Cohomology of group number 1974 of order 128

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

General information on the group

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

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    t13  +  2·t12  −  2·t10  −  t9  +  4·t8  −  4·t6  −  5·t5  +  2·t4  −  2·t2  −  2·t  −  1
    (t  +  1) · (t  −  1)3 · (t2  +  1)2 · (t4  +  1)2
  • The a-invariants are -∞,-∞,-3,-3. They were obtained using the filter regular HSOP of the Benson test.

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

Ring generators

The cohomology ring has 22 minimal generators of maximal degree 13:

  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. b_1_3, an element of degree 1
  5. a_5_2, a nilpotent element of degree 5
  6. a_5_3, a nilpotent element of degree 5
  7. a_5_4, a nilpotent element of degree 5
  8. a_5_5, a nilpotent element of degree 5
  9. a_5_7, a nilpotent element of degree 5
  10. a_5_8, a nilpotent element of degree 5
  11. a_5_9, a nilpotent element of degree 5
  12. b_5_6, an element of degree 5
  13. b_5_10, an element of degree 5
  14. c_8_20, a Duflot regular element of degree 8
  15. c_8_21, a Duflot regular element of degree 8
  16. a_9_18, a nilpotent element of degree 9
  17. a_9_15, a nilpotent element of degree 9
  18. a_9_10, a nilpotent element of degree 9
  19. a_9_14, a nilpotent element of degree 9
  20. a_9_19, a nilpotent element of degree 9
  21. b_9_24, an element of degree 9
  22. a_13_29, a nilpotent element of degree 13

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

Ring relations

There are 181 minimal relations of maximal degree 26:

