Cohomology of group number 554 of order 128

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128


General information on the group

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


Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    t9  −  t8  +  t7  +  t5  −  t4  +  t3  +  t2  +  1

    (t  +  1) · (t  −  1)4 · (t2  +  1)2 · (t4  +  1)
  • The a-invariants are -∞,-∞,-4,-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 22 minimal generators of maximal degree 8:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_2, a nilpotent element of degree 1
  3. b_1_1, an element of degree 1
  4. a_2_3, a nilpotent element of degree 2
  5. a_2_1, a nilpotent element of degree 2
  6. b_2_5, an element of degree 2
  7. a_3_4, a nilpotent element of degree 3
  8. a_3_5, a nilpotent element of degree 3
  9. b_3_9, an element of degree 3
  10. b_3_10, an element of degree 3
  11. a_4_7, a nilpotent element of degree 4
  12. a_4_8, a nilpotent element of degree 4
  13. c_4_16, a Duflot regular element of degree 4
  14. a_5_0, a nilpotent element of degree 5
  15. b_5_23, an element of degree 5
  16. a_6_19, a nilpotent element of degree 6
  17. b_6_31, an element of degree 6
  18. a_7_27, a nilpotent element of degree 7
  19. b_7_41, an element of degree 7
  20. b_7_44, an element of degree 7
  21. a_8_35, a nilpotent element of degree 8
  22. c_8_58, 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 165 minimal relations of maximal degree 16:

  1. a_1_02
  2. a_1_0·a_1_2
  3. a_1_0·b_1_1 + a_1_22
  4. a_1_22·b_1_1
  5. a_2_3·a_1_0
  6. a_2_1·a_1_0 + a_2_3·a_1_2
  7. a_1_2·b_1_12 + a_2_3·b_1_1 + a_2_1·a_1_2
  8. a_1_2·b_1_12 + b_2_5·a_1_0
  9. a_2_32
  10. a_2_1·a_1_2·b_1_1 + a_2_3·a_2_1 + a_2_1·a_1_22
  11. a_2_1·a_1_2·b_1_1 + a_2_12 + a_2_1·a_1_22
  12. a_1_0·a_3_4 + a_2_1·a_1_22
  13. a_1_2·a_3_4
  14. a_1_0·a_3_5 + a_2_1·a_1_2·b_1_1
  15. b_1_1·a_3_4 + b_2_5·a_1_2·b_1_1 + a_2_3·b_2_5 + a_1_2·a_3_5 + a_2_1·a_1_22
  16. a_1_0·b_3_9 + b_2_5·a_1_22 + a_2_1·a_1_2·b_1_1
  17. a_1_2·b_3_9 + a_2_3·b_2_5
  18. b_1_1·a_3_4 + a_1_0·b_3_10
  19. b_1_1·a_3_5 + a_1_2·b_3_10 + a_2_1·b_2_5 + b_2_5·a_1_22 + a_2_1·a_1_2·b_1_1
  20. a_2_3·b_2_5·b_1_1 + a_2_1·b_2_5·a_1_2
  21. a_2_3·a_3_4
  22. a_2_3·b_3_9 + a_1_22·a_3_5
  23. a_1_2·b_1_1·b_3_10 + b_2_5·a_3_4
  24. a_2_3·b_2_5·b_1_1 + a_1_22·b_3_10 + a_2_1·a_3_4 + a_2_3·a_3_5 + a_1_22·a_3_5
  25. b_2_5·a_3_4 + a_2_3·b_3_10 + a_2_3·b_2_5·b_1_1 + a_2_1·a_3_5 + a_1_22·a_3_5
  26. a_4_7·b_1_1 + a_2_1·b_3_9 + a_2_1·b_1_13 + a_2_1·b_2_5·b_1_1 + a_2_3·b_2_5·b_1_1
       + a_2_1·a_3_5 + a_2_1·a_3_4 + a_2_3·a_3_5
  27. a_4_7·a_1_0
  28. a_4_7·a_1_2 + a_2_1·a_3_4 + a_1_22·a_3_5
  29. a_4_8·b_1_1 + b_2_52·a_1_2 + a_2_1·b_3_10 + a_2_1·b_3_9 + a_2_1·b_2_5·b_1_1
       + a_2_3·b_2_5·b_1_1 + a_2_1·a_3_5 + a_2_1·a_3_4 + a_2_3·a_3_5
  30. a_4_8·a_1_0 + a_2_1·a_3_4
  31. a_2_3·b_2_5·b_1_1 + a_4_8·a_1_2 + a_2_1·a_3_5 + a_2_1·a_3_4 + a_1_22·a_3_5
  32. a_3_42
  33. b_3_92 + b_2_5·b_1_14 + b_2_52·b_1_12 + a_2_3·b_2_52 + a_2_3·a_2_1·b_2_5
  34. a_3_4·b_3_10 + a_3_4·b_3_9 + a_3_52 + a_3_4·a_3_5 + b_2_5·a_1_2·a_3_5
       + a_2_3·a_2_1·b_2_5
  35. a_3_4·b_3_9 + a_2_3·b_1_1·b_3_10
  36. a_3_4·a_3_5 + a_2_1·a_1_2·b_3_10
  37. a_2_3·b_2_52 + a_3_52 + a_2_3·a_2_1·b_2_5 + a_2_1·a_1_2·a_3_5 + c_4_16·a_1_22
  38. a_3_5·b_3_9 + b_2_5·a_1_2·b_3_10 + b_2_5·a_4_7 + a_2_1·b_2_5·b_1_12 + a_2_1·b_2_52
       + b_2_5·a_1_2·a_3_5 + a_2_3·a_2_1·b_2_5
  39. a_2_3·a_4_7 + a_2_1·a_1_2·a_3_5
  40. a_2_1·a_4_7
  41. a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_4·b_3_9 + b_2_5·a_1_2·b_3_10 + b_2_5·a_4_8
       + a_2_1·b_2_52 + a_3_4·a_3_5 + b_2_5·a_1_2·a_3_5 + a_2_3·a_2_1·b_2_5
       + a_2_1·a_1_2·a_3_5 + c_4_16·a_1_2·b_1_1
  42. a_3_4·a_3_5 + a_2_3·a_4_8 + a_2_3·a_2_1·b_2_5
  43. a_3_4·b_3_9 + b_2_5·a_1_2·a_3_5 + a_2_1·a_4_8
  44. b_3_102 + b_1_13·b_3_9 + b_1_16 + b_2_5·b_1_14 + b_2_53 + b_1_1·a_5_0
       + b_2_5·a_1_2·b_3_10 + a_2_1·b_1_1·b_3_10 + a_2_1·b_1_1·b_3_9 + a_2_1·b_1_14
       + a_2_3·a_2_1·b_2_5 + a_2_1·a_1_2·a_3_5 + c_4_16·b_1_12
  45. a_1_0·a_5_0 + a_2_3·a_2_1·b_2_5
  46. a_3_4·b_3_9 + a_3_4·a_3_5 + a_1_2·a_5_0 + a_2_1·a_1_2·a_3_5
  47. a_1_0·b_5_23 + a_2_3·b_2_52 + a_3_52 + a_2_1·a_1_2·a_3_5
  48. b_3_102 + b_1_13·b_3_9 + b_1_16 + b_2_5·b_1_14 + b_2_53 + a_1_2·b_5_23
       + a_2_1·b_1_1·b_3_10 + a_2_1·b_1_1·b_3_9 + a_3_52 + a_3_4·a_3_5 + c_4_16·b_1_12
       + c_4_16·a_1_2·b_1_1
  49. a_4_7·a_3_5 + a_2_1·b_2_52·a_1_2 + a_2_3·a_2_1·b_3_10 + a_2_3·c_4_16·a_1_2
  50. a_4_7·a_3_4
  51. a_4_7·b_3_9 + a_2_1·b_1_12·b_3_9 + a_2_1·b_2_5·b_3_9 + a_2_1·b_2_5·b_1_13
       + a_2_1·b_2_52·b_1_1 + a_2_1·b_2_5·a_3_5 + a_2_3·b_2_5·a_3_5 + a_2_3·a_2_1·b_3_10
  52. a_2_3·b_2_5·b_3_10 + a_4_8·a_3_5 + a_2_1·b_2_52·a_1_2 + a_2_3·a_2_1·b_3_10
       + a_2_1·c_4_16·a_1_2 + a_2_3·c_4_16·a_1_2
  53. a_4_8·a_3_4 + a_2_3·b_2_5·a_3_5 + a_2_3·a_2_1·b_3_10 + a_2_3·c_4_16·a_1_2
  54. a_4_8·b_3_9 + a_4_7·b_3_10 + b_2_53·a_1_2 + a_2_1·b_1_12·b_3_10 + a_2_1·b_2_5·b_3_10
       + a_2_1·b_2_5·b_3_9 + a_2_1·b_2_5·b_1_13 + a_2_1·b_2_52·b_1_1 + a_2_1·b_2_52·a_1_2
       + a_2_3·b_2_5·a_3_5 + a_2_3·a_2_1·b_3_10 + a_2_1·c_4_16·a_1_2
  55. a_2_1·b_2_52·a_1_2 + a_2_3·a_5_0 + a_2_3·b_2_5·a_3_5
  56. a_4_8·b_3_10 + a_4_7·b_3_10 + b_2_52·a_3_5 + a_2_1·b_1_12·b_3_10 + a_2_1·b_1_12·b_3_9
       + a_2_1·b_1_15 + a_2_1·b_2_5·b_1_13 + a_2_1·a_5_0 + a_2_1·b_2_5·a_3_5
       + a_2_3·a_2_1·b_3_10 + a_2_1·c_4_16·b_1_1
  57. b_1_12·b_5_23 + b_1_14·b_3_9 + b_2_52·b_3_9 + b_2_53·b_1_1 + b_2_5·a_5_0
       + b_2_52·a_3_5 + b_2_53·a_1_2 + a_2_1·b_2_5·b_1_13 + a_2_1·b_2_52·b_1_1
       + a_2_1·b_2_5·a_3_5 + a_2_3·b_2_5·a_3_5 + a_2_3·a_2_1·b_3_10 + c_4_16·b_1_13
       + a_2_3·c_4_16·b_1_1 + a_2_1·c_4_16·a_1_2
  58. a_1_2·b_1_1·b_5_23 + a_2_3·b_2_5·b_3_10 + a_2_1·b_2_5·a_3_5 + a_2_1·b_2_52·a_1_2
       + a_2_3·b_2_5·a_3_5 + a_2_3·a_2_1·b_3_10 + a_2_3·c_4_16·b_1_1 + a_2_1·c_4_16·a_1_2
  59. a_4_8·b_3_10 + a_4_7·b_3_10 + b_2_52·a_3_5 + a_2_1·b_1_12·b_3_10 + a_2_1·b_1_12·b_3_9
       + a_2_1·b_1_15 + a_2_1·b_2_5·b_1_13 + a_2_3·b_5_23 + a_2_3·b_2_5·b_3_10
       + a_2_1·b_2_5·a_3_5 + a_2_1·b_2_52·a_1_2 + a_2_3·b_2_5·a_3_5 + a_2_1·c_4_16·b_1_1
       + a_2_3·c_4_16·b_1_1 + a_2_3·c_4_16·a_1_2
  60. a_6_19·b_1_1 + a_2_1·b_5_23 + a_2_1·b_1_12·b_3_10 + a_2_1·b_1_12·b_3_9
       + a_2_1·b_2_5·b_3_10 + a_2_1·b_2_5·b_3_9 + a_2_1·b_2_52·b_1_1 + a_2_3·b_2_5·a_3_5
       + a_2_3·a_2_1·b_3_10 + a_2_3·c_4_16·b_1_1
  61. a_6_19·a_1_0 + a_2_3·a_2_1·b_3_10 + a_2_3·c_4_16·a_1_2
  62. a_4_8·b_3_10 + a_4_7·b_3_10 + b_2_52·a_3_5 + a_2_1·b_1_12·b_3_10 + a_2_1·b_1_12·b_3_9
       + a_2_1·b_1_15 + a_2_1·b_2_5·b_1_13 + a_6_19·a_1_2 + a_2_1·b_2_5·a_3_5
       + a_2_1·b_2_52·a_1_2 + a_2_1·c_4_16·b_1_1 + a_2_1·c_4_16·a_1_2
  63. b_6_31·a_1_0 + a_2_1·b_2_52·a_1_2 + a_2_3·b_2_5·a_3_5 + a_2_3·c_4_16·a_1_2
  64. b_6_31·a_1_2 + b_2_5·a_5_0 + a_2_1·b_2_5·b_1_13 + a_2_3·b_2_5·b_3_10
       + a_2_1·b_2_5·a_3_5 + a_2_3·b_2_5·a_3_5 + a_2_1·c_4_16·a_1_2 + a_2_3·c_4_16·a_1_2
  65. a_4_72
  66. a_4_82 + b_2_5·a_3_52 + a_2_1·b_2_5·a_1_2·a_3_5 + b_2_5·c_4_16·a_1_22
       + a_2_3·a_2_1·c_4_16
  67. a_4_7·a_4_8 + a_2_3·b_2_5·a_4_8 + a_2_1·b_2_5·a_1_2·a_3_5
  68. b_3_9·a_5_0 + b_2_5·a_1_2·b_5_23 + b_2_52·a_1_2·b_3_10 + a_2_1·b_1_13·b_3_9
       + a_3_5·a_5_0 + b_2_5·a_3_52 + a_2_3·b_2_5·a_4_8 + a_2_1·b_2_5·a_1_2·a_3_5
       + b_2_5·c_4_16·a_1_2·b_1_1 + b_2_5·c_4_16·a_1_22 + a_2_1·c_4_16·a_1_22
  69. a_3_4·b_5_23 + b_2_5·a_3_52 + a_2_1·b_2_5·a_4_8 + b_2_5·c_4_16·a_1_2·b_1_1
       + a_2_3·b_2_5·c_4_16 + c_4_16·a_1_2·a_3_5 + b_2_5·c_4_16·a_1_22
       + a_2_1·c_4_16·a_1_22
  70. b_2_52·a_4_7 + a_2_1·b_1_1·b_5_23 + a_2_1·b_1_13·b_3_9 + a_2_1·b_2_52·b_1_12
       + a_3_5·a_5_0 + a_2_1·b_2_5·a_4_8 + a_2_3·b_2_5·a_4_8 + a_2_1·c_4_16·b_1_12
       + b_2_5·c_4_16·a_1_22 + a_2_3·a_2_1·c_4_16
  71. a_3_4·a_5_0 + a_2_1·a_1_2·b_5_23 + a_2_3·b_2_5·a_4_8 + a_2_1·b_2_5·a_1_2·a_3_5
       + a_2_3·a_2_1·c_4_16
  72. b_3_9·b_5_23 + b_2_5·b_1_1·b_5_23 + b_2_5·b_1_13·b_3_9 + b_2_5·b_1_16
       + b_2_52·b_1_14 + b_2_53·b_1_12 + b_3_10·a_5_0 + a_3_5·b_5_23
       + b_2_52·a_1_2·b_3_10 + b_2_52·a_4_7 + a_2_1·b_1_13·b_3_10 + a_2_1·b_2_5·b_1_1·b_3_9
       + a_2_1·b_2_52·b_1_12 + a_3_4·a_5_0 + a_2_1·b_2_5·a_4_8 + a_2_3·b_2_5·a_4_8
       + a_2_1·b_2_5·a_1_2·a_3_5 + c_4_16·b_1_1·b_3_9 + b_2_5·c_4_16·b_1_12
       + c_4_16·a_1_2·b_3_10 + a_2_1·b_2_5·c_4_16 + a_2_3·b_2_5·c_4_16 + c_4_16·a_1_2·a_3_5
