2_5³·b_8_16·a_1_2 − b_2_5³·b_8_15·a_1_2 + b_2_5⁴·a_7_12
        + b_2_5⁴·a_7_11 + b_2_5⁴·b_6_10·a_1_2 + b_2_5⁷·a_1_1 − a_1_2·a_7_12·a_7_13
        + a_1_2·a_7_11·a_7_13 + b_2_5³·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_0·a_1_2·a_7_12
133.  − b_8_17·a_7_11 − b_8_15·a_7_13 − b_8_15·a_7_12 + b_8_15·a_7_11 − b_6_10·b_8_17·a_1_2
        + b_6_10²·a_3_8 − b_2_5·b_6_10·a_7_12 + b_2_5·b_6_10²·a_1_2 + b_2_5²·b_10_24·a_1_2
        + b_2_5³·b_8_17·a_1_2 − b_2_5³·b_8_16·a_1_2 − b_2_5³·b_8_15·a_1_2 + b_2_5⁴·a_7_12
        + b_2_5⁴·a_7_11 + b_2_5⁴·b_6_10·a_1_2 − b_2_5⁶·a_3_8 − a_1_2·a_7_12·a_7_13
        − b_6_10·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_1·a_1_2·a_7_12
134. b_8_17·a_7_11 + b_8_16·a_7_13 + b_8_16·a_7_12 − b_8_15·a_7_13 + b_8_15·a_7_12
        + b_8_15·a_7_11 + b_6_10·b_8_17·a_1_2 − b_6_10²·a_3_8 + b_2_5·b_6_10·a_7_13
        − b_2_5·b_6_10·a_7_12 + b_2_5·b_6_10²·a_1_2 + b_2_5²·a_11_26 − b_2_5³·b_8_17·a_1_2
        − b_2_5³·b_8_16·a_1_2 + b_2_5⁴·a_7_13 − b_2_5⁴·a_7_12 − b_2_5⁴·b_6_10·a_1_2
        + b_2_5⁶·a_3_8 + a_1_2·a_7_12·a_7_13 + a_1_2·a_7_11·a_7_13
        + b_2_5³·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_0·a_1_2·a_7_12
        + b_2_5³·a_1_0·a_1_2·a_7_11
135. b_8_16·a_7_11 + b_8_15·a_7_13 − b_2_5·b_6_10·a_7_12 + b_2_5³·b_8_17·a_1_2
        − b_2_5³·b_8_16·a_1_2 + b_2_5³·b_8_15·a_1_2 − b_2_5⁴·a_7_12 − b_2_5⁴·a_7_11
        − b_2_5⁴·b_6_10·a_1_2 + a_12_22·a_3_8 + a_1_2·a_7_12·a_7_13 − a_1_2·a_7_11·a_7_13
        + b_6_10·a_1_1·a_1_2·a_7_12 + b_2_5³·a_1_1·a_1_2·a_7_12 − b_2_5³·a_1_0·a_1_2·a_7_11
136. a_7_11·a_9_20 + b_8_16·a_1_2·a_7_12 − b_8_15·a_1_2·a_7_12 + b_6_10·a_1_2·a_9_20
        − b_6_10²·a_1_2·a_3_8 + b_2_5·a_7_12·a_7_13 − b_2_5·a_7_11·a_7_13
        − b_2_5·b_6_10·a_1_2·a_7_13 + b_2_5·b_6_10·a_1_2·a_7_12 + b_2_5³·a_1_2·a_9_20
        + b_2_5⁴·a_1_2·a_7_13 + b_2_5⁴·a_1_2·a_7_12 − b_2_5⁴·a_1_2·a_7_11
        − b_2_5⁴·a_1_1·a_7_12 − b_2_5⁴·a_1_0·a_7_12 − b_2_5⁴·a_1_0·a_7_11
        + b_2_5⁶·a_1_2·a_3_8
137. b_8_16·b_8_17 − b_8_16² − b_8_15·b_8_17 + b_8_15·b_8_16 + b_8_15²
        + b_2_5·b_6_10·b_8_17 + b_2_5²·b_6_10² + b_2_5⁴·b_8_17 + b_2_5⁴·b_8_15
        + a_7_13·a_9_21 + a_7_13·a_9_20 − a_7_12·a_9_20 − b_8_15·a_1_2·a_7_12
        + b_6_10²·a_1_2·a_3_8 + b_2_5·a_7_11·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_12
        − b_2_5⁴·a_1_2·a_7_13 + b_2_5⁴·a_1_2·a_7_12 − b_2_5⁴·a_1_2·a_7_11
        − b_2_5⁴·a_1_1·a_7_12 − b_2_5⁴·a_1_0·a_7_12 + b_2_5⁴·a_1_0·a_7_11
        + b_2_5⁶·a_1_2·a_3_8 − b_2_5⁷·a_1_1·a_1_2
138.  − b_8_15² + b_2_5²·b_6_10² + b_2_5⁴·b_8_17 + b_2_5⁴·b_8_15 + b_2_5⁵·b_6_10
        + b_8_15·a_1_2·a_7_12 − b_2_5·a_7_11·a_7_13 + b_2_5·b_6_10·a_1_2·a_7_13
        + b_2_5·b_6_10·a_1_2·a_7_12 + b_2_5³·a_1_2·a_9_21 + b_2_5³·a_1_2·a_9_20
        − b_2_5⁴·a_1_2·a_7_13 + b_2_5⁴·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_7_11
        − b_2_5⁴·a_1_1·a_7_12 − b_2_5⁴·a_1_0·a_7_12 + b_2_5⁶·a_1_2·a_3_8
        − b_2_5⁷·a_1_1·a_1_2
139.  − b_8_16·b_8_17 − b_8_16² + b_8_15·b_8_17 − b_8_15·b_8_16 − b_8_15²
        − b_2_5·b_6_10·b_8_17 − b_2_5²·b_6_10² + b_2_5⁴·b_8_17 + b_2_5⁴·b_8_16
        + b_2_5⁴·b_8_15 − b_2_5⁵·b_6_10 − a_7_13·a_9_20 + a_7_12·a_9_20 + b_8_15·a_1_2·a_7_12
        + b_6_10·a_1_1·a_9_21 − b_6_10²·a_1_2·a_3_8 + b_2_5·a_7_12·a_7_13
        − b_2_5·a_7_11·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_12
        + b_2_5⁴·a_1_2·a_7_13 + b_2_5⁶·a_1_2·a_3_8
140. b_8_16² + b_8_15·b_8_17 + b_8_15·b_8_16 − b_2_5·b_6_10·b_8_17 + b_2_5⁴·b_8_16
        − b_2_5⁵·b_6_10 + a_7_13·a_9_20 − a_7_12·a_9_20 − b_8_16·a_1_2·a_7_12
        + b_6_10·a_1_2·a_9_21 + b_6_10·a_1_2·a_9_20 − b_6_10²·a_1_2·a_3_8
        − b_2_5·a_7_11·a_7_13 + b_2_5·b_6_10·a_1_2·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_12
        − b_2_5³·a_1_2·a_9_20 + b_2_5⁴·a_1_2·a_7_13 + b_2_5⁴·a_1_2·a_7_11
        − b_2_5⁴·a_1_1·a_7_12 − b_2_5⁴·a_1_0·a_7_12 − b_2_5⁷·a_1_1·a_1_2
141. b_8_16·b_8_17 + b_8_15·b_8_17 + b_8_15² − b_2_5·b_6_10·b_8_17 + b_2_5²·b_6_10²
        − b_2_5⁴·b_8_17 + b_2_5⁴·b_8_16 − b_2_5⁴·b_8_15 − b_2_5⁵·b_6_10 + a_7_11·a_9_21
        + b_8_16·a_1_2·a_7_12 − b_8_15·a_1_2·a_7_12 − b_6_10·a_1_2·a_9_20
        − b_6_10²·a_1_2·a_3_8 − b_2_5·a_7_12·a_7_13 + b_2_5·a_7_11·a_7_13
        + b_2_5·b_6_10·a_1_2·a_7_12 − b_2_5³·a_1_2·a_9_20 − b_2_5⁴·a_1_2·a_7_13
        + b_2_5⁴·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_7_11 + b_2_5⁴·a_1_1·a_7_12
        − b_2_5⁴·a_1_0·a_7_12 + b_2_5⁴·a_1_0·a_7_11 + b_2_5⁶·a_1_2·a_3_8
        + b_2_5⁷·a_1_1·a_1_2
142. b_8_16·b_8_17 + b_8_15·b_8_17 + b_8_15² − b_2_5·b_6_10·b_8_17 + b_2_5²·b_6_10²
        − b_2_5⁴·b_8_17 + b_2_5⁴·b_8_16 − b_2_5⁴·b_8_15 − b_2_5⁵·b_6_10 − a_7_13·a_9_20
        + a_7_12·a_9_21 − b_6_10·a_1_2·a_9_20 − b_2_5·a_7_12·a_7_13 + b_2_5·a_7_11·a_7_13
        + b_2_5·b_6_10·a_1_2·a_7_12 + b_2_5³·a_1_2·a_9_20 + b_2_5⁴·a_1_2·a_7_13
        − b_2_5⁴·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_7_11 − b_2_5⁴·a_1_0·a_7_12
        + b_2_5⁴·a_1_0·a_7_11 − b_2_5⁶·a_1_2·a_3_8
143. b_8_16² − b_8_15·b_8_16 + b_8_15² − b_2_5²·b_6_10² + b_2_5³·b_10_24
        − b_2_5⁴·b_8_17 − b_2_5⁵·b_6_10 + a_7_13·a_9_20 − a_7_12·a_9_20 − b_8_15·a_1_2·a_7_12
        − b_6_10·a_1_2·a_9_20 + b_2_5·a_7_12·a_7_13 + b_2_5·a_7_11·a_7_13
        − b_2_5·b_6_10·a_1_2·a_7_13 − b_2_5³·a_1_2·a_9_20 − b_2_5⁴·a_1_2·a_7_13
        + b_2_5⁴·a_1_2·a_7_11 + b_2_5⁴·a_1_0·a_7_12 − b_2_5⁶·a_1_2·a_3_8
144.  − b_8_17² − b_8_16·b_8_17 + b_8_16² + b_8_15·b_8_17 + b_6_10·b_10_24
        − b_2_5·b_6_10·b_8_17 − b_2_5⁴·b_8_16 + b_2_5⁵·b_6_10 + a_7_13·a_9_20 − a_7_12·a_9_20
        + b_8_15·a_1_2·a_7_12 − b_6_10·a_1_2·a_9_20 + b_6_10²·a_1_2·a_3_8
        − b_2_5·a_7_12·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_12
        − b_2_5³·a_1_2·a_9_20 − b_2_5⁴·a_1_0·a_7_11 + b_2_5⁶·a_1_2·a_3_8
145.  − b_8_16·b_8_17 − b_8_16² + b_8_15·b_8_17 − b_8_15·b_8_16 − b_8_15²
        − b_2_5·b_6_10·b_8_17 − b_2_5²·b_6_10² + b_2_5⁴·b_8_17 + b_2_5⁴·b_8_16
        + b_2_5⁴·b_8_15 − b_2_5⁵·b_6_10 + a_6_9·b_10_24 − a_7_13·a_9_20 + a_7_12·a_9_20
        + b_8_15·a_1_2·a_7_12 + b_2_5·a_7_12·a_7_13 − b_2_5·a_7_11·a_7_13
        − b_2_5·b_6_10·a_1_2·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_7_13
        − b_2_5⁴·a_1_1·a_7_12 − b_2_5⁴·a_1_0·a_7_12 − b_2_5⁴·a_1_0·a_7_11
        − b_2_5⁷·a_1_1·a_1_2
146. a_5_9·a_11_25 − b_6_10²·a_1_2·a_3_8 + b_2_5⁴·a_1_1·a_7_12 − b_2_5⁴·a_1_0·a_7_12
        − b_2_5⁴·a_1_0·a_7_11 − b_2_5⁷·a_1_1·a_1_2
147.  − b_8_16·b_8_17 − b_8_16² + b_8_15·b_8_17 − b_8_15·b_8_16 − b_8_15²
        − b_2_5·b_6_10·b_8_17 − b_2_5²·b_6_10² + b_2_5⁴·b_8_17 + b_2_5⁴·b_8_16
        + b_2_5⁴·b_8_15 − b_2_5⁵·b_6_10 − a_7_13·a_9_20 + a_7_12·a_9_20 + a_5_9·a_11_26
        + b_8_15·a_1_2·a_7_12 − b_6_10²·a_1_2·a_3_8 + b_2_5·a_7_12·a_7_13
        − b_2_5·a_7_11·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_13 − b_2_5·b_6_10·a_1_2·a_7_12
        + b_2_5⁴·a_1_2·a_7_13 − b_2_5⁴·a_1_0·a_7_12 − b_2_5⁴·a_1_0·a_7_11
        + b_2_5⁶·a_1_2·a_3_8 − b_2_5⁷·a_1_1·a_1_2
148. b_8_16² + b_8_15² − b_2_5²·b_6_10² + b_2_5⁴·b_8_17 + b_2_5⁴·b_8_16
        + b_2_5⁴·b_8_15 + b_2_5⁵·b_6_10 + a_7_13·a_9_20 − a_7_12·a_9_20 + b_8_16·a_1_2·a_7_12
        + b_8_15·a_1_2·a_7_12 − b_6_10·a_1_2·a_9_20 − b_2_5·a_7_12·a_7_13
        + b_2_5²·a_1_2·a_11_26 − b_2_5³·a_1_2·a_9_20 + b_2_5⁴·a_1_2·a_7_13
        − b_2_5⁴·a_1_2·a_7_12 − b_2_5⁴·a_1_2·a_7_11 + b_2_5⁴·a_1_1·a_7_12
        + b_2_5⁴·a_1_0·a_7_12 − b_2_5⁴·a_1_0·a_7_11 + b_2_5⁶·a_1_2·a_3_8
        − b_2_5⁷·a_1_1·a_1_2
149. b_8_15·a_9_20 − b_2_5·b_8_16·a_7_12 − b_2_5·b_8_15·a_7_12 + b_2_5·b_6_10·b_8_17·a_1_2
        − b_2_5²·b_6_10·a_7_12 + b_2_5²·b_6_10²·a_1_2 + b_2_5⁴·b_8_16·a_1_2
        − b_2_5⁵·b_6_10·a_1_2 + a_1_2·a_7_12·a_9_21 − b_6_10·a_1_1·a_1_2·a_9_21
        − b_2_5·a_1_2·a_7_12·a_7_13 + b_2_5⁴·a_1_1·a_1_2·a_7_12 − b_2_5⁴·a_1_0·a_1_2·a_7_11
150. b_8_16·a_9_21 − b_8_16·a_9_20 + b_8_15·a_9_20 − b_2_5·b_6_10·a_9_20
        − b_2_5²·b_6_10·a_7_13 − b_2_5²·b_6_10²·a_1_2 + b_2_5⁴·a_9_20
        + b_2_5⁴·b_8_17·a_1_2 − b_2_5⁴·b_8_15·a_1_2 + b_2_5⁵·a_7_13 + b_2_5⁵·a_7_12
        − b_2_5⁵·a_7_11 + b_2_5⁵·b_6_10·a_1_2 + b_2_5⁷·a_3_8 + b_6_10·a_1_1·a_1_2·a_9_21
        + b_2_5·a_1_2·a_7_11·a_7_13 + b_2_5⁴·a_1_1·a_1_2·a_7_12 + b_2_5⁴·a_1_0·a_1_2·a_7_12
        − b_2_5⁴·a_1_0·a_1_2·a_7_11
151. b_8_15·a_9_21 − b_8_15·a_9_20 − b_2_5·b_8_16·a_7_12 − b_2_5·b_8_15·a_7_12
        − b_2_5·b_6_10·a_9_21 − b_2_5·b_6_10·b_8_17·a_1_2 − b_2_5²·b_6_10²·a_1_2
        − b_2_5⁴·a_9_20 + b_2_5⁴·b_8_16·a_1_2 − b_2_5⁴·b_8_15·a_1_2 − b_2_5⁵·a_7_13
        + b_2_5⁵·a_7_12 + b_2_5⁵·b_6_10·a_1_2 + b_2_5⁸·a_1_1 − b_6_10·a_1_1·a_1_2·a_9_21
        − b_2_5·a_1_2·a_7_11·a_7_13 − b_2_5⁴·a_1_1·a_1_2·a_7_12 + b_2_5⁴·a_1_0·a_1_2·a_7_12
        − b_2_5⁴·a_1_0·a_1_2·a_7_11
152. b_10_24·a_7_13 − b_8_17·a_9_21 + b_8_16·a_9_20 + b_8_15·a_9_20 + b_6_10²·a_5_9
        + b_2_5·b_8_15·a_7_12 + b_2_5·b_6_10·a_9_21 − b_2_5·b_6_10·a_9_20
        + b_2_5²·b_6_10·a_7_13 + b_2_5²·b_6_10·a_7_12 + b_2_5²·b_6_10²·a_1_2
        + b_2_5⁴·a_9_21 − b_2_5⁴·b_8_17·a_1_2 + b_2_5⁴·b_8_15·a_1_2 − b_2_5⁵·a_7_13
        + b_2_5⁵·a_7_11 − b_2_5⁷·a_3_8 + b_6_10·a_1_1·a_1_2·a_9_21
        − b_2_5·a_1_2·a_7_12·a_7_13 + b_2_5·a_1_2·a_7_11·a_7_13 + b_2_5⁴·a_1_1·a_1_2·a_7_12
        + b_2_5⁴·a_1_0·a_1_2·a_7_12 + b_2_5⁴·a_1_0·a_1_2·a_7_11
153. b_8_16·a_9_20 + b_8_15·a_9_20 + b_2_5·b_8_16·a_7_12 − b_2_5·b_8_15·a_7_12
        − b_2_5·b_6_10·a_9_20 + b_2_5²·b_6_10·a_7_12 + b_2_5²·b_6_10²·a_1_2
        + b_2_5³·b_10_24·a_1_2 + b_2_5⁴·b_8_17·a_1_2 − b_2_5⁴·b_8_15·a_1_2 − b_2_5⁷·a_3_8