       + b_2_5·c_4_16·a_1_22
  73. b_3_10·a_5_0 + a_3_5·b_5_23 + b_2_5·a_6_19 + b_2_52·a_1_2·b_3_10 + b_2_52·a_4_8
       + a_2_1·b_1_13·b_3_10 + a_2_1·b_2_5·b_1_1·b_3_10 + a_2_1·b_2_5·b_1_1·b_3_9
       + a_3_4·a_5_0 + a_2_1·b_2_5·a_4_8 + a_2_3·b_2_5·a_4_8 + a_2_1·b_2_5·a_1_2·a_3_5
       + c_4_16·a_1_2·b_3_10 + c_4_16·a_1_2·a_3_5
  74. a_3_4·a_5_0 + a_2_3·a_6_19 + a_2_1·b_2_5·a_1_2·a_3_5 + a_2_3·a_2_1·c_4_16
       + a_2_1·c_4_16·a_1_22
  75. a_3_4·a_5_0 + a_2_1·a_6_19 + a_2_1·b_2_5·a_1_2·a_3_5
  76. b_3_9·a_5_0 + a_2_1·b_1_13·b_3_9 + a_2_3·b_6_31 + a_3_4·a_5_0 + a_2_3·b_2_5·a_4_8
       + a_2_3·a_2_1·c_4_16 + a_2_1·c_4_16·a_1_22
  77. b_3_10·a_5_0 + b_3_9·a_5_0 + b_1_1·a_7_27 + a_2_1·b_3_9·b_3_10 + a_2_1·b_1_13·b_3_9
       + a_2_1·b_6_31 + a_2_1·b_2_5·b_1_1·b_3_10 + a_3_5·a_5_0 + a_2_1·b_2_5·a_4_8
       + a_2_1·b_2_5·a_1_2·a_3_5 + c_4_16·a_1_2·b_3_10 + b_2_5·c_4_16·a_1_2·b_1_1
       + a_2_1·b_2_5·c_4_16 + b_2_5·c_4_16·a_1_22 + a_2_3·a_2_1·c_4_16
       + a_2_1·c_4_16·a_1_22
  78. a_1_0·a_7_27 + a_2_1·b_2_5·a_1_2·a_3_5 + a_2_3·a_2_1·c_4_16 + a_2_1·c_4_16·a_1_22
  79. a_3_5·a_5_0 + a_3_4·a_5_0 + a_1_2·a_7_27 + a_2_3·b_2_5·a_4_8 + a_2_1·b_2_5·a_1_2·a_3_5
       + c_4_16·a_1_2·a_3_5 + b_2_5·c_4_16·a_1_22 + a_2_1·c_4_16·a_1_22
  80. b_1_1·b_7_41 + b_1_12·b_3_9·b_3_10 + b_1_15·b_3_9 + b_1_18 + b_6_31·b_1_12
       + b_2_5·b_3_9·b_3_10 + b_2_5·b_1_13·b_3_9 + b_2_5·b_1_16 + b_2_52·b_1_14
       + b_2_52·a_1_2·b_3_10 + b_2_52·a_4_8 + a_2_1·b_6_31 + a_2_1·b_2_5·b_1_1·b_3_9
       + a_3_5·a_5_0 + a_3_4·a_5_0 + b_2_5·a_3_52 + a_2_1·b_2_5·a_4_8 + c_4_16·b_1_14
       + b_2_5·c_4_16·a_1_22 + a_2_1·c_4_16·a_1_22
  81. a_1_0·b_7_41 + a_3_4·a_5_0 + a_2_1·b_2_5·a_1_2·a_3_5 + a_2_1·c_4_16·a_1_22
  82. b_3_9·a_5_0 + a_1_2·b_7_41 + b_2_52·a_1_2·b_3_10 + a_2_1·b_1_13·b_3_9 + b_2_5·a_3_52
       + a_2_1·b_2_5·a_4_8 + a_2_3·a_2_1·c_4_16 + a_2_1·c_4_16·a_1_22
  83. a_1_0·b_7_44 + b_2_5·c_4_16·a_1_2·b_1_1 + a_2_3·b_2_5·c_4_16 + c_4_16·a_1_2·a_3_5
       + a_2_3·a_2_1·c_4_16
  84. b_3_10·a_5_0 + a_1_2·b_7_44 + a_2_1·b_1_13·b_3_10 + c_4_16·a_1_2·b_3_10
       + a_2_3·b_2_5·c_4_16 + b_2_5·c_4_16·a_1_22 + a_2_3·a_2_1·c_4_16
       + a_2_1·c_4_16·a_1_22
  85. a_4_7·a_5_0 + c_4_16·a_1_22·a_3_5
  86. a_4_7·b_5_23 + a_2_1·b_1_14·b_3_9 + a_2_1·b_2_5·b_1_12·b_3_9 + a_2_1·b_2_5·b_1_15
       + a_2_1·b_2_52·b_3_9 + a_2_1·b_2_52·b_1_13 + a_4_8·a_5_0 + a_2_1·b_2_5·a_5_0
       + a_2_1·c_4_16·b_3_9 + a_2_1·c_4_16·b_1_13 + a_2_1·b_2_5·c_4_16·b_1_1
       + a_2_1·c_4_16·a_3_5 + a_2_3·c_4_16·a_3_5
  87. a_6_19·b_3_10 + a_4_8·b_5_23 + b_2_5·a_4_7·b_3_10 + b_2_52·a_5_0 + b_2_53·a_3_5
       + b_2_54·a_1_2 + a_2_1·b_1_1·b_3_9·b_3_10 + a_2_1·b_1_14·b_3_9 + a_2_1·b_1_17
       + a_2_1·b_2_5·b_1_12·b_3_10 + a_2_1·b_2_5·b_1_15 + a_2_1·b_2_52·b_1_13
       + a_4_8·a_5_0 + a_2_1·b_2_5·a_5_0 + a_2_1·b_2_52·a_3_5 + b_2_52·c_4_16·a_1_2
       + a_2_1·c_4_16·b_3_9 + a_2_1·c_4_16·b_1_13 + a_2_3·c_4_16·b_3_10 + a_2_1·c_4_16·a_3_5
       + a_2_1·c_4_16·a_3_4
  88. a_6_19·a_3_5 + a_4_8·a_5_0 + a_2_1·b_2_5·a_5_0 + a_2_1·b_2_52·a_3_5 + a_3_53
       + a_2_1·c_4_16·a_3_5 + a_2_1·c_4_16·a_3_4 + a_2_3·c_4_16·a_3_5 + c_4_16·a_1_22·a_3_5
  89. a_6_19·a_3_4 + a_2_1·c_4_16·a_3_4 + c_4_16·a_1_22·a_3_5
  90. a_6_19·b_3_9 + b_2_5·a_4_7·b_3_10 + a_2_1·b_1_1·b_3_9·b_3_10 + a_2_1·b_2_5·b_5_23
       + a_2_1·b_2_5·b_1_12·b_3_10 + a_2_1·b_2_5·b_1_12·b_3_9 + a_2_1·b_2_52·b_3_10
       + a_2_1·b_2_52·b_3_9 + a_2_1·b_2_52·b_1_13 + a_2_1·b_2_5·a_5_0 + a_3_53
       + a_2_1·c_4_16·b_3_9 + a_2_1·b_2_5·c_4_16·b_1_1 + a_2_1·b_2_5·c_4_16·a_1_2
  91. b_6_31·a_3_5 + b_6_31·a_3_4 + b_2_5·a_7_27 + b_2_5·a_4_7·b_3_10 + b_2_52·a_5_0
       + b_2_54·a_1_2 + a_2_1·b_2_52·b_1_13 + a_2_1·b_2_5·a_5_0 + a_3_53
       + b_2_5·c_4_16·a_3_5 + b_2_52·c_4_16·a_1_2 + a_2_1·c_4_16·a_3_5 + c_4_16·a_1_22·a_3_5
  92. a_2_1·b_2_5·a_5_0 + a_2_3·a_7_27 + a_2_3·c_4_16·a_3_5
  93. a_4_8·a_5_0 + a_2_1·a_7_27 + a_2_1·c_4_16·a_3_5 + a_2_1·b_2_5·c_4_16·a_1_2
  94. b_1_1·b_3_10·b_5_23 + b_1_13·b_3_9·b_3_10 + b_2_5·b_7_41 + b_2_5·b_1_1·b_3_9·b_3_10
       + b_2_5·b_1_14·b_3_9 + b_2_5·b_1_17 + b_2_5·b_6_31·b_1_1 + b_2_52·b_1_12·b_3_9
       + b_2_52·b_1_15 + b_2_53·b_3_10 + b_2_53·b_1_13 + b_6_31·a_3_5 + b_6_31·a_3_4
       + a_2_1·b_2_5·b_5_23 + a_2_1·b_2_5·b_1_12·b_3_9 + a_2_1·b_2_52·b_3_10
       + a_2_1·b_2_52·b_3_9 + b_2_5·a_4_8·a_3_5 + c_4_16·b_1_12·b_3_10
       + b_2_5·c_4_16·b_1_13 + b_2_52·c_4_16·a_1_2 + a_2_1·b_2_5·c_4_16·b_1_1
       + a_2_3·c_4_16·b_3_10 + a_2_1·b_2_5·c_4_16·a_1_2 + c_4_16·a_1_22·a_3_5
  95. a_2_3·b_7_41 + b_2_5·a_4_8·a_3_5 + a_2_1·b_2_5·c_4_16·a_1_2 + c_4_16·a_1_22·a_3_5
  96. b_2_5·a_4_7·b_3_10 + a_2_1·b_7_41 + a_2_1·b_1_1·b_3_9·b_3_10 + a_2_1·b_1_14·b_3_9
       + a_2_1·b_1_17 + a_2_1·b_6_31·b_1_1 + a_2_1·b_2_5·b_1_12·b_3_10
       + a_2_1·b_2_5·b_1_12·b_3_9 + a_2_1·b_2_5·b_1_15 + a_2_1·b_2_52·b_3_10
       + a_2_1·b_2_52·b_1_13 + a_2_1·b_2_5·a_5_0 + a_2_1·b_2_52·a_3_5
       + a_2_1·c_4_16·b_1_13 + a_2_1·b_2_5·c_4_16·a_1_2 + c_4_16·a_1_22·a_3_5
  97. b_1_12·b_7_44 + b_1_16·b_3_10 + b_1_19 + b_6_31·b_3_9 + b_2_5·b_1_1·b_3_9·b_3_10
       + b_2_5·b_1_14·b_3_10 + b_2_5·b_1_14·b_3_9 + b_2_5·b_6_31·b_1_1
       + b_2_52·b_1_12·b_3_9 + b_2_53·b_3_9 + b_2_53·b_1_13 + b_2_54·b_1_1 + b_6_31·a_3_5
       + b_6_31·a_3_4 + b_2_5·a_4_7·b_3_10 + b_2_53·a_3_5 + b_2_54·a_1_2
       + a_2_1·b_1_1·b_3_9·b_3_10 + a_2_1·b_1_14·b_3_9 + a_2_1·b_1_17
       + a_2_1·b_2_52·b_3_10 + a_2_1·b_2_52·b_3_9 + a_2_1·b_2_53·b_1_1 + a_2_1·b_2_5·a_5_0
       + c_4_16·b_1_12·b_3_10 + c_4_16·b_1_12·b_3_9 + c_4_16·b_1_15
       + b_2_5·c_4_16·b_1_13 + b_2_52·c_4_16·a_1_2 + a_2_1·c_4_16·b_3_9
       + a_2_1·b_2_5·c_4_16·b_1_1 + a_2_1·c_4_16·a_3_5
  98. a_1_2·b_1_1·b_7_44 + b_6_31·a_3_4 + a_2_3·c_4_16·b_3_10 + a_2_1·c_4_16·a_3_5
       + a_2_1·c_4_16·a_3_4
  99. b_6_31·a_3_4 + a_2_3·b_7_44 + a_4_8·a_5_0 + a_2_3·c_4_16·b_3_10 + a_2_1·c_4_16·a_3_4
  100. a_8_35·b_1_1 + b_6_31·a_3_4 + b_2_52·a_5_0 + b_2_54·a_1_2 + a_2_1·b_7_44
       + a_2_1·b_1_14·b_3_10 + a_2_1·b_1_17 + a_2_1·b_6_31·b_1_1 + a_2_1·b_2_52·b_3_10
       + a_2_1·b_2_52·b_3_9 + b_2_5·a_4_8·a_3_5 + a_2_1·b_2_5·a_5_0 + a_2_1·c_4_16·b_3_10
       + a_2_1·c_4_16·b_3_9 + a_2_1·c_4_16·b_1_13 + a_2_3·c_4_16·b_3_10 + a_2_1·c_4_16·a_3_5
       + a_2_3·c_4_16·a_3_5
  101. a_8_35·a_1_0 + c_4_16·a_1_22·a_3_5
  102. a_8_35·a_1_2 + a_4_8·a_5_0 + a_2_1·b_2_5·a_5_0 + a_2_1·b_2_52·a_3_5
       + a_2_1·c_4_16·a_3_4 + a_2_1·b_2_5·c_4_16·a_1_2 + a_2_3·c_4_16·a_3_5
       + c_4_16·a_1_22·a_3_5
  103. a_5_02
  104. a_4_7·a_6_19 + a_2_1·c_4_16·a_1_2·a_3_5
  105. a_5_0·b_5_23 + b_3_10·a_7_27 + a_4_8·b_6_31 + a_4_7·b_6_31 + b_2_53·a_1_2·b_3_10
       + a_2_1·b_1_15·b_3_9 + a_2_1·b_1_18 + a_2_1·b_6_31·b_1_12
       + a_2_1·b_2_5·b_1_1·b_5_23 + a_2_1·b_2_5·b_1_13·b_3_9 + a_2_1·b_2_5·b_1_16
       + a_2_1·b_2_52·b_1_1·b_3_9 + b_2_52·a_3_52 + a_4_8·a_3_52
       + b_2_5·c_4_16·a_1_2·b_3_10 + b_2_5·a_4_8·c_4_16 + b_2_5·a_4_7·c_4_16
       + a_2_1·c_4_16·b_1_1·b_3_9 + a_2_1·b_2_5·c_4_16·b_1_12 + c_4_16·a_3_52
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_16 + a_2_3·a_4_8·c_4_16
       + a_2_3·a_2_1·b_2_5·c_4_16 + c_4_162·a_1_2·b_1_1 + c_4_162·a_1_22
  106. a_2_3·b_2_5·b_6_31 + a_3_5·a_7_27 + a_4_8·a_6_19 + a_4_8·a_3_52 + c_4_16·a_3_52
       + a_2_3·a_2_1·b_2_5·c_4_16 + a_2_1·c_4_16·a_1_2·a_3_5
  107. a_3_4·a_7_27 + a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27 + a_2_1·b_2_52·a_4_8
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16
  108. a_5_0·b_5_23 + b_3_9·a_7_27 + a_4_7·b_6_31 + a_2_1·b_1_12·b_3_9·b_3_10
       + a_2_1·b_1_15·b_3_9 + a_2_1·b_6_31·b_1_12 + a_2_1·b_2_5·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_13·b_3_10 + a_2_1·b_2_5·b_6_31 + a_2_1·b_2_52·b_1_1·b_3_10
       + a_2_1·b_2_52·b_1_1·b_3_9 + a_2_1·b_2_53·b_1_12 + b_2_5·a_1_2·a_7_27
       + b_2_52·a_3_52 + a_2_1·b_2_52·a_4_8 + a_4_8·a_3_52 + c_4_16·a_1_2·b_5_23
       + b_2_5·a_4_7·c_4_16 + a_2_1·c_4_16·b_1_14 + a_2_1·b_2_5·c_4_16·b_1_12
       + a_2_1·b_2_52·c_4_16 + c_4_16·a_3_52 + b_2_5·c_4_16·a_1_2·a_3_5
       + a_2_3·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16 + a_2_1·c_4_16·a_1_2·a_3_5
       + c_4_162·a_1_2·b_1_1
  109. b_3_10·b_7_41 + b_1_14·b_3_9·b_3_10 + b_1_17·b_3_10 + b_1_17·b_3_9
       + b_6_31·b_1_1·b_3_10 + b_2_5·b_1_12·b_3_9·b_3_10 + b_2_5·b_1_15·b_3_10
       + b_2_5·b_1_18 + b_2_52·b_1_1·b_5_23 + b_2_52·b_1_13·b_3_10 + b_2_53·b_1_1·b_3_9
       + b_2_53·b_1_14 + b_2_55 + a_4_8·b_6_31 + a_4_7·b_6_31 + b_2_53·a_1_2·b_3_10
       + a_2_1·b_3_10·b_5_23 + a_2_1·b_6_31·b_1_12 + a_2_1·b_2_5·b_1_16
       + a_2_1·b_2_52·b_1_1·b_3_9 + a_2_1·b_2_52·b_1_14 + a_2_1·b_2_54 + a_4_8·a_6_19
       + b_2_5·a_1_2·a_7_27 + a_2_1·b_2_52·a_4_8 + c_4_16·b_1_13·b_3_10
       + c_4_16·b_1_13·b_3_9 + b_2_5·c_4_16·b_1_1·b_3_9 + b_2_52·c_4_16·b_1_12
       + a_2_1·c_4_16·b_1_1·b_3_10 + a_2_1·b_2_52·c_4_16 + a_2_1·a_4_8·c_4_16
       + a_2_1·c_4_16·a_1_2·a_3_5
  110. a_5_0·b_5_23 + a_3_5·b_7_41 + b_2_53·a_1_2·b_3_10 + b_2_53·a_4_8 + a_2_1·b_3_10·b_5_23
       + a_2_1·b_1_12·b_3_9·b_3_10 + a_2_1·b_1_15·b_3_9 + a_2_1·b_2_5·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_1·b_5_23 + a_2_1·b_2_5·b_1_16 + a_2_1·b_2_5·b_6_31
       + a_2_1·b_2_52·b_1_14 + a_2_3·b_2_5·b_6_31 + a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27
       + c_4_16·a_1_2·b_5_23 + b_2_5·c_4_16·a_1_2·b_3_10 + a_2_1·c_4_16·b_1_1·b_3_10
       + a_2_1·c_4_16·b_1_14 + c_4_16·a_3_52 + b_2_5·c_4_16·a_1_2·a_3_5
       + a_2_3·a_4_8·c_4_16 + c_4_162·a_1_2·b_1_1
  111. a_3_4·b_7_41 + a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27 + b_2_52·a_3_52 + a_4_8·a_3_52
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_16 + a_2_3·a_4_8·c_4_16
       + a_2_3·a_2_1·b_2_5·c_4_16
  112. b_3_9·b_7_41 + b_1_17·b_3_9 + b_6_31·b_1_1·b_3_9 + b_2_5·b_1_15·b_3_10
       + b_2_5·b_1_15·b_3_9 + b_2_5·b_1_18 + b_2_52·b_1_13·b_3_9 + b_2_53·b_1_1·b_3_10
       + b_2_53·b_1_14 + a_4_7·b_6_31 + b_2_53·a_4_8 + a_2_1·b_3_10·b_5_23
       + a_2_1·b_1_12·b_3_9·b_3_10 + a_2_1·b_6_31·b_1_12 + a_2_1·b_2_5·b_6_31
       + a_2_1·b_2_52·b_1_14 + a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27 + b_2_52·a_3_52
       + a_2_1·b_2_52·a_4_8 + c_4_16·b_1_13·b_3_9 + a_2_1·c_4_16·b_1_1·b_3_10
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_3·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16
  113. a_5_0·b_5_23 + b_2_5·a_1_2·b_7_44 + a_2_1·b_1_15·b_3_9 + a_2_1·b_2_52·b_1_1·b_3_9
       + a_2_1·b_2_53·b_1_12 + a_2_3·b_2_5·b_6_31 + a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27
       + b_2_52·a_3_52 + c_4_16·a_1_2·b_5_23 + a_2_1·c_4_16·b_1_14 + c_4_16·a_3_52
       + a_2_1·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16 + c_4_162·a_1_2·b_1_1
  114. a_3_4·b_7_44 + a_2_3·b_2_5·b_6_31 + b_2_5·a_1_2·a_7_27 + c_4_16·a_3_52
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_16
  115. a_4_7·b_6_31 + a_2_1·b_1_1·b_7_44 + a_2_1·b_1_15·b_3_10 + a_2_1·b_1_18
       + a_2_1·b_6_31·b_1_12 + a_2_1·b_2_5·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_1·b_5_23
       + a_2_1·b_2_5·b_1_13·b_3_10 + a_2_1·b_2_52·b_1_1·b_3_9 + a_2_1·b_2_53·b_1_12
       + a_4_8·a_6_19 + a_2_1·b_2_52·a_4_8 + a_2_1·c_4_16·b_1_1·b_3_10
       + a_2_1·c_4_16·b_1_1·b_3_9 + a_2_1·c_4_16·b_1_14
  116. a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27 + a_2_1·a_1_2·b_7_44 + a_2_1·b_2_52·a_4_8
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16
  117. b_3_9·b_7_44 + b_1_14·b_3_9·b_3_10 + b_1_17·b_3_9 + b_2_5·b_1_1·b_7_44
       + b_2_5·b_1_12·b_3_9·b_3_10 + b_2_5·b_1_15·b_3_10 + b_2_5·b_1_18
       + b_2_5·b_6_31·b_1_12 + b_2_52·b_3_9·b_3_10 + b_2_52·b_1_13·b_3_9
       + b_2_52·b_1_16 + b_2_53·b_1_1·b_3_10 + b_2_54·b_1_12 + a_3_5·b_7_44
       + b_2_53·a_4_8 + a_2_1·b_1_15·b_3_9 + a_2_1·b_2_5·b_1_13·b_3_9
       + a_2_1·b_2_5·b_1_16 + a_2_1·b_2_52·b_1_1·b_3_9 + a_2_1·b_2_52·b_1_14
       + a_2_1·b_2_53·b_1_12 + a_2_3·b_2_5·b_6_31 + b_2_5·a_1_2·a_7_27
       + a_2_1·b_2_52·a_4_8 + a_4_8·a_3_52 + c_4_16·b_3_9·b_3_10 + c_4_16·b_1_13·b_3_9
       + b_2_5·c_4_16·b_1_1·b_3_10 + c_4_16·a_1_2·b_5_23 + b_2_5·a_4_8·c_4_16
       + c_4_162·a_1_22
  118. b_5_232 + b_2_5·b_1_18 + b_2_52·b_1_16 + b_2_55 + b_2_53·a_1_2·b_3_10
       + a_2_3·b_2_5·b_6_31 + b_2_5·a_1_2·a_7_27 + a_2_1·b_2_52·a_4_8 + c_8_58·a_1_22
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_3·a_2_1·b_2_5·c_4_16 + a_2_1·c_4_16·a_1_2·a_3_5
       + c_4_162·b_1_12 + c_4_162·a_1_22
  119. a_5_0·b_5_23 + a_3_5·b_7_44 + b_2_5·a_8_35 + b_2_53·a_1_2·b_3_10 + b_2_53·a_4_8
       + a_2_1·b_1_15·b_3_9 + a_2_1·b_2_5·b_1_13·b_3_10 + a_2_1·b_2_5·b_1_16
       + a_2_1·b_2_5·b_6_31 + a_2_1·b_2_52·b_1_1·b_3_9 + a_2_1·b_2_54 + a_4_8·a_6_19
       + b_2_5·a_1_2·a_7_27 + b_2_52·a_3_52 + b_2_5·a_4_8·c_4_16 + a_2_1·c_4_16·b_1_14
       + a_2_1·b_2_5·c_4_16·b_1_12 + a_2_1·b_2_52·c_4_16 + c_4_16·a_3_52
       + a_2_1·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16 + a_2_1·c_4_16·a_1_2·a_3_5
       + c_4_162·a_1_2·b_1_1 + c_4_162·a_1_22
  120. a_4_8·a_6_19 + b_2_5·a_1_2·a_7_27 + a_2_1·b_2_52·a_4_8 + a_2_3·a_8_35 + a_4_8·a_3_52
       + b_2_5·c_4_16·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_16 + a_2_3·a_4_8·c_4_16
       + a_2_3·a_2_1·b_2_5·c_4_16
  121. b_2_5·a_1_2·a_7_27 + a_2_1·a_8_35 + a_2_1·b_2_52·a_4_8 + b_2_5·c_4_16·a_1_2·a_3_5
       + a_2_3·a_4_8·c_4_16 + a_2_3·a_2_1·b_2_5·c_4_16 + a_2_1·c_4_16·a_1_2·a_3_5
  122. b_6_31·a_5_0 + b_2_55·a_1_2 + a_2_1·b_6_31·b_1_13 + a_4_8·a_7_27
       + b_2_53·c_4_16·a_1_2 + a_4_8·c_4_16·a_3_5 + a_2_1·b_2_5·c_4_16·a_3_5
       + a_2_3·c_4_16·a_5_0 + a_2_3·b_2_5·c_4_16·a_3_5
  123. a_6_19·a_5_0 + a_2_3·b_2_5·a_7_27 + b_2_5·a_3_53 + a_2_1·c_4_16·a_5_0
       + a_2_3·a_2_1·c_4_16·b_3_10
  124. a_6_19·a_5_0 + a_4_7·a_7_27 + b_2_5·a_3_53 + a_2_1·c_4_16·a_5_0 + a_2_3·c_4_16·a_5_0
       + a_2_3·c_4_162·a_1_2
  125. a_4_8·b_7_41 + b_2_53·a_5_0 + b_2_54·a_3_5 + b_2_55·a_1_2
       + a_2_1·b_1_13·b_3_9·b_3_10 + a_2_1·b_1_16·b_3_10 + a_2_1·b_6_31·b_3_10
       + a_2_1·b_6_31·b_3_9 + a_2_1·b_2_5·b_7_41 + a_2_1·b_2_5·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_14·b_3_9 + a_2_1·b_2_52·b_5_23 + a_2_1·b_2_52·b_1_12·b_3_10
       + a_2_1·b_2_52·b_1_12·b_3_9 + a_2_1·b_2_53·b_3_10 + a_2_1·b_2_53·b_3_9
       + a_2_1·b_2_53·b_1_13 + a_6_19·a_5_0 + b_2_52·a_4_8·a_3_5 + a_2_1·b_2_53·a_3_5
       + b_2_5·a_3_53 + a_2_1·c_4_16·b_1_12·b_3_10 + a_2_1·b_2_5·c_4_16·b_3_9
       + a_2_1·b_2_52·c_4_16·b_1_1 + a_2_1·c_4_16·a_5_0 + a_2_3·b_2_5·c_4_16·a_3_5
       + a_2_3·a_2_1·c_4_16·b_3_10
  126. a_4_8·b_7_41 + a_4_7·b_7_41 + b_2_53·a_5_0 + b_2_54·a_3_5 + b_2_55·a_1_2
       + a_2_1·b_1_16·b_3_10 + a_2_1·b_1_19 + a_2_1·b_6_31·b_3_10 + a_2_1·b_6_31·b_1_13
       + a_2_1·b_2_5·b_1_14·b_3_10 + a_2_1·b_2_5·b_1_14·b_3_9 + a_2_1·b_2_52·b_5_23
       + a_2_1·b_2_52·b_1_12·b_3_10 + a_2_1·b_2_52·b_1_15 + a_2_1·b_2_53·b_3_9
       + a_6_19·a_5_0 + b_2_52·a_4_8·a_3_5 + a_2_1·b_2_5·a_7_27 + b_2_5·a_3_53
       + a_2_1·c_4_16·b_1_12·b_3_10 + a_2_1·c_4_16·b_1_12·b_3_9 + a_2_1·c_4_16·b_1_15
       + a_2_1·b_2_5·c_4_16·b_3_9 + a_2_1·b_2_52·c_4_16·b_1_1 + a_2_1·c_4_16·a_5_0
       + a_2_1·b_2_5·c_4_16·a_3_5 + a_2_3·b_2_5·c_4_16·a_3_5
  127. b_6_31·a_5_0 + b_2_55·a_1_2 + a_2_1·b_6_31·b_1_13 + a_2_3·b_2_5·b_7_44
       + a_2_1·b_2_5·a_7_27 + a_2_1·b_2_53·a_3_5 + b_2_5·a_3_53 + b_2_53·c_4_16·a_1_2
       + a_4_8·c_4_16·a_3_5 + a_2_1·c_4_16·a_5_0 + a_2_1·b_2_5·c_4_16·a_3_5
       + a_2_1·c_4_162·a_1_2 + a_2_3·c_4_162·a_1_2
  128. a_4_8·b_7_41 + a_4_7·b_7_44 + b_2_53·a_5_0 + b_2_54·a_3_5 + b_2_55·a_1_2
       + a_2_1·b_1_16·b_3_9 + a_2_1·b_1_19 + a_2_1·b_6_31·b_3_10
       + a_2_1·b_2_5·b_1_14·b_3_9 + a_2_1·b_2_5·b_6_31·b_1_1 + a_2_1·b_2_52·b_5_23
       + a_2_1·b_2_52·b_1_12·b_3_10 + a_2_1·b_2_53·b_1_13 + b_2_52·a_4_8·a_3_5
       + a_2_1·b_2_5·a_7_27 + a_2_1·b_2_53·a_3_5 + a_4_7·c_4_16·b_3_10
       + a_2_1·c_4_16·b_1_12·b_3_10 + a_2_1·c_4_16·b_1_15 + a_2_1·b_2_5·c_4_16·b_3_9
       + a_2_1·b_2_52·c_4_16·b_1_1 + a_2_1·c_4_16·a_5_0 + a_2_3·a_2_1·c_4_16·b_3_10
  129. a_6_19·b_5_23 + a_4_8·b_7_41 + b_2_5·a_4_8·b_5_23 + a_2_1·b_1_16·b_3_10
       + a_2_1·b_6_31·b_3_10 + a_2_1·b_6_31·b_3_9 + a_2_1·b_2_5·b_1_17
       + a_2_1·b_2_5·b_6_31·b_1_1 + a_2_1·b_2_52·b_5_23 + a_2_1·b_2_52·b_1_12·b_3_10
       + a_2_1·b_2_52·b_1_15 + a_2_1·b_2_54·b_1_1 + b_2_52·a_4_8·a_3_5
       + a_2_1·b_2_53·a_3_5 + b_2_5·a_3_53 + b_2_53·c_4_16·a_1_2
       + a_2_1·c_4_16·b_1_12·b_3_9 + a_2_1·b_2_5·c_4_16·b_3_9 + a_2_1·b_2_5·c_4_16·b_1_13
       + a_2_1·b_2_52·c_4_16·b_1_1 + a_4_8·c_4_16·a_3_5 + a_2_1·c_4_16·a_5_0
       + a_2_1·b_2_5·c_4_16·a_3_5 + a_2_3·c_8_58·a_1_2 + a_2_3·c_4_16·a_5_0
       + a_2_1·c_4_162·b_1_1 + a_2_3·c_4_162·b_1_1 + a_2_1·c_4_162·a_1_2
       + a_2_3·c_4_162·a_1_2
  130. b_6_31·b_5_23 + b_6_31·b_1_12·b_3_9 + b_2_52·b_7_44 + b_2_52·b_7_41