        − a_1_2·a_7_12·a_9_20 − b_6_10·a_1_1·a_1_2·a_9_21 − b_2_5·a_1_2·a_7_12·a_7_13
        + b_2_5⁴·a_1_1·a_1_2·a_7_12 − b_2_5⁴·a_1_0·a_1_2·a_7_12
154. b_10_24·a_7_11 + b_8_16·a_9_20 + b_8_15·a_9_20 + b_6_10·b_10_24·a_1_2 + b_6_10²·a_5_9
        − b_2_5·b_6_10·a_9_20 − b_2_5²·b_6_10·a_7_13 + b_2_5²·b_6_10·a_7_12
        + b_2_5²·b_6_10²·a_1_2 − b_2_5⁴·a_9_20 + b_2_5⁴·b_8_16·a_1_2 − b_2_5⁴·b_8_15·a_1_2
        − b_2_5⁵·a_7_13 − b_2_5⁵·a_7_11 − b_2_5⁵·b_6_10·a_1_2 − b_2_5⁷·a_3_8 + b_2_5⁸·a_1_1
        − a_1_2·a_7_12·a_9_20 − b_2_5⁴·a_1_1·a_1_2·a_7_12 − b_2_5⁴·a_1_0·a_1_2·a_7_12
155. b_10_24·a_7_12 − b_8_17·a_9_21 + b_8_17·a_9_20 − b_8_16·a_9_20 − b_8_15·a_9_20
        + b_6_10·b_10_24·a_1_2 + b_6_10²·a_5_9 − b_2_5·b_8_16·a_7_12 − b_2_5·b_6_10·a_9_21
        + b_2_5·b_6_10·a_9_20 − b_2_5·b_6_10·b_8_17·a_1_2 − b_2_5²·b_6_10·a_7_13
        + b_2_5²·b_6_10²·a_1_2 − b_2_5⁴·a_9_21 + b_2_5⁴·a_9_20 + b_2_5⁴·b_8_16·a_1_2
        − b_2_5⁴·b_8_15·a_1_2 − b_2_5⁵·a_7_13 + b_2_5⁵·a_7_12 + b_2_5⁵·a_7_11
        − b_2_5⁵·b_6_10·a_1_2 + b_2_5⁸·a_1_1 + a_1_2·a_7_12·a_9_20
        − b_6_10·a_1_1·a_1_2·a_9_21 + b_2_5·a_1_2·a_7_12·a_7_13 + b_2_5⁴·a_1_1·a_1_2·a_7_12
        − b_2_5⁴·a_1_0·a_1_2·a_7_12 − b_2_5⁴·a_1_0·a_1_2·a_7_11
156.  − b_8_17·a_9_20 + b_8_16·a_9_20 + b_8_15·a_9_20 + b_6_10·a_11_25 + b_6_10·b_10_24·a_1_2
        + b_6_10²·a_5_9 − b_2_5·b_8_16·a_7_12 + b_2_5·b_8_15·a_7_12 + b_2_5·b_6_10·a_9_21
        + b_2_5·b_6_10·a_9_20 − b_2_5²·b_6_10·a_7_13 − b_2_5²·b_6_10·a_7_12 + b_2_5⁴·a_9_21
        + b_2_5⁴·b_8_16·a_1_2 − b_2_5⁴·b_8_15·a_1_2 − b_2_5⁵·a_7_13 + b_2_5⁵·a_7_11
        + b_2_5⁵·b_6_10·a_1_2 − b_6_10·a_1_1·a_1_2·a_9_21 − b_2_5·a_1_2·a_7_12·a_7_13
        − b_2_5·a_1_2·a_7_11·a_7_13 + b_2_5⁴·a_1_1·a_1_2·a_7_12 − b_2_5⁴·a_1_0·a_1_2·a_7_11
157. a_6_9·a_11_25 + b_6_10·a_1_1·a_1_2·a_9_21 + b_2_5⁴·a_1_1·a_1_2·a_7_12
158.  − b_8_16·a_9_20 − b_8_15·a_9_20 − b_2_5·b_8_16·a_7_12 − b_2_5·b_6_10·b_8_17·a_1_2
        + b_2_5²·b_6_10·a_7_13 + b_2_5²·b_6_10·a_7_12 + b_2_5²·b_6_10²·a_1_2
        + b_2_5³·a_11_26 + b_2_5⁴·a_9_20 − b_2_5⁴·b_8_15·a_1_2 − b_2_5⁵·a_7_13
        − b_2_5⁵·a_7_12 + b_2_5⁵·a_7_11 − b_2_5⁵·b_6_10·a_1_2 + a_1_2·a_7_12·a_9_20
        + b_6_10·a_1_1·a_1_2·a_9_21 − b_2_5·a_1_2·a_7_12·a_7_13 − b_2_5·a_1_2·a_7_11·a_7_13
        + b_2_5⁴·a_1_1·a_1_2·a_7_12 + b_2_5⁴·a_1_0·a_1_2·a_7_11
159.  − b_8_17·a_9_21 + b_6_10·a_11_26 − b_2_5·b_8_16·a_7_12 + b_2_5·b_8_15·a_7_12
        + b_2_5·b_6_10·a_9_21 + b_2_5·b_6_10·b_8_17·a_1_2 − b_2_5²·b_6_10·a_7_13
        − b_2_5²·b_6_10·a_7_12 − b_2_5²·b_6_10²·a_1_2 − b_2_5⁴·a_9_20
        − b_2_5⁴·b_8_16·a_1_2 − b_2_5⁴·b_8_15·a_1_2 − b_2_5⁵·a_7_13 − b_2_5⁵·a_7_11
        − b_2_5⁵·b_6_10·a_1_2 + b_2_5⁷·a_3_8 − b_2_5⁸·a_1_1 + a_1_2·a_7_12·a_9_20
        + b_6_10·a_1_1·a_1_2·a_9_21 − b_2_5⁴·a_1_0·a_1_2·a_7_12
160. a_6_9·a_11_26 + b_6_10·a_1_1·a_1_2·a_9_21 − b_2_5⁴·a_1_1·a_1_2·a_7_12
        + b_2_5⁴·a_1_0·a_1_2·a_7_12 + b_2_5⁴·a_1_0·a_1_2·a_7_11
161. a_12_22·a_5_9 − b_6_10·a_1_1·a_1_2·a_9_21 + b_2_5⁴·a_1_1·a_1_2·a_7_12
        + b_2_5⁴·a_1_0·a_1_2·a_7_12 + b_2_5⁴·a_1_0·a_1_2·a_7_11
162.  − b_8_17·b_10_24 − b_8_16·b_10_24 − b_8_15·b_10_24 + b_6_10³ + b_2_5·b_6_10·b_10_24
        − b_2_5²·b_6_10·b_8_17 + b_2_5⁴·b_10_24 + b_2_5⁵·b_8_15 + a_9_20·a_9_21
        + a_7_13·a_11_25 + b_6_10²·a_1_2·a_5_9 + b_2_5·a_7_12·a_9_21 − b_2_5·a_7_12·a_9_20
        + b_2_5·b_6_10·a_1_2·a_9_21 − b_2_5·b_6_10·a_1_2·a_9_20 − b_2_5²·b_6_10·a_1_2·a_7_13
        + b_2_5⁴·a_1_2·a_9_21 − b_2_5⁴·a_1_2·a_9_20 − b_2_5⁵·a_1_2·a_7_12
        − b_2_5⁵·a_1_2·a_7_11 + b_2_5⁵·a_1_1·a_7_12 − b_2_5⁵·a_1_0·a_7_12
        − b_2_5⁵·a_1_0·a_7_11 − b_2_5⁷·a_1_2·a_3_8
163. b_8_17·b_10_24 − b_6_10³ − b_2_5²·b_6_10·b_8_17 − b_2_5⁵·b_8_17 − b_2_5⁵·b_8_15
        + b_2_5⁶·b_6_10 + b_6_10·a_1_2·a_11_25 + b_6_10²·a_1_2·a_5_9
        − b_2_5·b_6_10·a_1_2·a_9_21 − b_2_5·b_6_10·a_1_2·a_9_20 + b_2_5²·a_7_11·a_7_13
        − b_2_5⁴·a_1_2·a_9_20 + b_2_5⁵·a_1_2·a_7_12 − b_2_5⁵·a_1_2·a_7_11
        + b_2_5⁷·a_1_2·a_3_8
164.  − b_8_17·b_10_24 + b_6_10³ + b_2_5²·b_6_10·b_8_17 + b_2_5⁵·b_8_17 + b_2_5⁵·b_8_15
        − b_2_5⁶·b_6_10 + a_7_11·a_11_25 + b_6_10²·a_1_2·a_5_9 − b_2_5·a_7_12·a_9_21
        + b_2_5·b_6_10·a_1_2·a_9_21 + b_2_5·b_6_10·a_1_2·a_9_20 + b_2_5²·b_6_10·a_1_2·a_7_13
        − b_2_5²·b_6_10·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_9_21 + b_2_5⁵·a_1_2·a_7_13
        − b_2_5⁵·a_1_2·a_7_12 + b_2_5⁵·a_1_2·a_7_11 + b_2_5⁵·a_1_1·a_7_12
        − b_2_5⁵·a_1_0·a_7_12 − b_2_5⁵·a_1_0·a_7_11 − b_2_5⁸·a_1_1·a_1_2
165.  − b_8_16·b_10_24 − b_8_15·b_10_24 + b_2_5·b_6_10·b_10_24 + b_2_5²·b_6_10·b_8_17
        + b_2_5⁴·b_10_24 − b_2_5⁵·b_8_17 + b_2_5⁶·b_6_10 + a_9_20·a_9_21 + a_7_12·a_11_25
        + b_6_10²·a_1_2·a_5_9 − b_2_5·a_7_12·a_9_21 − b_2_5·a_7_12·a_9_20