       + b_2_52·b_1_1·b_3_9·b_3_10 + b_2_52·b_1_14·b_3_10 + b_2_52·b_1_14·b_3_9
       + b_2_52·b_6_31·b_1_1 + b_2_53·b_5_23 + b_2_53·b_1_12·b_3_10
       + b_2_53·b_1_12·b_3_9 + b_2_53·b_1_15 + b_2_54·b_3_9 + b_2_54·b_1_13
       + b_2_55·b_1_1 + b_6_31·a_5_0 + a_4_8·b_7_41 + b_2_5·a_4_8·b_5_23 + b_2_55·a_1_2
       + a_2_1·b_1_13·b_3_9·b_3_10 + a_2_1·b_1_16·b_3_10 + a_2_1·b_6_31·b_3_10
       + a_2_1·b_6_31·b_3_9 + a_2_1·b_6_31·b_1_13 + a_2_1·b_2_5·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_17 + a_2_1·b_2_5·b_6_31·b_1_1 + a_2_1·b_2_52·b_5_23
       + a_2_1·b_2_52·b_1_12·b_3_10 + a_2_1·b_2_52·b_1_15 + a_2_1·b_2_54·b_1_1
       + a_6_19·a_5_0 + b_2_52·a_4_8·a_3_5 + b_2_5·a_3_53 + c_4_16·b_6_31·b_1_1
       + b_2_52·c_4_16·b_3_10 + b_2_52·c_4_16·b_3_9 + b_2_5·c_4_16·a_5_0
       + b_2_53·c_4_16·a_1_2 + a_2_1·c_4_16·b_5_23 + a_2_1·c_4_16·b_1_12·b_3_10
       + a_2_1·c_4_16·b_1_12·b_3_9 + a_2_1·b_2_5·c_4_16·b_3_10 + a_2_3·c_8_58·b_1_1
       + a_4_8·c_4_16·a_3_5 + a_2_1·c_8_58·a_1_2 + a_2_1·c_4_16·a_5_0
       + a_2_3·b_2_5·c_4_16·a_3_5 + a_2_1·c_4_162·b_1_1 + a_2_1·c_4_162·a_1_2
  131. a_8_35·b_3_10 + b_6_31·a_5_0 + a_4_8·b_7_44 + b_2_53·a_5_0 + b_2_54·a_3_5
       + a_2_1·b_1_13·b_3_9·b_3_10 + a_2_1·b_1_16·b_3_10 + a_2_1·b_1_19
       + a_2_1·b_6_31·b_3_10 + a_2_1·b_6_31·b_1_13 + a_2_1·b_2_5·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_14·b_3_10 + a_2_1·b_2_5·b_6_31·b_1_1
       + a_2_1·b_2_52·b_1_12·b_3_10 + a_2_1·b_2_53·b_3_10 + a_2_1·b_2_53·b_1_13
       + a_2_1·b_2_54·b_1_1 + a_2_1·b_2_5·a_7_27 + b_2_52·c_4_16·a_3_5
       + b_2_53·c_4_16·a_1_2 + a_2_1·c_4_16·b_1_12·b_3_10 + a_2_1·b_2_5·c_4_16·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_13 + a_2_1·b_2_52·c_4_16·b_1_1 + a_2_1·c_4_16·a_5_0
       + a_2_1·b_2_5·c_4_16·a_3_5 + a_2_3·c_4_16·a_5_0 + a_2_3·b_2_5·c_4_16·a_3_5
       + a_2_1·c_4_162·b_1_1 + a_2_3·c_4_162·b_1_1
  132. b_6_31·a_5_0 + b_2_55·a_1_2 + a_2_1·b_6_31·b_1_13 + a_8_35·a_3_5
       + b_2_52·a_4_8·a_3_5 + a_2_1·b_2_5·a_7_27 + a_2_1·b_2_53·a_3_5 + b_2_5·a_3_53
       + b_2_53·c_4_16·a_1_2 + a_2_3·c_4_16·a_5_0
  133. a_8_35·a_3_4 + a_6_19·a_5_0 + a_2_1·c_4_16·a_5_0 + a_2_3·b_2_5·c_4_16·a_3_5
  134. a_8_35·b_3_9 + b_6_31·a_5_0 + b_2_53·a_5_0 + a_2_1·b_6_31·b_3_9 + a_2_1·b_6_31·b_1_13
       + a_2_1·b_2_5·b_7_44 + a_2_1·b_2_5·b_1_1·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_14·b_3_10
       + a_2_1·b_2_5·b_1_17 + a_2_1·b_2_5·b_6_31·b_1_1 + a_2_1·b_2_52·b_1_15
       + a_2_1·b_2_53·b_3_10 + a_6_19·a_5_0 + b_2_52·a_4_8·a_3_5 + a_2_1·b_2_53·a_3_5
       + b_2_5·a_3_53 + b_2_53·c_4_16·a_1_2 + a_2_1·b_2_5·c_4_16·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_13 + a_2_1·b_2_52·c_4_16·b_1_1 + a_4_8·c_4_16·a_3_5
       + a_2_3·c_4_16·a_5_0 + a_2_3·b_2_5·c_4_16·a_3_5 + a_2_3·a_2_1·c_4_16·b_3_10
       + a_2_1·c_4_162·a_1_2 + a_2_3·c_4_162·a_1_2
  135. a_6_192 + a_2_3·a_2_1·c_4_162
  136. a_5_0·b_7_44 + b_2_54·a_1_2·b_3_10 + a_2_1·b_1_17·b_3_10 + a_2_1·b_1_110
       + a_2_1·b_6_31·b_1_1·b_3_9 + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_15·b_3_10 + a_2_1·b_2_5·b_1_15·b_3_9
       + a_2_1·b_2_5·b_6_31·b_1_12 + a_2_1·b_2_52·b_1_13·b_3_9
       + a_2_1·b_2_53·b_1_1·b_3_9 + a_2_1·b_2_53·b_1_14 + a_2_1·b_2_54·b_1_12
       + a_5_0·a_7_27 + b_2_5·a_4_8·a_3_52 + c_4_16·a_1_2·b_7_44
       + b_2_52·c_4_16·a_1_2·b_3_10 + a_2_1·c_4_16·b_1_13·b_3_10
       + a_2_1·c_4_16·b_1_13·b_3_9 + a_2_1·c_4_16·b_1_16 + a_2_1·b_2_5·c_4_16·b_1_14
       + a_2_3·c_4_16·b_6_31 + c_4_16·a_1_2·a_7_27 + a_2_1·b_2_5·a_4_8·c_4_16
       + a_2_3·c_4_16·a_6_19 + a_2_3·b_2_5·a_4_8·c_4_16 + a_2_1·b_2_5·c_4_16·a_1_2·a_3_5
       + c_4_162·a_1_2·b_3_10 + a_2_3·b_2_5·c_4_162 + c_4_162·a_1_2·a_3_5
       + a_2_3·a_2_1·c_4_162
  137. b_1_16·b_3_9·b_3_10 + b_1_19·b_3_10 + b_1_112 + b_6_31·b_1_13·b_3_9 + b_6_312
       + b_2_5·b_1_14·b_3_9·b_3_10 + b_2_5·b_1_17·b_3_10 + b_2_5·b_1_110
       + b_2_52·b_1_12·b_3_9·b_3_10 + b_2_52·b_1_15·b_3_10 + b_2_52·b_1_18
       + b_2_52·b_6_31·b_1_12 + b_2_53·b_1_13·b_3_9 + b_2_54·b_1_14 + b_2_55·b_1_12
       + b_2_56 + b_2_54·a_1_2·b_3_10 + b_2_54·a_4_8 + a_2_1·b_1_17·b_3_10
       + a_2_1·b_1_17·b_3_9 + a_2_1·b_1_110 + a_2_1·b_6_31·b_1_14
       + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_15·b_3_9
       + a_2_1·b_2_5·b_6_31·b_1_12 + a_2_1·b_2_52·b_1_13·b_3_9 + a_2_1·b_2_52·b_1_16
       + a_2_1·b_2_53·b_1_14 + a_2_1·b_2_54·b_1_12 + a_5_0·a_7_27 + b_2_5·a_3_5·a_7_27
       + b_2_53·a_3_52 + a_2_1·b_2_53·a_4_8 + c_8_58·b_1_14 + c_4_16·b_1_15·b_3_9
       + c_4_16·b_1_18 + b_2_52·c_4_16·b_1_14 + b_2_54·c_4_16
       + a_2_1·c_4_16·b_1_13·b_3_10 + a_2_1·c_4_16·b_1_13·b_3_9 + a_2_1·c_4_16·b_1_16
       + a_2_1·b_2_5·c_4_16·b_1_14 + a_2_1·b_2_52·c_4_16·b_1_12 + c_4_16·a_1_2·a_7_27
       + b_2_5·c_4_16·a_3_52 + a_2_3·c_4_16·a_6_19 + a_2_3·b_2_5·a_4_8·c_4_16
       + c_4_162·a_1_2·a_3_5 + b_2_5·c_4_162·a_1_22
  138. b_5_23·b_7_41 + b_1_19·b_3_9 + b_6_31·b_1_13·b_3_9 + b_2_5·b_1_17·b_3_10
       + b_2_5·b_1_17·b_3_9 + b_2_5·b_1_110 + b_2_52·b_3_10·b_5_23 + b_2_52·b_1_1·b_7_44
       + b_2_52·b_1_12·b_3_9·b_3_10 + b_2_52·b_1_15·b_3_10 + b_2_52·b_1_18
       + b_2_53·b_1_1·b_5_23 + b_2_53·b_1_13·b_3_10 + b_2_53·b_1_16
       + b_2_54·b_1_1·b_3_9 + b_2_54·b_1_14 + b_2_55·b_1_12 + b_5_23·a_7_27
       + a_5_0·b_7_41 + b_2_52·a_1_2·b_7_44 + a_2_1·b_1_17·b_3_9 + a_2_1·b_1_110
       + a_2_1·b_6_31·b_1_14 + a_2_1·b_2_5·b_3_10·b_5_23
       + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_15·b_3_10
       + a_2_1·b_2_5·b_1_15·b_3_9 + a_2_1·b_2_5·b_1_18 + a_2_1·b_2_52·b_1_1·b_5_23
       + a_2_1·b_2_52·b_1_13·b_3_10 + a_2_1·b_2_52·b_1_13·b_3_9 + a_2_1·b_2_52·b_6_31
       + a_2_1·b_2_53·b_1_1·b_3_10 + a_2_1·b_2_53·b_1_1·b_3_9 + b_2_5·a_3_5·a_7_27
       + c_4_16·b_1_12·b_3_9·b_3_10 + c_4_16·b_1_18 + c_4_16·b_6_31·b_1_12
       + b_2_5·c_4_16·b_3_9·b_3_10 + b_2_5·c_4_16·b_1_13·b_3_9 + b_2_5·c_4_16·b_1_16
       + b_2_53·c_4_16·b_1_12 + b_2_5·c_4_16·a_6_19 + a_2_1·c_4_16·b_3_9·b_3_10
       + a_2_1·c_4_16·b_1_1·b_5_23 + a_2_1·c_4_16·b_1_13·b_3_10
       + a_2_1·c_4_16·b_1_13·b_3_9 + a_2_1·c_4_16·b_1_16
       + a_2_1·b_2_5·c_4_16·b_1_1·b_3_10 + a_2_1·b_2_53·c_4_16 + a_2_3·c_4_16·b_6_31
       + b_2_5·c_8_58·a_1_22 + b_2_5·c_4_16·a_3_52 + a_2_1·b_2_5·a_4_8·c_4_16
       + a_2_3·c_4_16·a_6_19 + a_2_1·b_2_5·c_4_16·a_1_2·a_3_5 + c_4_162·b_1_14
       + c_4_162·a_1_2·b_3_10 + b_2_5·c_4_162·a_1_2·b_1_1 + a_2_1·c_4_162·b_1_12
       + c_4_162·a_1_2·a_3_5 + b_2_5·c_4_162·a_1_22 + a_2_1·c_4_162·a_1_22
  139. a_5_0·b_7_41 + b_2_52·a_1_2·b_7_44 + a_2_1·b_1_14·b_3_9·b_3_10 + a_2_1·b_1_17·b_3_9
       + a_2_1·b_1_110 + a_2_1·b_6_31·b_1_14 + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_15·b_3_9 + a_2_1·b_2_5·b_1_18 + a_2_1·b_2_52·b_1_16
       + b_2_5·a_3_5·a_7_27 + b_2_53·a_3_52 + a_2_1·b_2_53·a_4_8
       + b_2_52·c_4_16·a_1_2·b_3_10 + a_2_1·c_4_16·b_1_16 + b_2_5·c_4_16·a_3_52
       + a_2_1·b_2_5·a_4_8·c_4_16 + a_2_3·c_4_16·a_6_19 + a_2_3·b_2_5·a_4_8·c_4_16
       + a_2_1·c_8_58·a_1_22 + a_2_1·b_2_5·c_4_16·a_1_2·a_3_5 + a_2_3·a_2_1·c_4_162
       + a_2_1·c_4_162·a_1_22
  140. b_5_23·b_7_44 + b_1_16·b_3_9·b_3_10 + b_1_19·b_3_9 + b_2_5·b_1_14·b_3_9·b_3_10
       + b_2_5·b_6_31·b_1_1·b_3_9 + b_2_5·b_6_31·b_1_14 + b_2_52·b_3_10·b_5_23
       + b_2_52·b_1_15·b_3_10 + b_2_52·b_1_15·b_3_9 + b_2_52·b_1_18
       + b_2_52·b_6_31·b_1_12 + b_2_53·b_3_9·b_3_10 + b_2_53·b_1_13·b_3_9
       + b_2_53·b_1_16 + b_2_53·b_6_31 + b_2_54·b_1_14 + b_2_55·b_1_12 + b_2_56
       + a_5_0·b_7_44 + a_5_0·b_7_41 + a_6_19·b_6_31 + b_2_5·a_4_8·b_6_31 + b_2_52·a_1_2·b_7_44
       + a_2_1·b_1_14·b_3_9·b_3_10 + a_2_1·b_1_17·b_3_10 + a_2_1·b_6_31·b_1_1·b_3_10
       + a_2_1·b_6_31·b_1_1·b_3_9 + a_2_1·b_6_31·b_1_14 + a_2_1·b_2_5·b_3_10·b_5_23
       + a_2_1·b_2_5·b_1_1·b_7_44 + a_2_1·b_2_5·b_1_15·b_3_10 + a_2_1·b_2_5·b_1_18
       + a_2_1·b_2_5·b_6_31·b_1_12 + a_2_1·b_2_52·b_3_9·b_3_10
       + a_2_1·b_2_52·b_1_13·b_3_9 + a_2_1·b_2_52·b_1_16 + a_2_1·b_2_52·b_6_31
       + a_2_1·b_2_53·b_1_1·b_3_9 + a_2_1·b_2_53·b_1_14 + a_2_1·b_2_55
       + b_2_5·a_3_5·a_7_27 + a_2_1·b_2_53·a_4_8 + b_2_5·a_4_8·a_3_52
       + c_4_16·b_3_10·b_5_23 + c_4_16·b_1_1·b_7_44 + c_4_16·b_1_15·b_3_9
       + b_2_5·c_4_16·b_1_13·b_3_9 + b_2_5·c_4_16·b_1_16 + b_2_52·c_4_16·b_1_1·b_3_10
       + b_2_52·c_4_16·b_1_1·b_3_9 + b_2_52·c_4_16·b_1_14 + b_2_5·c_8_58·a_1_2·b_1_1
       + b_2_5·c_4_16·a_6_19 + b_2_52·a_4_8·c_4_16 + a_2_1·c_4_16·b_1_1·b_5_23
       + a_2_1·c_4_16·b_1_13·b_3_10 + a_2_1·c_4_16·b_6_31 + a_2_1·b_2_5·c_4_16·b_1_1·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_14 + a_2_1·b_2_52·c_4_16·b_1_12 + a_2_3·c_4_16·b_6_31
       + a_2_3·b_2_5·c_8_58 + c_8_58·a_1_2·a_3_5 + c_4_16·a_1_2·a_7_27 + a_2_3·c_4_16·a_6_19
       + a_2_3·b_2_5·a_4_8·c_4_16 + a_2_3·a_2_1·c_8_58 + c_4_162·b_1_1·b_3_10
       + b_2_5·c_4_162·a_1_2·b_1_1 + a_2_1·c_4_162·b_1_12 + a_2_1·b_2_5·c_4_162
       + a_2_3·b_2_5·c_4_162 + c_4_162·a_1_2·a_3_5 + b_2_5·c_4_162·a_1_22
       + a_2_3·a_2_1·c_4_162
  141. b_5_23·a_7_27 + a_6_19·b_6_31 + b_2_5·a_4_8·b_6_31 + a_2_1·b_1_14·b_3_9·b_3_10
       + a_2_1·b_6_31·b_1_1·b_3_10 + a_2_1·b_6_31·b_1_1·b_3_9
       + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_15·b_3_10
       + a_2_1·b_2_52·b_3_9·b_3_10 + a_2_1·b_2_52·b_1_13·b_3_10 + a_4_8·a_8_35
       + b_2_5·a_3_5·a_7_27 + b_2_5·c_4_16·a_6_19 + b_2_52·c_4_16·a_1_2·b_3_10
       + b_2_52·a_4_8·c_4_16 + a_2_1·c_4_16·b_3_9·b_3_10 + a_2_1·c_4_16·b_1_13·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_1·b_3_9 + c_4_16·a_1_2·a_7_27 + b_2_5·c_4_16·a_3_52
       + a_2_1·b_2_5·c_4_16·a_1_2·a_3_5 + c_4_162·a_1_2·b_3_10 + b_2_5·c_4_162·a_1_2·b_1_1
       + b_2_5·c_4_162·a_1_22 + a_2_1·c_4_162·a_1_22
  142. b_5_23·b_7_44 + b_1_16·b_3_9·b_3_10 + b_1_19·b_3_9 + b_2_5·b_1_14·b_3_9·b_3_10
       + b_2_5·b_6_31·b_1_1·b_3_9 + b_2_5·b_6_31·b_1_14 + b_2_52·b_3_10·b_5_23
       + b_2_52·b_1_15·b_3_10 + b_2_52·b_1_15·b_3_9 + b_2_52·b_1_18
       + b_2_52·b_6_31·b_1_12 + b_2_53·b_3_9·b_3_10 + b_2_53·b_1_13·b_3_9
       + b_2_53·b_1_16 + b_2_53·b_6_31 + b_2_54·b_1_14 + b_2_55·b_1_12 + b_2_56
       + a_5_0·b_7_44 + a_5_0·b_7_41 + b_2_52·a_8_35 + b_2_53·a_6_19 + b_2_54·a_4_8
       + a_2_1·b_1_14·b_3_9·b_3_10 + a_2_1·b_1_17·b_3_10 + a_2_1·b_6_31·b_1_1·b_3_9
       + a_2_1·b_6_31·b_1_14 + a_2_1·b_2_5·b_1_1·b_7_44 + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_15·b_3_10 + a_2_1·b_2_5·b_1_18 + a_2_1·b_2_5·b_6_31·b_1_12
       + a_2_1·b_2_52·b_3_9·b_3_10 + a_2_1·b_2_52·b_1_13·b_3_9 + a_2_1·b_2_52·b_1_16
       + a_2_1·b_2_53·b_1_14 + a_2_1·b_2_54·b_1_12 + a_5_0·a_7_27 + b_2_5·a_3_5·a_7_27
       + b_2_53·a_3_52 + b_2_5·a_4_8·a_3_52 + c_4_16·b_3_10·b_5_23 + c_4_16·b_1_1·b_7_44
       + c_4_16·b_1_15·b_3_9 + b_2_5·c_4_16·b_1_13·b_3_9 + b_2_5·c_4_16·b_1_16
       + b_2_52·c_4_16·b_1_1·b_3_10 + b_2_52·c_4_16·b_1_1·b_3_9 + b_2_52·c_4_16·b_1_14
       + b_2_5·c_8_58·a_1_2·b_1_1 + b_2_5·c_4_16·a_6_19 + b_2_52·a_4_8·c_4_16
       + a_2_1·c_4_16·b_1_1·b_5_23 + a_2_1·c_4_16·b_1_13·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_14 + a_2_1·b_2_52·c_4_16·b_1_12 + a_2_3·b_2_5·c_8_58
       + c_8_58·a_1_2·a_3_5 + c_4_16·a_1_2·a_7_27 + a_2_1·b_2_5·a_4_8·c_4_16
       + a_2_3·c_4_16·a_6_19 + a_2_3·b_2_5·a_4_8·c_4_16 + c_4_162·b_1_1·b_3_10
       + b_2_5·c_4_162·a_1_2·b_1_1 + a_2_1·c_4_162·b_1_12 + a_2_1·b_2_5·c_4_162
       + a_2_3·b_2_5·c_4_162 + c_4_162·a_1_2·a_3_5 + a_2_3·a_2_1·c_4_162
       + a_2_1·c_4_162·a_1_22
  143. a_5_0·a_7_27 + a_2_1·b_2_53·a_4_8 + a_2_3·b_2_5·a_8_35 + c_4_16·a_1_2·a_7_27
       + a_2_1·b_2_5·a_4_8·c_4_16 + a_2_3·c_4_16·a_6_19 + a_2_1·b_2_5·c_4_16·a_1_2·a_3_5
       + c_4_162·a_1_2·a_3_5 + b_2_5·c_4_162·a_1_22 + a_2_3·a_2_1·c_4_162
  144. b_5_23·a_7_27 + a_6_19·b_6_31 + b_2_5·a_4_8·b_6_31 + a_2_1·b_1_14·b_3_9·b_3_10
       + a_2_1·b_6_31·b_1_1·b_3_10 + a_2_1·b_6_31·b_1_1·b_3_9
       + a_2_1·b_2_5·b_1_12·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_15·b_3_10
       + a_2_1·b_2_52·b_3_9·b_3_10 + a_2_1·b_2_52·b_1_13·b_3_10 + b_2_53·a_3_52
       + a_2_1·b_2_5·a_8_35 + b_2_5·c_4_16·a_6_19 + b_2_52·c_4_16·a_1_2·b_3_10
       + b_2_52·a_4_8·c_4_16 + a_2_1·c_4_16·b_3_9·b_3_10 + a_2_1·c_4_16·b_1_13·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_1·b_3_9 + c_4_16·a_1_2·a_7_27 + a_2_3·b_2_5·a_4_8·c_4_16
       + a_2_1·b_2_5·c_4_16·a_1_2·a_3_5 + c_4_162·a_1_2·b_3_10 + b_2_5·c_4_162·a_1_2·b_1_1
       + b_2_5·c_4_162·a_1_22 + a_2_3·a_2_1·c_4_162
  145. a_5_0·a_7_27 + a_4_7·a_8_35 + a_2_1·b_2_53·a_4_8 + c_4_16·a_1_2·a_7_27
       + a_2_1·b_2_5·a_4_8·c_4_16 + a_2_3·c_4_16·a_6_19 + c_4_162·a_1_2·a_3_5
       + b_2_5·c_4_162·a_1_22 + a_2_3·a_2_1·c_4_162 + a_2_1·c_4_162·a_1_22
  146. a_6_19·a_7_27 + a_2_1·b_2_52·a_7_27 + a_2_1·b_2_54·a_3_5 + a_3_52·a_7_27
       + b_2_52·a_3_53 + a_2_1·b_2_52·c_4_16·a_3_5 + a_2_3·c_4_16·a_7_27 + c_4_16·a_3_53
       + a_2_1·c_4_162·a_3_5 + a_2_1·c_4_162·a_3_4 + a_2_1·b_2_5·c_4_162·a_1_2
  147. a_6_19·b_7_41 + b_2_52·a_4_8·b_5_23 + b_2_54·a_5_0 + b_2_55·a_3_5 + b_2_56·a_1_2
       + a_2_1·b_1_15·b_3_9·b_3_10 + a_2_1·b_1_18·b_3_10 + a_2_1·b_1_18·b_3_9
       + a_2_1·b_6_31·b_1_12·b_3_10 + a_2_1·b_2_5·b_1_19 + a_2_1·b_2_5·b_6_31·b_3_10
       + a_2_1·b_2_5·b_6_31·b_3_9 + a_2_1·b_2_52·b_7_44 + a_2_1·b_2_52·b_7_41
       + a_2_1·b_2_52·b_1_14·b_3_9 + a_2_1·b_2_52·b_1_17 + a_2_1·b_2_53·b_1_12·b_3_10
       + a_2_1·b_2_53·b_1_12·b_3_9 + a_2_1·b_2_54·b_3_10 + a_2_1·b_2_54·b_3_9
       + a_2_1·b_2_54·b_1_13 + a_2_1·b_2_52·a_7_27 + b_2_52·a_3_53
       + b_2_54·c_4_16·a_1_2 + a_2_1·c_4_16·b_7_41 + a_2_1·c_4_16·b_1_14·b_3_10
       + a_2_1·c_4_16·b_1_14·b_3_9 + a_2_1·b_2_5·c_4_16·b_1_12·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_12·b_3_9 + a_2_1·b_2_52·c_4_16·b_1_13
       + a_2_1·b_2_53·c_4_16·b_1_1 + b_2_5·a_4_8·c_4_16·a_3_5 + a_2_1·b_2_52·c_4_16·a_3_5
       + c_8_58·a_1_22·a_3_5 + c_4_16·a_3_53 + a_2_1·b_2_5·c_4_162·a_1_2
       + c_4_162·a_1_22·a_3_5
  148. b_6_31·b_7_41 + b_6_31·b_1_1·b_3_9·b_3_10 + b_6_31·b_1_14·b_3_9 + b_6_31·b_1_17
       + b_6_312·b_1_1 + b_2_5·b_1_1·b_3_10·b_7_44 + b_2_5·b_1_18·b_3_10
       + b_2_5·b_1_18·b_3_9 + b_2_5·b_1_111 + b_2_5·b_6_31·b_1_12·b_3_9
       + b_2_5·b_6_31·b_1_15 + b_2_52·b_1_13·b_3_9·b_3_10 + b_2_52·b_6_31·b_3_10
       + b_2_52·b_6_31·b_1_13 + b_2_53·b_7_41 + b_2_53·b_1_17 + b_2_53·b_6_31·b_1_1
       + b_2_54·b_1_12·b_3_10 + b_2_54·b_1_12·b_3_9 + b_2_54·b_1_15 + b_2_55·b_3_10
       + b_2_55·b_3_9 + b_6_31·a_7_27 + a_6_19·b_7_44 + b_2_5·a_4_8·b_7_44
       + b_2_52·a_4_8·b_5_23 + a_2_1·b_1_18·b_3_10 + a_2_1·b_1_18·b_3_9 + a_2_1·b_1_111
       + a_2_1·b_6_31·b_1_12·b_3_10 + a_2_1·b_2_5·b_6_31·b_3_9 + a_2_1·b_2_52·b_7_44
       + a_2_1·b_2_52·b_1_17 + a_2_1·b_2_53·b_5_23 + a_2_1·b_2_53·b_1_12·b_3_10
       + a_2_1·b_2_54·b_3_9 + a_2_1·b_2_54·b_1_13 + a_2_1·b_2_55·b_1_1
       + b_2_53·a_4_8·a_3_5 + a_2_1·b_2_52·a_7_27 + a_2_1·b_2_54·a_3_5 + a_3_52·a_7_27
       + c_4_16·b_6_31·b_1_13 + b_2_5·c_4_16·b_1_1·b_3_9·b_3_10
       + b_2_5·c_4_16·b_1_14·b_3_10 + b_2_5·c_4_16·b_1_14·b_3_9
       + b_2_52·c_4_16·b_1_12·b_3_10 + b_2_52·c_4_16·b_1_12·b_3_9
       + b_2_53·c_4_16·b_1_13 + b_2_54·c_4_16·b_1_1 + a_4_8·c_4_16·b_5_23
       + b_2_5·c_4_16·a_7_27 + a_2_1·c_4_16·b_7_44 + a_2_1·c_4_16·b_1_14·b_3_10
       + a_2_1·c_4_16·b_1_14·b_3_9 + a_2_1·b_2_5·c_4_16·b_1_12·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_15 + a_2_1·b_2_52·c_4_16·b_1_13
       + a_2_1·b_2_53·c_4_16·b_1_1 + b_2_5·a_4_8·c_4_16·a_3_5 + a_2_1·b_2_5·c_8_58·a_1_2
       + a_2_3·c_8_58·a_3_5 + b_2_5·c_4_162·b_1_13 + b_2_5·c_4_162·a_3_5
       + a_2_1·c_4_162·b_3_10 + a_2_1·c_4_162·b_3_9 + a_2_1·c_4_162·b_1_13
       + a_2_1·b_2_5·c_4_162·b_1_1 + a_2_3·c_4_162·b_3_10 + c_4_162·a_1_22·a_3_5
  149. a_6_19·b_7_44 + b_2_5·a_4_8·b_7_44 + b_2_52·a_4_8·b_5_23 + b_2_53·a_7_27
       + b_2_55·a_3_5 + b_2_56·a_1_2 + a_2_1·b_1_1·b_3_10·b_7_44
       + a_2_1·b_2_52·b_1_14·b_3_9 + a_2_1·b_2_53·b_1_12·b_3_9 + a_2_1·b_2_54·b_3_10
       + a_2_1·b_2_54·b_3_9 + a_2_1·b_2_55·b_1_1 + b_2_53·a_4_8·a_3_5
       + a_2_1·b_2_52·a_7_27 + a_2_1·b_2_54·a_3_5 + a_3_52·a_7_27 + b_2_52·a_3_53
       + a_4_8·c_4_16·b_5_23 + b_2_52·c_4_16·a_5_0 + b_2_53·c_4_16·a_3_5
       + a_2_1·c_4_16·b_7_44 + a_2_1·c_4_16·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_12·b_3_9 + a_2_1·b_2_5·c_4_16·b_1_15
       + a_2_1·b_2_52·c_4_16·b_3_10 + a_2_3·c_4_16·b_7_44 + a_2_1·c_8_58·a_3_4
       + a_2_3·c_4_16·a_7_27 + c_4_16·a_3_53 + b_2_52·c_4_162·a_1_2
       + a_2_1·c_4_162·b_3_10 + a_2_1·c_4_162·b_3_9 + a_2_1·b_2_5·c_4_162·b_1_1
       + a_2_1·c_4_162·a_3_5 + a_2_1·c_4_162·a_3_4 + a_2_1·b_2_5·c_4_162·a_1_2
       + a_2_3·c_4_162·a_3_5
  150. b_6_31·b_7_41 + b_6_31·b_1_1·b_3_9·b_3_10 + b_6_31·b_1_14·b_3_9 + b_6_31·b_1_17