        + b_2_5·b_8_16·a_1_2·a_7_12 + b_2_5·b_6_10·a_1_2·a_9_21 + b_2_5²·a_7_12·a_7_13
        + b_2_5²·a_7_11·a_7_13 − b_2_5²·b_6_10·a_1_2·a_7_13 − b_2_5²·b_6_10·a_1_2·a_7_12
        − b_2_5⁴·a_1_2·a_9_21 − b_2_5⁴·a_1_2·a_9_20 + b_2_5⁵·a_1_2·a_7_12
        + b_2_5⁵·a_1_2·a_7_11 − b_2_5⁵·a_1_1·a_7_12 + b_2_5⁵·a_1_0·a_7_12
        + b_2_5⁵·a_1_0·a_7_11
166.  − b_8_17·b_10_24 + b_8_16·b_10_24 − b_8_15·b_10_24 + b_6_10³ + b_2_5·b_6_10·b_10_24
        + b_2_5³·b_6_10² + b_2_5⁴·b_10_24 − b_2_5⁵·b_8_17 + b_2_5⁵·b_8_16 + a_7_13·a_11_26
        − b_6_10²·a_1_2·a_5_9 + b_2_5·a_7_12·a_9_21 + b_2_5·a_7_12·a_9_20
        + b_2_5·b_8_16·a_1_2·a_7_12 + b_2_5·b_6_10·a_1_2·a_9_21 − b_2_5·b_6_10·a_1_2·a_9_20
        + b_2_5²·a_7_11·a_7_13 + b_2_5²·b_6_10·a_1_2·a_7_13 + b_2_5²·b_6_10·a_1_2·a_7_12
        − b_2_5⁴·a_1_2·a_9_21 − b_2_5⁴·a_1_2·a_9_20 − b_2_5⁵·a_1_2·a_7_13
        − b_2_5⁵·a_1_2·a_7_12 + b_2_5⁵·a_1_2·a_7_11 + b_2_5⁵·a_1_0·a_7_12
        − b_2_5⁵·a_1_0·a_7_11 + b_2_5⁷·a_1_2·a_3_8 + b_2_5⁸·a_1_1·a_1_2
167. b_2_5·a_7_12·a_9_21 − b_2_5·b_6_10·a_1_2·a_9_20 − b_2_5²·a_7_12·a_7_13
        + b_2_5²·b_6_10·a_1_2·a_7_13 − b_2_5²·b_6_10·a_1_2·a_7_12 + b_2_5³·a_1_2·a_11_26
        − b_2_5⁴·a_1_2·a_9_21 + b_2_5⁴·a_1_2·a_9_20 + b_2_5⁵·a_1_2·a_7_11
        − b_2_5⁷·a_1_2·a_3_8
168. b_8_17·b_10_24 − b_8_16·b_10_24 + b_8_15·b_10_24 − b_6_10³ − b_2_5·b_6_10·b_10_24
        − b_2_5³·b_6_10² − b_2_5⁴·b_10_24 + b_2_5⁵·b_8_17 − b_2_5⁵·b_8_16
        + b_6_10·a_1_1·a_11_26 + b_6_10²·a_1_2·a_5_9 + b_2_5·a_7_12·a_9_21
        − b_2_5·a_7_12·a_9_20 + b_2_5·b_8_16·a_1_2·a_7_12 + b_2_5·b_6_10·a_1_2·a_9_21
        + b_2_5·b_6_10·a_1_2·a_9_20 + b_2_5²·a_7_12·a_7_13 + b_2_5²·a_7_11·a_7_13
        + b_2_5²·b_6_10·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_9_21 − b_2_5⁴·a_1_2·a_9_20
        − b_2_5⁵·a_1_2·a_7_13 − b_2_5⁵·a_1_2·a_7_11 − b_2_5⁵·a_1_0·a_7_11
        − b_2_5⁷·a_1_2·a_3_8
169. b_8_17·b_10_24 + b_8_15·b_10_24 − b_6_10³ − b_2_5·b_6_10·b_10_24
        − b_2_5²·b_6_10·b_8_17 + b_2_5³·b_6_10² − b_2_5⁴·b_10_24 − b_2_5⁵·b_8_17
        + b_2_5⁵·b_8_16 + b_2_5⁵·b_8_15 + b_6_10·a_1_2·a_11_26 + b_6_10²·a_1_2·a_5_9
        − b_2_5·a_7_12·a_9_20 + b_2_5·b_8_16·a_1_2·a_7_12 + b_2_5·b_6_10·a_1_2·a_9_21
        − b_2_5²·a_7_12·a_7_13 + b_2_5²·a_7_11·a_7_13 + b_2_5²·b_6_10·a_1_2·a_7_13
        − b_2_5⁴·a_1_2·a_9_21 + b_2_5⁴·a_1_2·a_9_20 + b_2_5⁵·a_1_2·a_7_12
        − b_2_5⁵·a_1_2·a_7_11 + b_2_5⁵·a_1_0·a_7_12 − b_2_5⁵·a_1_0·a_7_11
        + b_2_5⁷·a_1_2·a_3_8 − b_2_5⁸·a_1_1·a_1_2
170. b_8_17·b_10_24 + b_8_16·b_10_24 + b_8_15·b_10_24 − b_6_10³ − b_2_5·b_6_10·b_10_24
        + b_2_5²·b_6_10·b_8_17 − b_2_5⁴·b_10_24 − b_2_5⁵·b_8_15 + a_7_11·a_11_26
        + b_6_10²·a_1_2·a_5_9 + b_2_5·a_7_12·a_9_21 + b_2_5·a_7_12·a_9_20
        − b_2_5·b_6_10·a_1_2·a_9_21 − b_2_5²·a_7_12·a_7_13 + b_2_5²·a_7_11·a_7_13
        − b_2_5²·b_6_10·a_1_2·a_7_13 − b_2_5²·b_6_10·a_1_2·a_7_12 − b_2_5⁴·a_1_2·a_9_20
        + b_2_5⁵·a_1_2·a_7_12 − b_2_5⁵·a_1_1·a_7_12 − b_2_5⁷·a_1_2·a_3_8
171. b_8_17·b_10_24 + b_8_16·b_10_24 + b_8_15·b_10_24 − b_6_10³ − b_2_5·b_6_10·b_10_24
        + b_2_5²·b_6_10·b_8_17 − b_2_5⁴·b_10_24 − b_2_5⁵·b_8_15 + a_9_20·a_9_21
        + a_7_12·a_11_26 + b_6_10²·a_1_2·a_5_9 + b_2_5·a_7_12·a_9_21 − b_2_5·a_7_12·a_9_20
        + b_2_5·b_8_16·a_1_2·a_7_12 + b_2_5²·a_7_12·a_7_13 − b_2_5²·a_7_11·a_7_13
        − b_2_5²·b_6_10·a_1_2·a_7_12 − b_2_5⁴·a_1_2·a_9_21 − b_2_5⁵·a_1_2·a_7_13
        + b_2_5⁵·a_1_2·a_7_12 + b_2_5⁵·a_1_1·a_7_12 + b_2_5⁵·a_1_0·a_7_12
        + b_2_5⁵·a_1_0·a_7_11 + b_2_5⁷·a_1_2·a_3_8 − b_2_5⁸·a_1_1·a_1_2
172. b_8_16·b_10_24 + b_8_15·b_10_24 − b_2_5·b_6_10·b_10_24 − b_2_5²·b_6_10·b_8_17
        − b_2_5⁴·b_10_24 + b_2_5⁵·b_8_17 − b_2_5⁶·b_6_10 + b_6_10·a_12_22 − a_9_20·a_9_21
        + b_6_10²·a_1_2·a_5_9 − b_2_5·a_7_12·a_9_20 + b_2_5·b_8_16·a_1_2·a_7_12
        − b_2_5·b_6_10·a_1_2·a_9_21 + b_2_5²·a_7_12·a_7_13 + b_2_5²·b_6_10·a_1_2·a_7_13
        + b_2_5²·b_6_10·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_9_21 − b_2_5⁴·a_1_2·a_9_20
        + b_2_5⁵·a_1_2·a_7_13 − b_2_5⁵·a_1_2·a_7_12 − b_2_5⁵·a_1_1·a_7_12
        − b_2_5⁵·a_1_0·a_7_12 − b_2_5⁵·a_1_0·a_7_11 + b_2_5⁷·a_1_2·a_3_8
173. a_6_9·a_12_22
174. a_1_1·a_17_34 + b_2_5⁵·a_1_1·a_7_12 − b_2_5⁵·a_1_0·a_7_12 − b_2_5⁵·a_1_0·a_7_11
175. a_1_0·a_17_34 + b_2_5⁵·a_1_1·a_7_12 − b_2_5⁵·a_1_0·a_7_12 − b_2_5⁵·a_1_0·a_7_11
        − b_2_5⁷·a_1_2·a_3_8
176. b_10_24·a_9_20 + b_8_17·a_11_25 + b_8_16·a_11_25 + b_6_10²·a_7_13 − b_6_10²·a_7_12
        + b_6_10³·a_1_1 − b_2_5·b_6_10·b_10_24·a_1_2 + b_2_5²·b_6_10·a_9_21
        + b_2_5²·b_6_10·a_9_20 − b_2_5²·b_6_10·b_8_17·a_1_2 − b_2_5³·b_6_10·a_7_13
        − b_2_5³·b_6_10²·a_1_2 + b_2_5⁵·a_9_21 − b_2_5⁵·a_9_20 + b_2_5⁵·b_8_17·a_1_2
        + b_2_5⁵·b_8_16·a_1_2 − b_2_5⁵·b_8_15·a_1_2 + b_2_5⁶·a_7_13 − b_2_5⁶·b_6_10·a_1_2