       + b_6_312·b_1_1 + b_2_5·b_1_1·b_3_10·b_7_44 + b_2_5·b_1_18·b_3_10
       + b_2_5·b_1_18·b_3_9 + b_2_5·b_1_111 + b_2_5·b_6_31·b_1_12·b_3_9
       + b_2_5·b_6_31·b_1_15 + b_2_52·b_1_13·b_3_9·b_3_10 + b_2_52·b_6_31·b_3_10
       + b_2_52·b_6_31·b_1_13 + b_2_53·b_7_41 + b_2_53·b_1_17 + b_2_53·b_6_31·b_1_1
       + b_2_54·b_1_12·b_3_10 + b_2_54·b_1_12·b_3_9 + b_2_54·b_1_15 + b_2_55·b_3_10
       + b_2_55·b_3_9 + a_6_19·b_7_41 + b_2_52·a_4_8·b_5_23 + b_2_53·a_7_27 + b_2_55·a_3_5
       + b_2_56·a_1_2 + a_2_1·b_1_18·b_3_9 + a_2_1·b_1_111 + a_2_1·b_6_31·b_1_12·b_3_10
       + a_2_1·b_6_31·b_1_12·b_3_9 + a_2_1·b_2_5·b_1_16·b_3_10 + a_2_1·b_2_5·b_6_31·b_3_10
       + a_2_1·b_2_52·b_1_1·b_3_9·b_3_10 + a_2_1·b_2_52·b_1_14·b_3_10
       + a_2_1·b_2_53·b_5_23 + a_2_1·b_2_53·b_1_12·b_3_10 + a_2_1·b_2_53·b_1_15
       + a_2_1·b_2_54·b_3_10 + a_2_1·b_2_55·b_1_1 + a_2_1·b_2_52·a_7_27
       + a_2_1·b_2_54·a_3_5 + c_4_16·b_6_31·b_1_13 + b_2_5·c_4_16·b_1_1·b_3_9·b_3_10
       + b_2_5·c_4_16·b_1_14·b_3_10 + b_2_5·c_4_16·b_1_14·b_3_9
       + b_2_52·c_4_16·b_1_12·b_3_10 + b_2_52·c_4_16·b_1_12·b_3_9
       + b_2_53·c_4_16·b_1_13 + b_2_54·c_4_16·b_1_1 + b_2_52·c_4_16·a_5_0
       + b_2_54·c_4_16·a_1_2 + a_2_1·c_8_58·b_1_13 + a_2_1·c_4_16·b_1_1·b_3_9·b_3_10
       + a_2_1·c_4_16·b_1_14·b_3_10 + a_2_1·c_4_16·b_1_14·b_3_9
       + a_2_1·c_4_16·b_6_31·b_1_1 + a_2_1·b_2_5·c_4_16·b_1_15
       + a_2_1·b_2_52·c_4_16·b_1_13 + a_2_1·b_2_53·c_4_16·b_1_1
       + a_2_1·b_2_52·c_4_16·a_3_5 + a_2_3·c_4_16·a_7_27 + c_4_16·a_3_53
       + b_2_5·c_4_162·b_1_13 + a_2_1·c_4_162·b_1_13 + a_2_3·c_4_162·a_3_5
  151. b_1_110·b_3_10 + b_1_110·b_3_9 + b_1_113 + b_6_31·b_7_44 + b_6_31·b_7_41
       + b_6_31·b_1_1·b_3_9·b_3_10 + b_6_31·b_1_14·b_3_10 + b_2_5·b_1_15·b_3_9·b_3_10
       + b_2_5·b_1_18·b_3_10 + b_2_5·b_1_18·b_3_9 + b_2_5·b_6_31·b_1_12·b_3_10
       + b_2_5·b_6_31·b_1_12·b_3_9 + b_2_52·b_1_13·b_3_9·b_3_10 + b_2_52·b_1_16·b_3_9
       + b_2_52·b_6_31·b_1_13 + b_2_53·b_7_44 + b_2_53·b_7_41 + b_2_53·b_1_17
       + b_2_53·b_6_31·b_1_1 + b_2_54·b_1_15 + b_2_56·b_1_1 + b_6_31·a_7_27
       + b_2_5·a_4_8·b_7_44 + b_2_52·a_4_8·b_5_23 + b_2_54·a_5_0 + b_2_56·a_1_2
       + a_2_1·b_1_15·b_3_9·b_3_10 + a_2_1·b_1_18·b_3_10 + a_2_1·b_1_111
       + a_2_1·b_6_31·b_1_12·b_3_10 + a_2_1·b_2_5·b_1_13·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_16·b_3_10 + a_2_1·b_2_5·b_6_31·b_3_9
       + a_2_1·b_2_52·b_1_1·b_3_9·b_3_10 + a_2_1·b_2_52·b_1_14·b_3_10
       + a_2_1·b_2_52·b_1_14·b_3_9 + a_2_1·b_2_52·b_1_17 + a_2_1·b_2_53·b_5_23
       + a_2_1·b_2_53·b_1_12·b_3_9 + a_2_1·b_2_54·b_1_13 + a_2_1·b_2_55·b_1_1
       + b_2_5·a_4_8·a_7_27 + a_2_1·b_2_52·a_7_27 + a_2_1·b_2_54·a_3_5
       + c_8_58·b_1_12·b_3_9 + c_8_58·b_1_15 + c_4_16·b_1_19 + c_4_16·b_6_31·b_3_10
       + c_4_16·b_6_31·b_3_9 + b_2_5·c_8_58·b_1_13 + b_2_5·c_4_16·b_1_14·b_3_9
       + b_2_5·c_4_16·b_6_31·b_1_1 + b_2_52·c_4_16·b_5_23 + b_2_53·c_4_16·b_3_10
       + b_2_53·c_4_16·b_3_9 + b_2_53·c_4_16·b_1_13 + b_2_5·c_4_16·a_7_27
       + b_2_54·c_4_16·a_1_2 + a_2_1·c_4_16·b_7_44 + a_2_1·c_4_16·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·c_8_58·b_1_1 + a_2_1·b_2_52·c_4_16·b_1_13
       + a_2_1·b_2_53·c_4_16·b_1_1 + a_2_3·c_8_58·b_3_10 + a_2_3·c_4_16·b_7_44
       + b_2_5·a_4_8·c_4_16·a_3_5 + a_2_1·c_8_58·a_3_5 + a_2_1·c_4_16·a_7_27
       + a_2_1·b_2_5·c_8_58·a_1_2 + c_4_16·a_3_53 + b_2_52·c_4_162·b_1_1
       + b_2_5·c_4_162·a_3_5 + a_2_1·c_4_162·b_3_10 + a_2_1·c_4_162·b_3_9
       + a_2_1·c_4_162·b_1_13 + a_2_3·c_4_162·b_3_10 + a_2_1·c_4_162·a_3_4
       + a_2_1·b_2_5·c_4_162·a_1_2 + c_4_162·a_1_22·a_3_5
  152. a_8_35·a_5_0 + a_2_1·b_2_52·a_7_27 + a_2_1·b_2_54·a_3_5 + a_3_52·a_7_27
       + c_4_162·a_1_22·a_3_5
  153. a_8_35·b_5_23 + a_6_19·b_7_44 + a_6_19·b_7_41 + b_2_5·a_4_8·b_7_44 + b_2_54·a_5_0
       + b_2_55·a_3_5 + b_2_56·a_1_2 + a_2_1·b_1_1·b_3_10·b_7_44
       + a_2_1·b_1_15·b_3_9·b_3_10 + a_2_1·b_1_18·b_3_10 + a_2_1·b_1_18·b_3_9
       + a_2_1·b_6_31·b_1_12·b_3_10 + a_2_1·b_6_31·b_1_12·b_3_9
       + a_2_1·b_2_5·b_1_13·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_19 + a_2_1·b_2_5·b_6_31·b_3_10
       + a_2_1·b_2_5·b_6_31·b_1_13 + a_2_1·b_2_53·b_1_12·b_3_9 + a_2_1·b_2_54·b_3_10
       + a_2_1·b_2_55·b_1_1 + b_2_5·a_4_8·a_7_27 + a_2_1·b_2_52·a_7_27 + a_2_1·b_2_54·a_3_5
       + b_2_52·a_3_53 + a_4_8·c_4_16·b_5_23 + b_2_54·c_4_16·a_1_2 + a_2_1·c_4_16·b_7_41
       + a_2_1·c_4_16·b_1_1·b_3_9·b_3_10 + a_2_1·c_4_16·b_1_14·b_3_9
       + a_2_1·c_4_16·b_1_17 + a_2_1·c_4_16·b_6_31·b_1_1 + a_2_1·b_2_5·c_4_16·b_5_23
       + a_2_1·b_2_5·c_4_16·b_1_12·b_3_10 + a_2_1·b_2_5·c_4_16·b_1_15
       + a_2_1·b_2_52·c_4_16·b_3_10 + a_2_1·b_2_52·c_4_16·b_1_13 + a_2_3·c_4_16·b_7_44
       + b_2_5·a_4_8·c_4_16·a_3_5 + a_2_1·c_4_16·a_7_27 + a_2_3·c_4_16·a_7_27
       + b_2_52·c_4_162·a_1_2 + a_2_1·c_4_162·b_1_13 + a_2_3·c_4_162·b_3_10
       + a_2_1·c_4_162·a_3_5 + a_2_1·c_4_162·a_3_4 + a_2_1·b_2_5·c_4_162·a_1_2
       + a_2_3·c_4_162·a_3_5
  154. a_7_272 + b_2_54·a_3_52 + b_2_52·a_4_8·a_3_52 + b_2_52·c_4_16·a_3_52
       + c_4_162·a_3_52
  155. b_7_412 + b_1_114 + b_6_312·b_1_12 + b_2_5·b_1_19·b_3_9 + b_2_52·b_1_17·b_3_9
       + b_2_53·b_1_15·b_3_9 + b_2_53·b_1_18 + b_2_54·b_1_13·b_3_9 + b_2_54·b_1_16
       + b_2_56·b_1_12 + b_2_57 + b_2_55·a_1_2·b_3_10 + a_2_1·b_2_5·b_1_17·b_3_10
       + a_2_1·b_2_5·b_1_17·b_3_9 + a_2_1·b_2_52·b_1_15·b_3_10
       + a_2_1·b_2_52·b_1_15·b_3_9 + a_2_1·b_2_53·b_1_13·b_3_10
       + a_2_1·b_2_53·b_1_13·b_3_9 + a_2_1·b_2_54·b_1_1·b_3_10
       + a_2_1·b_2_54·b_1_1·b_3_9 + b_2_52·a_3_5·a_7_27 + b_2_54·a_3_52
       + a_2_1·b_2_54·a_4_8 + a_4_8·a_3_5·a_7_27 + b_2_5·c_4_16·b_1_18
       + b_2_52·c_4_16·b_1_16 + b_2_53·c_4_16·b_1_14 + b_2_54·c_4_16·b_1_12
       + a_2_1·b_2_52·a_4_8·c_4_16 + c_4_162·b_1_16 + a_2_1·c_4_162·a_1_2·a_3_5
  156. b_7_442 + b_1_111·b_3_9 + b_2_5·b_1_112 + b_2_5·b_6_312 + b_2_52·b_1_17·b_3_9
       + b_2_52·b_1_110 + b_2_53·b_1_15·b_3_9 + b_2_54·b_1_13·b_3_9 + b_2_54·b_1_16
       + b_2_55·b_1_14 + b_2_56·b_1_12 + b_2_55·a_1_2·b_3_10 + a_2_1·b_1_19·b_3_10
       + a_2_1·b_1_19·b_3_9 + a_2_1·b_2_52·b_1_15·b_3_10 + a_2_1·b_2_52·b_1_15·b_3_9
       + a_2_1·b_2_53·b_1_13·b_3_10 + a_2_1·b_2_53·b_1_13·b_3_9
       + a_2_1·b_2_54·b_1_1·b_3_10 + a_2_1·b_2_54·b_1_1·b_3_9 + b_2_52·a_3_5·a_7_27
       + b_2_52·a_4_8·a_3_52 + c_4_16·b_1_110 + b_2_52·c_4_16·b_1_16
       + b_2_53·c_4_16·b_1_14 + b_2_54·c_4_16·b_1_12 + b_2_53·c_4_16·a_1_2·b_3_10
       + c_4_16·a_3_5·a_7_27 + a_2_1·b_2_52·a_4_8·c_4_16 + a_2_3·c_4_16·a_8_35
       + a_4_8·c_4_16·a_3_52 + a_2_1·c_8_58·a_1_2·a_3_5 + c_4_162·b_1_13·b_3_9
       + b_2_53·c_4_162 + c_4_162·a_1_2·b_5_23 + a_2_1·c_4_162·b_1_1·b_3_10
       + a_2_1·c_4_162·b_1_1·b_3_9 + c_4_16·c_8_58·a_1_22 + c_4_162·a_3_52
       + a_2_1·a_4_8·c_4_162 + a_2_3·a_2_1·b_2_5·c_4_162 + c_4_163·b_1_12
       + c_4_163·a_1_2·b_1_1 + c_4_163·a_1_22
  157. b_7_41·b_7_44 + b_1_111·b_3_9 + b_6_31·b_1_15·b_3_10 + b_6_31·b_1_18
       + b_6_312·b_1_12 + b_2_5·b_1_112 + b_2_5·b_6_31·b_1_13·b_3_9
       + b_2_5·b_6_31·b_1_16 + b_2_5·b_6_312 + b_2_52·b_3_10·b_7_44
       + b_2_52·b_6_31·b_1_14 + b_2_53·b_1_1·b_7_44 + b_2_53·b_1_12·b_3_9·b_3_10
       + b_2_53·b_1_15·b_3_10 + b_2_53·b_1_15·b_3_9 + b_2_53·b_1_18
       + b_2_53·b_6_31·b_1_12 + b_2_54·b_1_1·b_5_23 + b_2_54·b_1_13·b_3_10
       + b_2_54·b_1_13·b_3_9 + b_2_55·b_1_1·b_3_9 + b_2_55·b_1_14 + b_2_56·b_1_12
       + b_2_57 + a_7_27·b_7_44 + b_2_53·a_1_2·b_7_44 + b_2_55·a_1_2·b_3_10 + b_2_55·a_4_8
       + a_2_1·b_1_19·b_3_10 + a_2_1·b_6_31·b_1_13·b_3_9 + a_2_1·b_6_312
       + a_2_1·b_2_5·b_1_14·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_17·b_3_9
       + a_2_1·b_2_5·b_1_110 + a_2_1·b_2_5·b_6_31·b_1_1·b_3_10
       + a_2_1·b_2_5·b_6_31·b_1_1·b_3_9 + a_2_1·b_2_52·b_3_10·b_5_23
       + a_2_1·b_2_52·b_1_1·b_7_44 + a_2_1·b_2_52·b_1_15·b_3_10
       + a_2_1·b_2_52·b_1_15·b_3_9 + a_2_1·b_2_52·b_1_18
       + a_2_1·b_2_52·b_6_31·b_1_12 + a_2_1·b_2_53·b_3_9·b_3_10
       + a_2_1·b_2_53·b_1_1·b_5_23 + a_2_1·b_2_53·b_1_13·b_3_10
       + a_2_1·b_2_54·b_1_1·b_3_10 + a_2_1·b_2_54·b_1_14 + a_2_1·b_2_56
       + b_2_52·a_3_5·a_7_27 + b_2_54·a_3_52 + a_2_1·b_2_54·a_4_8
       + b_2_52·a_4_8·a_3_52 + c_8_58·b_1_13·b_3_9 + c_8_58·b_1_16 + c_4_16·b_1_110
       + c_4_16·b_6_31·b_1_1·b_3_10 + c_4_16·b_6_31·b_1_14 + b_2_5·c_4_16·b_1_15·b_3_10
       + b_2_5·c_4_16·b_1_18 + b_2_52·c_4_16·b_1_13·b_3_9 + b_2_52·c_4_16·b_1_16