        + b_2_5⁸·a_3_8 − b_2_5⁹·a_1_1 − b_2_5·a_1_2·a_7_12·a_9_20
        + b_2_5²·a_1_2·a_7_11·a_7_13
177. b_10_24·a_9_21 + b_10_24·a_9_20 + b_8_15·a_11_25 + b_6_10²·a_7_13 + b_6_10²·a_7_12
        + b_6_10³·a_1_2 − b_6_10³·a_1_1 + b_2_5·b_6_10·b_10_24·a_1_2 − b_2_5²·b_8_16·a_7_12
        − b_2_5²·b_6_10·a_9_21 + b_2_5²·b_6_10·a_9_20 + b_2_5²·b_6_10·b_8_17·a_1_2
        − b_2_5³·b_6_10·a_7_13 − b_2_5³·b_6_10²·a_1_2 + b_2_5⁴·b_10_24·a_1_2
        + b_2_5⁵·a_9_21 + b_2_5⁵·a_9_20 + b_2_5⁵·b_8_16·a_1_2 + b_2_5⁵·b_8_15·a_1_2
        − b_2_5⁶·a_7_12 + b_2_5⁶·a_7_11 − b_2_5⁶·b_6_10·a_1_2 + b_2_5⁸·a_3_8 + b_2_5⁹·a_1_1
        + b_2_5·a_1_2·a_7_12·a_9_20 − b_2_5²·a_1_2·a_7_12·a_7_13
        − b_2_5⁵·a_1_1·a_1_2·a_7_12 + b_2_5⁵·a_1_0·a_1_2·a_7_12
        + b_2_5⁵·a_1_0·a_1_2·a_7_11
178. b_10_24·a_9_21 + b_10_24·a_9_20 + b_6_10²·a_7_13 + b_6_10²·a_7_12 + b_6_10³·a_1_2
        − b_6_10³·a_1_1 − b_2_5·b_6_10·b_10_24·a_1_2 + b_2_5²·b_6_10·b_8_17·a_1_2
        + b_2_5³·b_6_10²·a_1_2 + b_2_5⁴·a_11_26 − b_2_5⁵·a_9_21 − b_2_5⁵·b_8_17·a_1_2
        + b_2_5⁵·b_8_15·a_1_2 − b_2_5⁶·a_7_13 − b_2_5⁶·b_6_10·a_1_2 + b_2_5⁸·a_3_8
        + b_2_5⁹·a_1_1 − a_1_2·a_7_12·a_11_25 + b_2_5·a_1_2·a_7_12·a_9_20
        + b_2_5²·a_1_2·a_7_12·a_7_13 − b_2_5²·a_1_2·a_7_11·a_7_13
        − b_2_5⁵·a_1_0·a_1_2·a_7_11
179. b_10_24·a_9_21 − b_8_17·a_11_25 − b_6_10²·a_7_12 + b_6_10³·a_1_2 + b_6_10³·a_1_1
        + b_2_5²·b_8_16·a_7_12 − b_2_5²·b_6_10·a_9_21 + b_2_5²·b_6_10·a_9_20
        − b_2_5³·b_6_10·a_7_13 − b_2_5³·b_6_10²·a_1_2 + b_2_5⁴·b_10_24·a_1_2
        − b_2_5⁵·a_9_20 − b_2_5⁶·a_7_13 − b_2_5⁶·a_7_12 + b_2_5⁶·a_7_11
        − b_2_5⁶·b_6_10·a_1_2 − b_2_5⁸·a_3_8 − b_2_5⁹·a_1_1 + b_6_10·a_1_1·a_1_2·a_11_26
        − b_2_5·a_1_2·a_7_12·a_9_20 − b_2_5²·a_1_2·a_7_12·a_7_13
        + b_2_5²·a_1_2·a_7_11·a_7_13 − b_2_5⁵·a_1_0·a_1_2·a_7_12
        − b_2_5⁵·a_1_0·a_1_2·a_7_11
180. b_10_24·a_9_20 − b_6_10²·a_7_13 + b_6_10²·a_7_12 + b_6_10³·a_1_2
        + b_2_5·b_6_10·a_11_26 − b_2_5·b_6_10·b_10_24·a_1_2 − b_2_5²·b_6_10·a_9_20
        + b_2_5²·b_6_10·b_8_17·a_1_2 − b_2_5³·b_6_10·a_7_13 − b_2_5³·b_6_10·a_7_12
        − b_2_5³·b_6_10²·a_1_2 + b_2_5⁴·b_10_24·a_1_2 − b_2_5⁵·a_9_20
        − b_2_5⁵·b_8_17·a_1_2 − b_2_5⁵·b_8_15·a_1_2 − b_2_5⁶·a_7_13 − b_2_5⁶·a_7_12
        + b_2_5⁶·a_7_11 − b_2_5⁶·b_6_10·a_1_2 − b_2_5⁸·a_3_8 − a_1_2·a_7_12·a_11_25
        − b_2_5·a_1_2·a_7_12·a_9_20 + b_2_5²·a_1_2·a_7_12·a_7_13
        − b_2_5²·a_1_2·a_7_11·a_7_13 + b_2_5⁵·a_1_0·a_1_2·a_7_12
181. b_10_24·a_9_21 − b_10_24·a_9_20 + b_8_17·a_11_26 + b_8_17·a_11_25 + b_6_10²·a_7_13
        + b_6_10³·a_1_2 − b_6_10³·a_1_1 − b_2_5·b_6_10·b_10_24·a_1_2 − b_2_5²·b_6_10·a_9_21
        − b_2_5²·b_6_10·b_8_17·a_1_2 + b_2_5³·b_6_10·a_7_12 + b_2_5⁴·b_10_24·a_1_2
        − b_2_5⁵·a_9_21 − b_2_5⁵·a_9_20 + b_2_5⁵·b_8_15·a_1_2 + b_2_5⁶·a_7_11
        + b_2_5⁶·b_6_10·a_1_2 − b_2_5⁹·a_1_1 + b_2_5·a_1_2·a_7_12·a_9_20
        − b_2_5²·a_1_2·a_7_12·a_7_13 − b_2_5⁵·a_1_0·a_1_2·a_7_12
        + b_2_5⁵·a_1_0·a_1_2·a_7_11
182. b_8_16·a_11_26 − b_2_5²·b_6_10·a_9_21 + b_2_5²·b_6_10·a_9_20
        + b_2_5²·b_6_10·b_8_17·a_1_2 + b_2_5³·b_6_10·a_7_12 − b_2_5³·b_6_10²·a_1_2
        + b_2_5⁴·b_10_24·a_1_2 + b_2_5⁵·a_9_21 − b_2_5⁵·b_8_17·a_1_2 − b_2_5⁵·b_8_15·a_1_2
        − b_2_5⁶·a_7_13 − b_2_5⁶·a_7_12 − b_2_5⁶·b_6_10·a_1_2 + b_2_5⁹·a_1_1
        + b_2_5·a_1_2·a_7_12·a_9_20 + b_2_5²·a_1_2·a_7_12·a_7_13
        + b_2_5²·a_1_2·a_7_11·a_7_13 + b_2_5⁵·a_1_1·a_1_2·a_7_12
        − b_2_5⁵·a_1_0·a_1_2·a_7_12
183. b_10_24·a_9_21 − b_10_24·a_9_20 + b_8_15·a_11_26 − b_6_10²·a_7_12 − b_6_10³·a_1_2
        − b_6_10³·a_1_1 + b_2_5·b_6_10·b_10_24·a_1_2 + b_2_5²·b_8_16·a_7_12
        + b_2_5²·b_6_10·a_9_20 + b_2_5²·b_6_10·b_8_17·a_1_2 + b_2_5³·b_6_10·a_7_12
        − b_2_5³·b_6_10²·a_1_2 − b_2_5⁴·b_10_24·a_1_2 + b_2_5⁵·a_9_21 + b_2_5⁵·a_9_20
        + b_2_5⁵·b_8_17·a_1_2 + b_2_5⁵·b_8_16·a_1_2 + b_2_5⁶·a_7_12 + b_2_5⁹·a_1_1
        − a_1_2·a_7_12·a_11_25 − b_2_5²·a_1_2·a_7_12·a_7_13 + b_2_5²·a_1_2·a_7_11·a_7_13
        − b_2_5⁵·a_1_1·a_1_2·a_7_12 + b_2_5⁵·a_1_0·a_1_2·a_7_12
        − b_2_5⁵·a_1_0·a_1_2·a_7_11
184. a_12_22·a_7_13 − a_1_2·a_7_12·a_11_25 − b_2_5·a_1_2·a_7_12·a_9_20
        + b_2_5²·a_1_2·a_7_12·a_7_13 + b_2_5²·a_1_2·a_7_11·a_7_13
        − b_2_5⁵·a_1_1·a_1_2·a_7_12 − b_2_5⁵·a_1_0·a_1_2·a_7_12
        − b_2_5⁵·a_1_0·a_1_2·a_7_11
185.  − b_10_24·a_9_21 + b_8_17·a_11_25 + b_6_10²·a_7_12 − b_6_10³·a_1_2 − b_6_10³·a_1_1
        − b_2_5²·b_8_16·a_7_12 + b_2_5²·b_6_10·a_9_21 − b_2_5²·b_6_10·a_9_20
        + b_2_5³·b_6_10·a_7_13 + b_2_5³·b_6_10²·a_1_2 − b_2_5⁴·b_10_24·a_1_2
        + b_2_5⁵·a_9_20 + b_2_5⁶·a_7_13 + b_2_5⁶·a_7_12 − b_2_5⁶·a_7_11
        + b_2_5⁶·b_6_10·a_1_2 + b_2_5⁸·a_3_8 + b_2_5⁹·a_1_1 + a_12_22·a_7_11
        − a_1_2·a_7_12·a_11_25 + b_2_5·a_1_2·a_7_12·a_9_20 − b_2_5²·a_1_2·a_7_11·a_7_13
        − b_2_5⁵·a_1_1·a_1_2·a_7_12
186.  − b_10_24·a_9_21 + b_8_17·a_11_25 + b_6_10²·a_7_12 − b_6_10³·a_1_2 − b_6_10³·a_1_1
        − b_2_5²·b_8_16·a_7_12 + b_2_5²·b_6_10·a_9_21 − b_2_5²·b_6_10·a_9_20
        + b_2_5³·b_6_10·a_7_13 + b_2_5³·b_6_10²·a_1_2 − b_2_5⁴·b_10_24·a_1_2
        + b_2_5⁵·a_9_20 + b_2_5⁶·a_7_13 + b_2_5⁶·a_7_12 − b_2_5⁶·a_7_11
        + b_2_5⁶·b_6_10·a_1_2 + b_2_5⁸·a_3_8 + b_2_5⁹·a_1_1 + a_12_22·a_7_12
        + b_2_5⁵·a_1_1·a_1_2·a_7_12 − b_2_5⁵·a_1_0·a_1_2·a_7_12
        − b_2_5⁵·a_1_0·a_1_2·a_7_11
187. a_2_2·a_17_34 − b_2_5⁵·a_1_1·a_1_2·a_7_12
188. a_2_3·a_17_34 + b_2_5⁵·a_1_1·a_1_2·a_7_12 + b_2_5⁵·a_1_0·a_1_2·a_7_12
        + b_2_5⁵·a_1_0·a_1_2·a_7_11
189. a_2_4·a_17_34 + b_2_5⁵·a_1_0·a_1_2·a_7_12 + b_2_5⁵·a_1_0·a_1_2·a_7_11
190.  − b_10_24·a_9_21 + b_8_17·a_11_25 + b_6_10²·a_7_12 − b_6_10³·a_1_2 − b_6_10³·a_1_1
        − b_2_5²·b_8_16·a_7_12 + b_2_5²·b_6_10·a_9_21 − b_2_5²·b_6_10·a_9_20
        + b_2_5³·b_6_10·a_7_13 + b_2_5³·b_6_10²·a_1_2 − b_2_5⁴·b_10_24·a_1_2
        + b_2_5⁵·a_9_20 + b_2_5⁶·a_7_13 + b_2_5⁶·a_7_12 − b_2_5⁶·a_7_11
        + b_2_5⁶·b_6_10·a_1_2 + b_2_5⁸·a_3_8 + b_2_5⁹·a_1_1 + a_18_27·a_1_1
        + b_2_5·a_1_2·a_7_12·a_9_20 + b_2_5²·a_1_2·a_7_12·a_7_13
        − b_2_5²·a_1_2·a_7_11·a_7_13 + b_2_5⁵·a_1_0·a_1_2·a_7_12
        + b_2_5⁵·a_1_0·a_1_2·a_7_11
191. a_18_27·a_1_0 + b_2_5⁵·a_1_1·a_1_2·a_7_12 + b_2_5⁵·a_1_0·a_1_2·a_7_12
        − b_2_5⁵·a_1_0·a_1_2·a_7_11
192.  − b_10_24² + b_6_10²·b_8_17 − b_2_5²·b_6_10·b_10_24 − b_2_5³·b_6_10·b_8_17
        − b_2_5⁴·b_6_10² − b_2_5⁵·b_10_24 + b_2_5⁶·b_8_16 − b_2_5⁶·b_8_15 − b_2_5⁷·b_6_10
        + a_9_20·a_11_25 + b_6_10²·a_1_1·a_7_12 − b_6_10³·a_1_1·a_1_2 + b_2_5²·a_7_12·a_9_20
        − b_2_5²·b_6_10·a_1_2·a_9_21 − b_2_5²·b_6_10·a_1_2·a_9_20 − b_2_5⁵·a_1_2·a_9_21
        + b_2_5⁶·a_1_2·a_7_13 + b_2_5⁶·a_1_2·a_7_12 − b_2_5⁶·a_1_2·a_7_11
        − b_2_5⁶·a_1_0·a_7_12 − b_2_5⁸·a_1_2·a_3_8 + b_2_5⁹·a_1_1·a_1_2
193.  − b_10_24² + b_6_10²·b_8_17 − b_2_5²·b_6_10·b_10_24 − b_2_5³·b_6_10·b_8_17
        − b_2_5⁴·b_6_10² − b_2_5⁵·b_10_24 + b_2_5⁶·b_8_16 − b_2_5⁶·b_8_15 − b_2_5⁷·b_6_10
        + b_6_10²·a_1_2·a_7_13 − b_6_10²·a_1_2·a_7_12 + b_6_10²·a_1_1·a_7_12
        + b_6_10³·a_1_1·a_1_2 − b_2_5²·a_7_12·a_9_20 − b_2_5²·b_6_10·a_1_2·a_9_21
        − b_2_5²·b_6_10·a_1_2·a_9_20 + b_2_5³·a_7_12·a_7_13 − b_2_5³·a_7_11·a_7_13
        + b_2_5³·b_6_10·a_1_2·a_7_12 + b_2_5⁴·a_1_2·a_11_26 + b_2_5⁵·a_1_2·a_9_21
        + b_2_5⁵·a_1_2·a_9_20 + b_2_5⁶·a_1_2·a_7_13 − b_2_5⁶·a_1_2·a_7_12
        + b_2_5⁶·a_1_2·a_7_11 + b_2_5⁶·a_1_0·a_7_12 − b_2_5⁶·a_1_0·a_7_11
        + b_2_5⁸·a_1_2·a_3_8
194. b_10_24² − b_6_10²·b_8_17 + b_2_5²·b_6_10·b_10_24 + b_2_5³·b_6_10·b_8_17
        + b_2_5⁴·b_6_10² + b_2_5⁵·b_10_24 − b_2_5⁶·b_8_16 + b_2_5⁶·b_8_15 + b_2_5⁷·b_6_10
        + a_9_21·a_11_25 − b_6_10·a_7_12·a_7_13 + b_6_10²·a_1_2·a_7_12 + b_6_10²·a_1_1·a_7_12
        + b_6_10³·a_1_1·a_1_2 + b_2_5·b_6_10·a_1_2·a_11_26 + b_2_5²·a_7_12·a_9_20
        − b_2_5²·b_8_16·a_1_2·a_7_12 − b_2_5³·b_6_10·a_1_2·a_7_13
        − b_2_5³·b_6_10·a_1_2·a_7_12 + b_2_5⁶·a_1_2·a_7_12 − b_2_5⁶·a_1_2·a_7_11
        + b_2_5⁶·a_1_1·a_7_12 − b_2_5⁶·a_1_0·a_7_12 + b_2_5⁶·a_1_0·a_7_11
        + b_2_5⁸·a_1_2·a_3_8 − b_2_5⁹·a_1_1·a_1_2
195.  − b_10_24² + b_6_10²·b_8_17 − b_2_5²·b_6_10·b_10_24 − b_2_5³·b_6_10·b_8_17
        − b_2_5⁴·b_6_10² − b_2_5⁵·b_10_24 + b_2_5⁶·b_8_16 − b_2_5⁶·b_8_15 − b_2_5⁷·b_6_10
        + a_9_21·a_11_25 + a_9_20·a_11_26 − b_6_10²·a_1_2·a_7_12 − b_6_10³·a_1_1·a_1_2
        − b_2_5²·a_7_12·a_9_20 − b_2_5²·b_8_16·a_1_2·a_7_12 + b_2_5²·b_6_10·a_1_2·a_9_21
        + b_2_5³·a_7_12·a_7_13 − b_2_5³·b_6_10·a_1_2·a_7_13 − b_2_5⁵·a_1_2·a_9_21
        + b_2_5⁵·a_1_2·a_9_20 − b_2_5⁶·a_1_2·a_7_13 + b_2_5⁶·a_1_2·a_7_12
        + b_2_5⁶·a_1_1·a_7_12 + b_2_5⁶·a_1_0·a_7_11 − b_2_5⁸·a_1_2·a_3_8
        − b_2_5⁹·a_1_1·a_1_2
196. b_10_24² − b_6_10²·b_8_17 + b_2_5²·b_6_10·b_10_24 + b_2_5³·b_6_10·b_8_17
        + b_2_5⁴·b_6_10² + b_2_5⁵·b_10_24 − b_2_5⁶·b_8_16 + b_2_5⁶·b_8_15 + b_2_5⁷·b_6_10
        + a_9_21·a_11_26 + a_9_21·a_11_25 − b_6_10·a_7_12·a_7_13 + b_6_10²·a_1_2·a_7_12
        + b_6_10²·a_1_1·a_7_12 + b_6_10³·a_1_1·a_1_2 − b_2_5²·b_8_16·a_1_2·a_7_12
        + b_2_5²·b_6_10·a_1_2·a_9_21 − b_2_5³·a_7_11·a_7_13 − b_2_5³·b_6_10·a_1_2·a_7_13
        − b_2_5³·b_6_10·a_1_2·a_7_12 + b_2_5⁵·a_1_2·a_9_20 + b_2_5⁶·a_1_2·a_7_13
        − b_2_5⁶·a_1_2·a_7_11 + b_2_5⁶·a_1_1·a_7_12 + b_2_5⁶·a_1_0·a_7_12
        + b_2_5⁸·a_1_2·a_3_8 + b_2_5⁹·a_1_1·a_1_2
197.  − b_10_24² + b_6_10²·b_8_17 − b_2_5²·b_6_10·b_10_24 − b_2_5³·b_6_10·b_8_17
        − b_2_5⁴·b_6_10² − b_2_5⁵·b_10_24 + b_2_5⁶·b_8_16 − b_2_5⁶·b_8_15 − b_2_5⁷·b_6_10
        + b_8_17·a_12_22 − a_9_21·a_11_25 − b_6_10·a_7_12·a_7_13 + b_6_10²·a_1_2·a_7_12