       + b_2_53·c_4_16·b_1_1·b_3_10 + b_2_53·c_4_16·b_1_14 + b_2_54·c_4_16·b_1_12
       + b_2_55·c_4_16 + b_2_5·c_4_16·a_1_2·b_7_44 + b_2_5·c_4_16·a_8_35
       + b_2_53·a_4_8·c_4_16 + a_2_1·c_8_58·b_1_14 + a_2_1·c_4_16·b_1_1·b_7_44
       + a_2_1·c_4_16·b_1_12·b_3_9·b_3_10 + a_2_1·c_4_16·b_1_15·b_3_10
       + a_2_1·b_2_5·c_8_58·b_1_12 + a_2_1·b_2_5·c_4_16·b_3_9·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_1·b_5_23 + a_2_1·b_2_5·c_4_16·b_1_13·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_16 + a_2_1·b_2_52·c_4_16·b_1_1·b_3_9
       + a_2_1·b_2_52·c_4_16·b_1_14 + b_2_5·c_8_58·a_1_2·a_3_5 + a_2_1·c_4_16·a_8_35
       + a_2_1·a_4_8·c_8_58 + a_2_1·b_2_52·a_4_8·c_4_16 + a_2_3·a_4_8·c_8_58
       + a_2_3·a_2_1·b_2_5·c_8_58 + a_4_8·c_4_16·a_3_52 + a_2_1·c_8_58·a_1_2·a_3_5
       + c_4_162·b_1_13·b_3_10 + c_4_162·b_1_16 + b_2_5·c_4_162·b_1_1·b_3_9
       + b_2_5·c_4_162·b_1_14 + b_2_52·c_4_162·b_1_12 + b_2_5·a_4_8·c_4_162
       + a_2_1·c_4_162·b_1_1·b_3_10 + a_2_1·c_4_162·b_1_1·b_3_9
       + a_2_1·b_2_5·c_4_162·b_1_12 + c_4_162·a_3_52 + a_2_1·c_4_162·a_1_2·a_3_5
       + c_4_163·a_1_2·b_1_1 + c_4_163·a_1_22
  158. b_7_41·b_7_44 + b_1_111·b_3_9 + b_6_31·b_1_15·b_3_10 + b_6_31·b_1_18
       + b_6_312·b_1_12 + b_2_5·b_1_112 + b_2_5·b_6_31·b_1_13·b_3_9
       + b_2_5·b_6_31·b_1_16 + b_2_5·b_6_312 + b_2_52·b_3_10·b_7_44
       + b_2_52·b_6_31·b_1_14 + b_2_53·b_1_1·b_7_44 + b_2_53·b_1_12·b_3_9·b_3_10
       + b_2_53·b_1_15·b_3_10 + b_2_53·b_1_15·b_3_9 + b_2_53·b_1_18
       + b_2_53·b_6_31·b_1_12 + b_2_54·b_1_1·b_5_23 + b_2_54·b_1_13·b_3_10
       + b_2_54·b_1_13·b_3_9 + b_2_55·b_1_1·b_3_9 + b_2_55·b_1_14 + b_2_56·b_1_12
       + b_2_57 + a_7_27·b_7_41 + b_2_53·a_8_35 + b_2_55·a_4_8 + a_2_1·b_1_19·b_3_10
       + a_2_1·b_1_112 + a_2_1·b_6_31·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_14·b_3_9·b_3_10
       + a_2_1·b_2_5·b_1_17·b_3_9 + a_2_1·b_2_5·b_6_31·b_1_1·b_3_10
       + a_2_1·b_2_52·b_1_1·b_7_44 + a_2_1·b_2_52·b_1_12·b_3_9·b_3_10
       + a_2_1·b_2_52·b_1_15·b_3_10 + a_2_1·b_2_52·b_1_18
       + a_2_1·b_2_52·b_6_31·b_1_12 + a_2_1·b_2_53·b_3_9·b_3_10
       + a_2_1·b_2_53·b_1_13·b_3_10 + a_2_1·b_2_53·b_1_13·b_3_9 + a_2_1·b_2_53·b_6_31
       + a_2_1·b_2_54·b_1_1·b_3_10 + a_2_1·b_2_54·b_1_1·b_3_9 + a_2_1·b_2_54·b_1_14
       + a_2_1·b_2_55·b_1_12 + a_2_1·b_2_54·a_4_8 + a_4_8·a_3_5·a_7_27
       + b_2_52·a_4_8·a_3_52 + c_8_58·b_1_13·b_3_9 + c_8_58·b_1_16 + c_4_16·b_1_110
       + c_4_16·b_6_31·b_1_1·b_3_10 + c_4_16·b_6_31·b_1_14 + b_2_5·c_4_16·b_1_15·b_3_10
       + b_2_5·c_4_16·b_1_18 + b_2_52·c_4_16·b_1_13·b_3_9 + b_2_52·c_4_16·b_1_16
       + b_2_53·c_4_16·b_1_1·b_3_10 + b_2_53·c_4_16·b_1_14 + b_2_54·c_4_16·b_1_12
       + b_2_55·c_4_16 + a_4_8·c_4_16·b_6_31 + b_2_52·c_4_16·a_6_19
       + a_2_1·c_8_58·b_1_1·b_3_9 + a_2_1·c_8_58·b_1_14 + a_2_1·c_4_16·b_3_10·b_5_23
       + a_2_1·c_4_16·b_1_1·b_7_44 + a_2_1·c_4_16·b_1_12·b_3_9·b_3_10
       + a_2_1·c_4_16·b_1_15·b_3_10 + a_2_1·c_4_16·b_1_15·b_3_9
       + a_2_1·b_2_5·c_4_16·b_1_1·b_5_23 + a_2_1·b_2_5·c_4_16·b_1_16
       + a_2_1·b_2_52·c_4_16·b_1_1·b_3_9 + a_2_1·b_2_52·c_4_16·b_1_14
       + a_2_1·b_2_53·c_4_16·b_1_12 + c_4_16·a_3_5·a_7_27 + b_2_5·c_8_58·a_1_2·a_3_5
       + a_2_1·a_4_8·c_8_58 + a_2_3·a_2_1·b_2_5·c_8_58 + a_2_1·c_8_58·a_1_2·a_3_5
       + c_4_162·b_1_13·b_3_10 + c_4_162·b_1_16 + b_2_5·c_4_162·b_1_1·b_3_9
       + b_2_5·c_4_162·b_1_14 + b_2_52·c_4_162·b_1_12 + a_2_1·c_4_162·b_1_14
       + c_4_162·a_3_52 + a_2_3·a_2_1·b_2_5·c_4_162
  159. b_7_442 + b_1_111·b_3_9 + b_2_5·b_1_112 + b_2_5·b_6_312 + b_2_52·b_1_17·b_3_9
       + b_2_52·b_1_110 + b_2_53·b_1_15·b_3_9 + b_2_54·b_1_13·b_3_9 + b_2_54·b_1_16
       + b_2_55·b_1_14 + b_2_56·b_1_12 + a_7_27·b_7_41 + b_2_52·a_4_8·b_6_31
       + b_2_55·a_1_2·b_3_10 + a_2_1·b_6_31·b_1_13·b_3_10 + a_2_1·b_6_31·b_1_13·b_3_9
       + a_2_1·b_6_31·b_1_16 + a_2_1·b_6_312 + a_2_1·b_2_5·b_3_10·b_7_44
       + a_2_1·b_2_5·b_1_14·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_17·b_3_9
       + a_2_1·b_2_5·b_1_110 + a_2_1·b_2_5·b_6_31·b_1_1·b_3_10
       + a_2_1·b_2_5·b_6_31·b_1_1·b_3_9 + a_2_1·b_2_5·b_6_31·b_1_14
       + a_2_1·b_2_52·b_3_10·b_5_23 + a_2_1·b_2_52·b_1_1·b_7_44 + a_2_1·b_2_52·b_1_18
       + a_2_1·b_2_52·b_6_31·b_1_12 + a_2_1·b_2_53·b_1_1·b_5_23
       + a_2_1·b_2_53·b_1_13·b_3_9 + a_2_1·b_2_54·b_1_14 + a_2_1·b_2_56
       + b_2_54·a_3_52 + a_2_1·b_2_52·a_8_35 + a_2_1·b_2_54·a_4_8 + a_4_8·a_3_5·a_7_27
       + b_2_52·a_4_8·a_3_52 + c_4_16·b_1_110 + b_2_52·c_4_16·b_1_16
       + b_2_53·c_4_16·b_1_14 + b_2_54·c_4_16·b_1_12 + b_2_5·c_4_16·a_1_2·b_7_44
       + b_2_53·a_4_8·c_4_16 + a_2_1·c_4_16·b_3_10·b_5_23 + a_2_1·c_4_16·b_1_15·b_3_10
       + a_2_1·c_4_16·b_1_15·b_3_9 + a_2_1·c_4_16·b_6_31·b_1_12
       + a_2_1·b_2_5·c_4_16·b_1_1·b_5_23 + a_2_1·b_2_5·c_4_16·b_1_13·b_3_9
       + a_2_1·b_2_5·c_4_16·b_6_31 + a_2_1·b_2_52·c_4_16·b_1_1·b_3_10
       + a_2_1·b_2_54·c_4_16 + c_4_16·a_3_5·a_7_27 + c_4_162·b_1_13·b_3_9
       + b_2_53·c_4_162 + c_4_162·a_1_2·b_5_23 + b_2_5·c_4_162·a_1_2·b_3_10
       + a_2_1·c_4_162·b_1_1·b_3_9 + a_2_1·b_2_5·c_4_162·b_1_12 + c_4_16·c_8_58·a_1_22
       + c_4_162·a_3_52 + b_2_5·c_4_162·a_1_2·a_3_5 + a_2_3·a_4_8·c_4_162
       + a_2_3·a_2_1·b_2_5·c_4_162 + a_2_1·c_4_162·a_1_2·a_3_5 + c_4_163·b_1_12
       + c_4_163·a_1_2·b_1_1 + c_4_163·a_1_22
  160. b_7_41·b_7_44 + b_1_111·b_3_9 + b_6_31·b_1_15·b_3_10 + b_6_31·b_1_18
       + b_6_312·b_1_12 + b_2_5·b_1_112 + b_2_5·b_6_31·b_1_13·b_3_9
       + b_2_5·b_6_31·b_1_16 + b_2_5·b_6_312 + b_2_52·b_3_10·b_7_44
       + b_2_52·b_6_31·b_1_14 + b_2_53·b_1_1·b_7_44 + b_2_53·b_1_12·b_3_9·b_3_10
       + b_2_53·b_1_15·b_3_10 + b_2_53·b_1_15·b_3_9 + b_2_53·b_1_18
       + b_2_53·b_6_31·b_1_12 + b_2_54·b_1_1·b_5_23 + b_2_54·b_1_13·b_3_10
       + b_2_54·b_1_13·b_3_9 + b_2_55·b_1_1·b_3_9 + b_2_55·b_1_14 + b_2_56·b_1_12
       + b_2_57 + a_7_27·b_7_44 + b_2_53·a_1_2·b_7_44 + b_2_55·a_1_2·b_3_10 + b_2_55·a_4_8
       + a_2_1·b_1_19·b_3_10 + a_2_1·b_6_31·b_1_13·b_3_9 + a_2_1·b_6_312
       + a_2_1·b_2_5·b_1_14·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_17·b_3_9
       + a_2_1·b_2_5·b_1_110 + a_2_1·b_2_5·b_6_31·b_1_1·b_3_10
       + a_2_1·b_2_5·b_6_31·b_1_1·b_3_9 + a_2_1·b_2_52·b_3_10·b_5_23
       + a_2_1·b_2_52·b_1_1·b_7_44 + a_2_1·b_2_52·b_1_15·b_3_10
       + a_2_1·b_2_52·b_1_15·b_3_9 + a_2_1·b_2_52·b_1_18
       + a_2_1·b_2_52·b_6_31·b_1_12 + a_2_1·b_2_53·b_3_9·b_3_10
       + a_2_1·b_2_53·b_1_1·b_5_23 + a_2_1·b_2_53·b_1_13·b_3_10
       + a_2_1·b_2_54·b_1_1·b_3_10 + a_2_1·b_2_54·b_1_14 + a_2_1·b_2_56 + a_6_19·a_8_35
       + b_2_52·a_3_5·a_7_27 + b_2_54·a_3_52 + a_2_1·b_2_54·a_4_8 + a_4_8·a_3_5·a_7_27
       + c_8_58·b_1_13·b_3_9 + c_8_58·b_1_16 + c_4_16·b_1_110
       + c_4_16·b_6_31·b_1_1·b_3_10 + c_4_16·b_6_31·b_1_14 + b_2_5·c_4_16·b_1_15·b_3_10
       + b_2_5·c_4_16·b_1_18 + b_2_52·c_4_16·b_1_13·b_3_9 + b_2_52·c_4_16·b_1_16
       + b_2_53·c_4_16·b_1_1·b_3_10 + b_2_53·c_4_16·b_1_14 + b_2_54·c_4_16·b_1_12
       + b_2_55·c_4_16 + b_2_5·c_4_16·a_1_2·b_7_44 + b_2_5·c_4_16·a_8_35
       + b_2_53·a_4_8·c_4_16 + a_2_1·c_8_58·b_1_14 + a_2_1·c_4_16·b_1_1·b_7_44
       + a_2_1·c_4_16·b_1_12·b_3_9·b_3_10 + a_2_1·c_4_16·b_1_15·b_3_10
       + a_2_1·b_2_5·c_8_58·b_1_12 + a_2_1·b_2_5·c_4_16·b_3_9·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_1·b_5_23 + a_2_1·b_2_5·c_4_16·b_1_13·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_16 + a_2_1·b_2_52·c_4_16·b_1_1·b_3_9
       + a_2_1·b_2_52·c_4_16·b_1_14 + b_2_5·c_8_58·a_1_2·a_3_5 + a_2_1·a_4_8·c_8_58
       + a_2_3·a_4_8·c_8_58 + a_2_3·a_2_1·b_2_5·c_8_58 + a_4_8·c_4_16·a_3_52
       + a_2_1·c_8_58·a_1_2·a_3_5 + c_4_162·b_1_13·b_3_10 + c_4_162·b_1_16
       + b_2_5·c_4_162·b_1_1·b_3_9 + b_2_5·c_4_162·b_1_14 + b_2_52·c_4_162·b_1_12
       + b_2_5·a_4_8·c_4_162 + a_2_1·c_4_162·b_1_1·b_3_10 + a_2_1·c_4_162·b_1_1·b_3_9
       + a_2_1·b_2_5·c_4_162·b_1_12 + c_4_162·a_3_52 + c_4_163·a_1_2·b_1_1
       + c_4_163·a_1_22
  161. b_7_442 + b_1_111·b_3_9 + b_2_5·b_1_112 + b_2_5·b_6_312 + b_2_52·b_1_17·b_3_9
       + b_2_52·b_1_110 + b_2_53·b_1_15·b_3_9 + b_2_54·b_1_13·b_3_9 + b_2_54·b_1_16
       + b_2_55·b_1_14 + b_2_56·b_1_12 + a_7_27·b_7_44 + b_6_31·a_8_35
       + b_2_52·a_4_8·b_6_31 + b_2_55·a_1_2·b_3_10 + a_2_1·b_1_19·b_3_10
       + a_2_1·b_1_19·b_3_9 + a_2_1·b_6_31·b_3_9·b_3_10 + a_2_1·b_6_31·b_1_13·b_3_10