        + b_2_5²·a_7_12·a_9_20 − b_2_5²·b_8_16·a_1_2·a_7_12 − b_2_5²·b_6_10·a_1_2·a_9_21
        + b_2_5³·a_7_11·a_7_13 + b_2_5³·b_6_10·a_1_2·a_7_13 − b_2_5⁵·a_1_2·a_9_20
        − b_2_5⁶·a_1_2·a_7_13 + b_2_5⁶·a_1_2·a_7_11 + b_2_5⁶·a_1_0·a_7_12
        − b_2_5⁶·a_1_0·a_7_11 + b_2_5⁸·a_1_2·a_3_8 − b_2_5⁹·a_1_1·a_1_2
198. b_10_24² − b_6_10²·b_8_17 + b_2_5²·b_6_10·b_10_24 + b_2_5³·b_6_10·b_8_17
        + b_2_5⁴·b_6_10² + b_2_5⁵·b_10_24 − b_2_5⁶·b_8_16 + b_2_5⁶·b_8_15 + b_2_5⁷·b_6_10
        + b_8_16·a_12_22 − b_6_10²·a_1_2·a_7_13 + b_6_10²·a_1_2·a_7_12
        − b_6_10²·a_1_1·a_7_12 − b_6_10³·a_1_1·a_1_2 + b_2_5²·b_8_16·a_1_2·a_7_12
        + b_2_5²·b_6_10·a_1_2·a_9_21 − b_2_5²·b_6_10·a_1_2·a_9_20 − b_2_5³·a_7_12·a_7_13
        − b_2_5³·a_7_11·a_7_13 + b_2_5³·b_6_10·a_1_2·a_7_12 + b_2_5⁶·a_1_2·a_7_11
        − b_2_5⁶·a_1_1·a_7_12 − b_2_5⁶·a_1_0·a_7_12 + b_2_5⁶·a_1_0·a_7_11
        − b_2_5⁸·a_1_2·a_3_8
199. b_8_15·a_12_22 + a_9_21·a_11_25 − b_6_10·a_7_12·a_7_13 + b_6_10²·a_1_2·a_7_13
        − b_6_10²·a_1_1·a_7_12 − b_6_10³·a_1_1·a_1_2 − b_2_5²·b_6_10·a_1_2·a_9_21
        + b_2_5²·b_6_10·a_1_2·a_9_20 + b_2_5³·a_7_12·a_7_13 − b_2_5³·a_7_11·a_7_13
        − b_2_5³·b_6_10·a_1_2·a_7_13 + b_2_5³·b_6_10·a_1_2·a_7_12 − b_2_5⁵·a_1_2·a_9_21
        − b_2_5⁵·a_1_2·a_9_20 + b_2_5⁶·a_1_2·a_7_12 − b_2_5⁶·a_1_2·a_7_11
        + b_2_5⁶·a_1_1·a_7_12 − b_2_5⁸·a_1_2·a_3_8 + b_2_5⁹·a_1_1·a_1_2
200. a_3_8·a_17_34 + b_2_5⁸·a_1_2·a_3_8
201. a_2_2·a_18_27
202. a_2_3·a_18_27
203. a_2_4·a_18_27
204. a_1_1·a_19_41 − b_6_10²·a_1_1·a_7_12 − b_6_10³·a_1_1·a_1_2 + b_2_5⁶·a_1_1·a_7_12
205. a_1_0·a_19_41 − b_2_5⁶·a_1_1·a_7_12 − b_2_5⁶·a_1_0·a_7_12 + b_2_5⁸·a_1_2·a_3_8
        + b_2_5⁹·a_1_1·a_1_2

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 243

Data used for Benson′s test

• The computation is incomplete, Benson′s criterion does not apply up to degree 20.
• The following will eventually be a filter regular homogeneous system of parameters:
  1. c_18_37, a Duflot regular element of degree 18
  2. b_6_10² + b_2_5²·b_8_17 + b_2_5²·b_8_15 + b_2_5³·b_6_10 + b_2_5⁶, an element of degree 12
  3. b_2_5, an element of degree 2

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 243

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. a_1_2 → 0, an element of degree 1
4. a_2_2 → 0, an element of degree 2
5. a_2_3 → 0, an element of degree 2
6. a_2_4 → 0, an element of degree 2
7. b_2_5 → 0, an element of degree 2
8. a_3_8 → 0, an element of degree 3
9. a_5_9 → 0, an element of degree 5
10. a_6_9 → 0, an element of degree 6
11. b_6_10 → 0, an element of degree 6
12. a_7_11 → 0, an element of degree 7
13. a_7_12 → 0, an element of degree 7
14. a_7_13 → 0, an element of degree 7
15. b_8_15 → 0, an element of degree 8
16. b_8_16 → 0, an element of degree 8
17. b_8_17 → 0, an element of degree 8
18. a_9_20 → 0, an element of degree 9
19. a_9_21 → 0, an element of degree 9
20. b_10_24 → 0, an element of degree 10
21. a_11_25 → 0, an element of degree 11
22. a_11_26 → 0, an element of degree 11
23. a_12_22 → 0, an element of degree 12
24. a_17_34 → 0, an element of degree 17
25. a_18_27 → 0, an element of degree 18
26. c_18_37 →  − c_2_0⁹, an element of degree 18
27. a_19_41 → 0, an element of degree 19
28. a_20_36 → 0, an element of degree 20

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

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. a_1_2 → a_1_1, an element of degree 1
4. a_2_2 → 0, an element of degree 2
5. a_2_3 → 0, an element of degree 2
6. a_2_4 → 0, an element of degree 2
7. b_2_5 → c_2_4, an element of degree 2
8. a_3_8 → 0, an element of degree 3
9. a_5_9 → 0, an element of degree 5
10. a_6_9 → 0, an element of degree 6
11. b_6_10 →  − c_2_5³, an element of degree 6
12. a_7_11 → c_2_5³·a_1_1 − c_2_4³·a_1_2, an element of degree 7
13. a_7_12 → c_2_5³·a_1_2 − c_2_5³·a_1_1 + c_2_4³·a_1_2, an element of degree 7
14. a_7_13 → c_2_5³·a_1_2 − c_2_5³·a_1_1 + c_2_4·c_2_5²·a_1_1 + c_2_4²·c_2_5·a_1_2, an element of degree 7
15. b_8_15 →  − c_2_5³·a_1_1·a_1_2 − c_2_4·c_2_5³ + c_2_4³·c_2_5, an element of degree 8
16. b_8_16 →  − c_2_5³·a_1_1·a_1_2 + c_2_4²·c_2_5·a_1_1·a_1_2 − c_2_4³·a_1_1·a_1_2
       + c_2_4²·c_2_5², an element of degree 8
17. b_8_17 → c_2_5³·a_1_1·a_1_2 + c_2_4²·c_2_5·a_1_1·a_1_2 + c_2_4³·a_1_1·a_1_2 + c_2_5⁴
       − c_2_4·c_2_5³ + c_2_4²·c_2_5² − c_2_4³·c_2_5, an element of degree 8
18. a_9_20 →  − c_2_5⁴·a_1_1 − c_2_4·c_2_5³·a_1_2 − c_2_4²·c_2_5²·a_1_2 − c_2_4²·c_2_5²·a_1_1
       + c_2_4³·c_2_5·a_1_2 − c_2_4³·c_2_5·a_1_1 + c_2_4⁴·a_1_2, an element of degree 9
19. a_9_21 →  − c_2_5⁴·a_1_2 + c_2_5⁴·a_1_1 − c_2_4·c_2_5³·a_1_2 − c_2_4²·c_2_5²·a_1_2
       − c_2_4²·c_2_5²·a_1_1 + c_2_4³·c_2_5·a_1_2 + c_2_4³·c_2_5·a_1_1 + c_2_4⁴·a_1_2, an element of degree 9
20. b_10_24 → c_2_5⁴·a_1_1·a_1_2 − c_2_4·c_2_5³·a_1_1·a_1_2 + c_2_4²·c_2_5²·a_1_1·a_1_2
       + c_2_4³·c_2_5·a_1_1·a_1_2 − c_2_5⁵ − c_2_4·c_2_5⁴ − c_2_4²·c_2_5³
       − c_2_4⁴·c_2_5, an element of degree 10
21. a_11_25 →  − c_2_5⁵·a_1_1 − c_2_4·c_2_5⁴·a_1_2 + c_2_4·c_2_5⁴·a_1_1 + c_2_4²·c_2_5³·a_1_2
       + c_2_4²·c_2_5³·a_1_1 − c_2_4⁴·c_2_5·a_1_2 + c_2_4⁴·c_2_5·a_1_1, an element of degree 11
22. a_11_26 → c_2_5⁵·a_1_2 − c_2_5⁵·a_1_1 + c_2_4·c_2_5⁴·a_1_2 − c_2_4·c_2_5⁴·a_1_1
       − c_2_4²·c_2_5³·a_1_1 + c_2_4³·c_2_5²·a_1_2 + c_2_4³·c_2_5²·a_1_1
       + c_2_4⁴·c_2_5·a_1_2 − c_2_4⁴·c_2_5·a_1_1 + c_2_4⁵·a_1_2, an element of degree 11
23. a_12_22 → c_2_5⁵·a_1_1·a_1_2 + c_2_4·c_2_5⁴·a_1_1·a_1_2 − c_2_4²·c_2_5³·a_1_1·a_1_2
       + c_2_4³·c_2_5²·a_1_1·a_1_2 − c_2_4⁴·c_2_5·a_1_1·a_1_2, an element of degree 12
24. a_17_34 → c_2_4·c_2_5⁷·a_1_2 + c_2_4·c_2_5⁷·a_1_1 − c_2_4²·c_2_5⁶·a_1_2
       − c_2_4²·c_2_5⁶·a_1_1 − c_2_4²·c_2_5⁶·a_1_0 + c_2_4³·c_2_5⁵·a_1_1
       + c_2_4⁴·c_2_5⁴·a_1_2 + c_2_4⁴·c_2_5⁴·a_1_1 − c_2_4⁴·c_2_5⁴·a_1_0
       + c_2_4⁵·c_2_5³·a_1_1 + c_2_4⁶·c_2_5²·a_1_2 − c_2_4⁶·c_2_5²·a_1_0
       + c_2_4⁷·c_2_5·a_1_2 + c_2_4⁷·c_2_5·a_1_1 + c_2_3·c_2_4·c_2_5⁶·a_1_1
       − c_2_3·c_2_4³·c_2_5⁴·a_1_1 − c_2_3·c_2_4⁴·c_2_5³·a_1_2
       + c_2_3·c_2_4⁶·c_2_5·a_1_2 − c_2_3³·c_2_4·c_2_5⁴·a_1_1
       + c_2_3³·c_2_4²·c_2_5³·a_1_2 + c_2_3³·c_2_4³·c_2_5²·a_1_1
       − c_2_3³·c_2_4⁴·c_2_5·a_1_2, an element of degree 17
25. a_18_27 → c_2_5⁸·a_1_1·a_1_2 − c_2_4·c_2_5⁷·a_1_1·a_1_2 + c_2_4²·c_2_5⁶·a_1_1·a_1_2
       − c_2_4²·c_2_5⁶·a_1_0·a_1_2 − c_2_4⁴·c_2_5⁴·a_1_0·a_1_2
       + c_2_4⁵·c_2_5³·a_1_1·a_1_2 − c_2_4⁶·c_2_5²·a_1_1·a_1_2
       − c_2_4⁶·c_2_5²·a_1_0·a_1_2 + c_2_4⁸·a_1_1·a_1_2 + c_2_3·c_2_4·c_2_5⁶·a_1_1·a_1_2
       − c_2_3·c_2_4³·c_2_5⁴·a_1_1·a_1_2 − c_2_3³·c_2_4·c_2_5⁴·a_1_1·a_1_2
       + c_2_3³·c_2_4³·c_2_5²·a_1_1·a_1_2, an element of degree 18
26. c_18_37 → c_2_4·c_2_5⁷·a_1_1·a_1_2 − c_2_4²·c_2_5⁶·a_1_1·a_1_2
       − c_2_4²·c_2_5⁶·a_1_0·a_1_2 − c_2_4²·c_2_5⁶·a_1_0·a_1_1
       + c_2_4³·c_2_5⁵·a_1_1·a_1_2 − c_2_4⁴·c_2_5⁴·a_1_1·a_1_2
       − c_2_4⁴·c_2_5⁴·a_1_0·a_1_2 − c_2_4⁴·c_2_5⁴·a_1_0·a_1_1
       − c_2_4⁵·c_2_5³·a_1_1·a_1_2 − c_2_4⁶·c_2_5²·a_1_0·a_1_2
       − c_2_4⁶·c_2_5²·a_1_0·a_1_1 + c_2_3·c_2_4·c_2_5⁶·a_1_1·a_1_2
       − c_2_3·c_2_4³·c_2_5⁴·a_1_1·a_1_2 + c_2_3·c_2_4⁴·c_2_5³·a_1_1·a_1_2
       − c_2_3·c_2_4⁶·c_2_5·a_1_1·a_1_2 − c_2_3³·c_2_4·c_2_5⁴·a_1_1·a_1_2
       − c_2_3³·c_2_4²·c_2_5³·a_1_1·a_1_2 + c_2_3³·c_2_4³·c_2_5²·a_1_1·a_1_2
       + c_2_3³·c_2_4⁴·c_2_5·a_1_1·a_1_2 + c_2_5⁹ − c_2_4·c_2_5⁸ + c_2_4⁴·c_2_5⁵
       − c_2_4⁵·c_2_5⁴ + c_2_4⁷·c_2_5² − c_2_4⁸·c_2_5 − c_2_3·c_2_4²·c_2_5⁶
       − c_2_3·c_2_4⁴·c_2_5⁴ − c_2_3·c_2_4⁶·c_2_5² + c_2_3³·c_2_5⁶
       + c_2_3³·c_2_4²·c_2_5⁴ + c_2_3³·c_2_4⁴·c_2_5² + c_2_3³·c_2_4⁶ − c_2_3⁹, an element of degree 18
27. a_19_41 →  − c_2_4²·c_2_5⁶·a_1_0·a_1_1·a_1_2 − c_2_4⁴·c_2_5⁴·a_1_0·a_1_1·a_1_2
       − c_2_4⁶·c_2_5²·a_1_0·a_1_1·a_1_2 + c_2_5⁹·a_1_2 + c_2_5⁹·a_1_1
       + c_2_4·c_2_5⁸·a_1_2 + c_2_4·c_2_5⁸·a_1_1 − c_2_4²·c_2_5⁷·a_1_2
       − c_2_4²·c_2_5⁷·a_1_1 + c_2_4²·c_2_5⁷·a_1_0 + c_2_4³·c_2_5⁶·a_1_1
       + c_2_4⁴·c_2_5⁵·a_1_2 + c_2_4⁴·c_2_5⁵·a_1_1 + c_2_4⁴·c_2_5⁵·a_1_0
       + c_2_4⁵·c_2_5⁴·a_1_2 − c_2_4⁵·c_2_5⁴·a_1_1 + c_2_4⁶·c_2_5³·a_1_2
       + c_2_4⁶·c_2_5³·a_1_1 + c_2_4⁶·c_2_5³·a_1_0 − c_2_4⁷·c_2_5²·a_1_1
       + c_2_4⁸·c_2_5·a_1_2 + c_2_4⁹·a_1_2 − c_2_3·c_2_4·c_2_5⁷·a_1_1
       + c_2_3·c_2_4³·c_2_5⁵·a_1_1 + c_2_3·c_2_4⁴·c_2_5⁴·a_1_2
       − c_2_3·c_2_4⁶·c_2_5²·a_1_2 + c_2_3³·c_2_4·c_2_5⁵·a_1_1
       − c_2_3³·c_2_4²·c_2_5⁴·a_1_2 − c_2_3³·c_2_4³·c_2_5³·a_1_1
       + c_2_3³·c_2_4⁴·c_2_5²·a_1_2, an element of degree 19
28. a_20_36 → c_2_5⁹·a_1_1·a_1_2 + c_2_4²·c_2_5⁷·a_1_0·a_1_2 − c_2_4²·c_2_5⁷·a_1_0·a_1_1
       − c_2_4³·c_2_5⁶·a_1_1·a_1_2 + c_2_4³·c_2_5⁶·a_1_0·a_1_2
       − c_2_4³·c_2_5⁶·a_1_0·a_1_1 + c_2_4⁴·c_2_5⁵·a_1_1·a_1_2
       + c_2_4⁴·c_2_5⁵·a_1_0·a_1_2 − c_2_4⁴·c_2_5⁵·a_1_0·a_1_1
       − c_2_4⁵·c_2_5⁴·a_1_1·a_1_2 + c_2_4⁵·c_2_5⁴·a_1_0·a_1_2
       − c_2_4⁵·c_2_5⁴·a_1_0·a_1_1 + c_2_4⁶·c_2_5³·a_1_1·a_1_2
       + c_2_4⁶·c_2_5³·a_1_0·a_1_2 − c_2_4⁶·c_2_5³·a_1_0·a_1_1
       + c_2_4⁷·c_2_5²·a_1_1·a_1_2 + c_2_4⁷·c_2_5²·a_1_0·a_1_2
       − c_2_4⁷·c_2_5²·a_1_0·a_1_1 + c_2_4⁹·a_1_1·a_1_2 − c_2_3·c_2_4·c_2_5⁷·a_1_1·a_1_2
       − c_2_3·c_2_4²·c_2_5⁶·a_1_1·a_1_2 + c_2_3·c_2_4³·c_2_5⁵·a_1_1·a_1_2
       − c_2_3·c_2_4⁴·c_2_5⁴·a_1_1·a_1_2 + c_2_3·c_2_4⁵·c_2_5³·a_1_1·a_1_2
       − c_2_3·c_2_4⁶·c_2_5²·a_1_1·a_1_2 − c_2_3·c_2_4⁷·c_2_5·a_1_1·a_1_2
       + c_2_3³·c_2_4·c_2_5⁵·a_1_1·a_1_2 + c_2_3³·c_2_4³·c_2_5³·a_1_1·a_1_2
       + c_2_3³·c_2_4⁵·c_2_5·a_1_1·a_1_2, an element of degree 20

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