       + a_2_1·b_6_31·b_1_13·b_3_9 + a_2_1·b_6_31·b_1_16 + a_2_1·b_2_5·b_1_17·b_3_9
       + a_2_1·b_2_5·b_1_110 + a_2_1·b_2_52·b_1_12·b_3_9·b_3_10
       + a_2_1·b_2_52·b_1_15·b_3_10 + a_2_1·b_2_53·b_3_9·b_3_10
       + a_2_1·b_2_53·b_1_1·b_5_23 + a_2_1·b_2_53·b_1_16 + a_2_1·b_2_53·b_6_31
       + a_2_1·b_2_54·b_1_1·b_3_10 + a_2_1·b_2_54·b_1_1·b_3_9 + a_2_1·b_2_54·b_1_14
       + a_2_1·b_2_55·b_1_12 + a_2_1·b_2_56 + b_2_54·a_3_52 + b_2_52·a_4_8·a_3_52
       + c_4_16·b_1_110 + b_2_52·c_4_16·b_1_16 + b_2_53·c_4_16·b_1_14
       + b_2_54·c_4_16·b_1_12 + a_4_8·c_4_16·b_6_31 + b_2_5·c_4_16·a_1_2·b_7_44
       + b_2_5·c_4_16·a_8_35 + b_2_53·c_4_16·a_1_2·b_3_10 + b_2_53·a_4_8·c_4_16
       + a_2_1·c_8_58·b_1_14 + a_2_1·c_4_16·b_1_15·b_3_10 + a_2_1·c_4_16·b_1_18
       + a_2_1·c_4_16·b_6_31·b_1_12 + a_2_1·b_2_5·c_4_16·b_1_1·b_5_23
       + a_2_1·b_2_5·c_4_16·b_1_13·b_3_9 + a_2_1·b_2_52·c_4_16·b_1_1·b_3_9
       + a_2_1·b_2_52·c_4_16·b_1_14 + b_2_52·c_4_16·a_3_52
       + a_2_1·b_2_52·a_4_8·c_4_16 + a_4_8·c_4_16·a_3_52 + a_2_1·c_8_58·a_1_2·a_3_5
       + c_4_162·b_1_13·b_3_9 + b_2_53·c_4_162 + c_4_162·a_1_2·b_5_23
       + b_2_5·a_4_8·c_4_162 + a_2_1·c_4_162·b_1_1·b_3_10 + a_2_1·c_4_162·b_1_14
       + a_2_1·b_2_5·c_4_162·b_1_12 + a_2_1·b_2_52·c_4_162 + c_4_16·c_8_58·a_1_22
       + c_4_162·a_3_52 + b_2_5·c_4_162·a_1_2·a_3_5 + a_2_1·a_4_8·c_4_162
       + a_2_3·a_2_1·b_2_5·c_4_162 + a_2_1·c_4_162·a_1_2·a_3_5 + c_4_163·b_1_12
  162. a_8_35·b_7_41 + b_2_52·a_4_8·b_7_44 + b_2_55·a_5_0 + b_2_56·a_3_5 + b_2_57·a_1_2
       + a_2_1·b_6_31·b_7_44 + a_2_1·b_6_31·b_1_1·b_3_9·b_3_10 + a_2_1·b_6_31·b_1_14·b_3_10
       + a_2_1·b_6_312·b_1_1 + a_2_1·b_2_5·b_1_18·b_3_10
       + a_2_1·b_2_5·b_6_31·b_1_12·b_3_10 + a_2_1·b_2_5·b_6_31·b_1_12·b_3_9
       + a_2_1·b_2_5·b_6_31·b_1_15 + a_2_1·b_2_52·b_1_13·b_3_9·b_3_10
       + a_2_1·b_2_52·b_1_16·b_3_10 + a_2_1·b_2_52·b_1_19 + a_2_1·b_2_52·b_6_31·b_3_10
       + a_2_1·b_2_52·b_6_31·b_3_9 + a_2_1·b_2_52·b_6_31·b_1_13
       + a_2_1·b_2_53·b_1_14·b_3_10 + a_2_1·b_2_53·b_1_14·b_3_9 + a_2_1·b_2_53·b_1_17
       + a_2_1·b_2_53·b_6_31·b_1_1 + b_2_54·a_4_8·a_3_5 + a_2_1·b_2_53·a_7_27
       + b_2_54·c_4_16·a_3_5 + b_2_55·c_4_16·a_1_2 + a_2_1·c_4_16·b_6_31·b_3_10
       + a_2_1·b_2_5·c_4_16·b_7_41 + a_2_1·b_2_5·c_4_16·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_14·b_3_10 + a_2_1·b_2_53·c_4_16·b_3_9
       + a_2_1·b_2_53·c_4_16·b_1_13 + a_4_8·c_4_16·a_7_27 + a_2_1·b_2_53·c_4_16·a_3_5
       + a_2_1·b_2_52·c_4_162·b_1_1 + a_4_8·c_4_162·a_3_5 + a_2_1·c_4_162·a_5_0
       + a_2_1·b_2_5·c_4_162·a_3_5 + a_2_3·b_2_5·c_4_162·a_3_5
       + a_2_3·a_2_1·c_4_162·b_3_10
  163. a_8_35·b_7_44 + b_2_52·a_4_8·b_7_44 + b_2_55·a_5_0 + b_2_56·a_3_5 + b_2_57·a_1_2
       + a_2_1·b_6_31·b_7_44 + a_2_1·b_6_31·b_1_1·b_3_9·b_3_10 + a_2_1·b_6_31·b_1_14·b_3_9
       + a_2_1·b_2_5·b_1_15·b_3_9·b_3_10 + a_2_1·b_2_5·b_1_18·b_3_9
       + a_2_1·b_2_5·b_6_31·b_1_12·b_3_10 + a_2_1·b_2_5·b_6_31·b_1_12·b_3_9
       + a_2_1·b_2_5·b_6_31·b_1_15 + a_2_1·b_2_52·b_1_16·b_3_9 + a_2_1·b_2_52·b_1_19
       + a_2_1·b_2_52·b_6_31·b_3_9 + a_2_1·b_2_53·b_7_44
       + a_2_1·b_2_53·b_1_1·b_3_9·b_3_10 + a_2_1·b_2_53·b_1_14·b_3_10
       + a_2_1·b_2_53·b_1_14·b_3_9 + a_2_1·b_2_54·b_1_12·b_3_10 + a_2_1·b_2_54·b_1_15
       + a_2_1·b_2_55·b_3_9 + a_2_1·b_2_56·b_1_1 + b_2_52·a_4_8·a_7_27
       + a_2_1·b_2_53·a_7_27 + a_2_1·b_2_55·a_3_5 + b_2_5·a_3_52·a_7_27
       + a_4_8·c_4_16·b_7_44 + b_2_53·c_4_16·a_5_0 + b_2_54·c_4_16·a_3_5
       + a_2_1·c_4_16·b_1_13·b_3_9·b_3_10 + a_2_1·c_4_16·b_1_16·b_3_10
       + a_2_1·c_4_16·b_1_19 + a_2_1·c_4_16·b_6_31·b_3_9 + a_2_1·b_2_5·c_8_58·b_1_13
       + a_2_1·b_2_5·c_4_16·b_7_44 + a_2_1·b_2_5·c_4_16·b_1_1·b_3_9·b_3_10
       + a_2_1·b_2_5·c_4_16·b_1_14·b_3_9 + a_2_1·b_2_5·c_4_16·b_6_31·b_1_1
       + a_2_1·b_2_52·c_4_16·b_1_12·b_3_10 + a_2_1·b_2_53·c_4_16·b_3_9
       + b_2_52·a_4_8·c_4_16·a_3_5 + a_2_1·b_2_5·c_4_16·a_7_27 + a_2_3·c_8_58·a_5_0
       + a_2_3·a_2_1·c_8_58·b_3_10 + b_2_5·c_4_16·a_3_53 + b_2_52·c_4_162·a_3_5
       + a_2_1·c_4_162·b_1_12·b_3_10 + a_2_1·b_2_5·c_4_162·b_1_13
       + a_4_8·c_4_162·a_3_5 + a_2_1·b_2_5·c_4_162·a_3_5 + a_2_3·c_4_16·c_8_58·a_1_2
       + a_2_3·a_2_1·c_4_162·b_3_10 + a_2_1·c_4_163·b_1_1 + a_2_3·c_4_163·b_1_1
       + a_2_1·c_4_163·a_1_2 + a_2_3·c_4_163·a_1_2
  164. a_8_35·a_7_27 + b_2_52·a_4_8·a_7_27 + b_2_54·a_4_8·a_3_5 + a_2_1·b_2_53·a_7_27
       + a_2_1·b_2_55·a_3_5 + a_4_8·c_4_16·a_7_27 + b_2_52·a_4_8·c_4_16·a_3_5
       + a_2_1·b_2_5·c_4_16·a_7_27 + a_2_1·b_2_53·c_4_16·a_3_5 + a_2_3·b_2_5·c_4_16·a_7_27
       + a_4_8·c_4_162·a_3_5 + a_2_1·b_2_5·c_4_162·a_3_5
  165. a_8_352 + b_2_53·a_4_8·a_3_52 + b_2_53·c_4_16·a_3_52


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 16.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_4_16, a Duflot regular element of degree 4
    2. c_8_58, a Duflot regular element of degree 8
    3. b_1_14 + b_2_5·b_1_12 + b_2_52, an element of degree 4
    4. b_3_9, an element of degree 3
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 8, 12, 15].
  • 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_00, an element of degree 1
  2. a_1_20, an element of degree 1
  3. b_1_10, an element of degree 1
  4. a_2_30, an element of degree 2
  5. a_2_10, an element of degree 2
  6. b_2_50, an element of degree 2
  7. a_3_40, an element of degree 3
  8. a_3_50, an element of degree 3
  9. b_3_90, an element of degree 3
  10. b_3_100, an element of degree 3
  11. a_4_70, an element of degree 4
  12. a_4_80, an element of degree 4
  13. c_4_16c_1_04, an element of degree 4
  14. a_5_00, an element of degree 5
  15. b_5_230, an element of degree 5
  16. a_6_190, an element of degree 6
  17. b_6_310, an element of degree 6
  18. a_7_270, an element of degree 7
  19. b_7_410, an element of degree 7
  20. b_7_440, an element of degree 7
  21. a_8_350, an element of degree 8
  22. c_8_58c_1_18, an element of degree 8

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

  1. a_1_00, an element of degree 1
  2. a_1_20, an element of degree 1
  3. b_1_1c_1_3, an element of degree 1
  4. a_2_30, an element of degree 2
  5. a_2_10, an element of degree 2
  6. b_2_5c_1_22, an element of degree 2
  7. a_3_40, an element of degree 3
  8. a_3_50, an element of degree 3
  9. b_3_9c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  10. b_3_10c_1_33 + c_1_23 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  11. a_4_70, an element of degree 4
  12. a_4_80, an element of degree 4
  13. c_4_16c_1_2·c_1_33 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  14. a_5_00, an element of degree 5
  15. b_5_23c_1_22·c_1_33 + c_1_25 + c_1_02·c_1_33 + c_1_04·c_1_3, an element of degree 5
  16. a_6_190, an element of degree 6
  17. b_6_31c_1_22·c_1_34 + c_1_23·c_1_33 + c_1_24·c_1_32 + c_1_26 + c_1_12·c_1_34
       + c_1_14·c_1_32 + c_1_0·c_1_35 + c_1_0·c_1_2·c_1_34 + c_1_0·c_1_22·c_1_33
       + c_1_02·c_1_34 + c_1_02·c_1_2·c_1_33 + c_1_02·c_1_24, an element of degree 6
  18. a_7_270, an element of degree 7
  19. b_7_41c_1_37 + c_1_2·c_1_36 + c_1_23·c_1_34 + c_1_24·c_1_33 + c_1_25·c_1_32
       + c_1_27 + c_1_12·c_1_35 + c_1_14·c_1_33 + c_1_0·c_1_36
       + c_1_0·c_1_23·c_1_33 + c_1_0·c_1_24·c_1_32 + c_1_02·c_1_22·c_1_33
       + c_1_02·c_1_23·c_1_32 + c_1_04·c_1_33, an element of degree 7
  20. b_7_44c_1_25·c_1_32 + c_1_26·c_1_3 + c_1_27 + c_1_12·c_1_2·c_1_34
       + c_1_14·c_1_2·c_1_32 + c_1_0·c_1_36 + c_1_0·c_1_24·c_1_32 + c_1_02·c_1_35
       + c_1_02·c_1_2·c_1_34 + c_1_02·c_1_24·c_1_3 + c_1_02·c_1_25 + c_1_03·c_1_34
       + c_1_04·c_1_33 + c_1_04·c_1_2·c_1_32 + c_1_04·c_1_23 + c_1_05·c_1_32
       + c_1_06·c_1_3, an element of degree 7
  21. a_8_350, an element of degree 8
  22. c_8_58c_1_24·c_1_34 + c_1_26·c_1_32 + c_1_27·c_1_3 + c_1_12·c_1_2·c_1_35
       + c_1_12·c_1_22·c_1_34 + c_1_12·c_1_24·c_1_32 + 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_14·c_1_24 + c_1_18
       + c_1_0·c_1_37 + c_1_0·c_1_23·c_1_34 + c_1_02·c_1_36 + c_1_02·c_1_2·c_1_35
       + c_1_02·c_1_24·c_1_32 + c_1_02·c_1_25·c_1_3 + c_1_04·c_1_2·c_1_33
       + c_1_04·c_1_24, an element of degree 8


About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128




Simon A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany

E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2



Last change: 25.08.2009