  1. a_1_0·a_1_2
  2. a_1_0·b_1_3 + a_1_22 + a_1_1·a_1_2 + a_1_12 + a_1_0·a_1_1
  3. a_1_1·b_1_32 + a_1_1·a_1_2·b_1_3 + a_1_12·b_1_3 + a_1_1·a_1_22 + a_1_12·a_1_2
       + a_1_13 + a_1_0·a_1_12 + a_1_03
  4. a_1_1·b_1_32 + a_1_22·b_1_3 + a_1_1·a_1_22 + a_1_12·a_1_2 + a_1_03
  5. a_1_02·a_1_13
  6. a_1_03·a_1_12
  7. a_1_2·a_5_2
  8. a_1_1·a_5_2 + a_1_0·a_5_3
  9. a_1_2·a_5_3 + a_1_1·a_5_4 + a_1_1·a_5_3
  10. a_1_1·a_5_2 + a_1_0·a_5_4
  11. b_1_3·a_5_2 + a_1_2·a_5_4 + a_1_1·a_5_3 + a_1_1·a_5_2
  12. a_1_2·a_5_5 + a_1_2·a_5_3
  13. a_1_0·a_5_7
  14. a_1_1·a_5_5 + a_1_1·a_5_3 + a_1_1·a_5_2 + a_1_0·a_5_8
  15. b_1_3·a_5_2 + a_1_2·a_5_8 + a_1_1·a_5_7 + a_1_1·a_5_3 + a_1_1·a_5_2
  16. a_1_2·a_5_3 + a_1_1·a_5_9 + a_1_1·a_5_8 + a_1_1·a_5_7 + a_1_1·a_5_5
  17. a_1_1·a_5_5 + a_1_1·a_5_3 + a_1_1·a_5_2 + a_1_0·a_5_9 + a_1_0·a_5_5
  18. b_1_3·a_5_5 + b_1_3·a_5_3 + a_1_2·a_5_9 + a_1_2·a_5_3 + a_1_1·a_5_8 + a_1_1·a_5_5
  19. b_1_3·a_5_5 + a_1_1·b_5_6 + a_1_2·a_5_7 + a_1_1·a_5_7 + a_1_1·a_5_2
  20. b_1_3·a_5_2 + a_1_0·b_5_6 + a_1_1·a_5_5 + a_1_1·a_5_3 + a_1_1·a_5_2 + a_1_0·a_5_5
       + a_1_0·a_5_2
  21. b_1_3·a_5_4 + b_1_3·a_5_3 + a_1_2·b_5_6 + a_1_1·a_5_7
  22. b_1_3·a_5_8 + b_1_3·a_5_4 + a_1_1·b_5_10 + a_1_1·a_5_8 + a_1_1·a_5_7 + a_1_1·a_5_3
       + a_1_1·a_5_2
  23. a_1_0·b_5_10 + a_1_2·a_5_7 + a_1_2·a_5_3 + a_1_1·a_5_8 + a_1_1·a_5_7 + a_1_1·a_5_3
       + a_1_0·a_5_2
  24. b_1_3·a_5_7 + b_1_3·a_5_5 + b_1_3·a_5_3 + b_1_3·a_5_2 + a_1_2·b_5_10 + a_1_1·a_5_8
       + a_1_1·a_5_5 + a_1_1·a_5_3 + a_1_1·a_5_2
  25. a_1_22·b_5_6 + a_1_1·a_1_2·b_5_6 + a_1_12·b_5_6 + a_1_1·a_1_2·a_5_7 + a_1_12·a_5_8
       + a_1_12·a_5_7 + a_1_12·a_5_4 + a_1_12·a_5_3 + a_1_0·a_1_1·a_5_8 + a_1_0·a_1_1·a_5_3
  26. a_1_1·b_1_3·b_5_10 + a_1_1·a_1_2·b_5_6 + a_1_1·a_1_2·a_5_7 + a_1_1·a_1_2·a_5_4
       + a_1_12·a_5_8 + a_1_12·a_5_4 + a_1_12·a_5_3 + a_1_0·a_1_1·a_5_8 + a_1_02·a_5_5
       + a_1_02·a_5_3
  27. a_1_1·b_1_3·b_5_6 + a_1_1·a_1_2·b_5_6 + a_1_12·b_5_10 + a_1_12·b_5_6
       + a_1_1·a_1_2·a_5_7 + a_1_12·a_5_8 + a_1_12·a_5_7 + a_1_12·a_5_3 + a_1_02·a_5_2
  28. a_1_1·b_1_3·b_5_6 + a_1_22·b_5_10 + a_1_1·a_1_2·b_5_10 + a_1_1·a_1_2·b_5_6
       + a_1_12·b_5_6 + a_1_12·a_5_8 + a_1_12·a_5_3 + a_1_0·a_1_1·a_5_8 + a_1_02·a_5_2
  29. a_1_02·a_1_12·a_5_3 + a_1_03·a_1_1·a_5_8 + a_1_03·a_1_1·a_5_3
  30. a_5_2·a_5_4 + a_5_2·a_5_3
  31. a_5_4·a_5_5 + a_5_3·a_5_5 + a_5_3·a_5_4 + a_5_32
  32. a_5_2·a_5_7
  33. a_5_5·a_5_7 + a_5_3·a_5_7
  34. a_5_3·a_5_5 + a_5_32 + a_5_2·a_5_8 + a_5_2·a_5_3
  35. a_5_4·a_5_8 + a_5_42 + a_5_3·a_5_8 + a_5_3·a_5_7 + a_5_3·a_5_4
  36. a_5_3·a_5_9 + a_5_3·a_5_8 + a_5_3·a_5_7 + a_5_3·a_5_5 + a_5_3·a_5_4 + a_5_32
  37. a_5_3·a_5_5 + a_5_32 + a_5_2·a_5_9 + a_5_2·a_5_5 + a_5_2·a_5_3
  38. a_5_5·a_5_9 + a_5_5·a_5_8 + a_5_52 + a_5_3·a_5_7 + a_5_3·a_5_4 + a_5_32
  39. a_5_92 + a_5_82 + a_5_72 + a_5_52 + a_5_42 + a_5_32 + a_1_2·b_1_34·a_5_9
  40. a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_8 + a_5_5·a_5_8 + a_5_4·a_5_9 + a_5_4·a_5_7 + a_5_42
       + a_5_3·a_5_8 + a_5_3·a_5_5 + a_5_32
  41. a_5_2·b_5_6 + a_5_42 + a_5_3·a_5_5 + a_5_3·a_5_4 + a_5_2·a_5_5 + a_5_22
  42. a_5_5·b_5_6 + a_5_3·b_5_6 + a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_8 + a_5_52 + a_5_4·a_5_7
       + a_5_42 + a_5_3·a_5_7 + a_5_32 + a_5_2·a_5_5 + a_5_2·a_5_3
  43. a_5_8·b_5_6 + a_5_4·b_5_6 + a_5_3·b_5_10 + a_5_82 + a_5_7·a_5_9 + a_5_7·a_5_8 + a_5_72
       + a_5_5·a_5_8 + a_5_4·a_5_7 + a_5_42 + a_5_3·a_5_7 + a_5_32 + a_5_2·a_5_3
  44. a_5_2·b_5_10 + a_5_4·a_5_7 + a_5_3·a_5_8 + a_5_3·a_5_4 + a_5_22
  45. a_5_8·b_5_6 + a_5_5·b_5_10 + a_5_4·b_5_6 + a_5_7·a_5_8 + a_5_72 + a_5_5·a_5_8
       + a_5_4·a_5_7 + a_5_3·a_5_7 + a_5_32 + a_5_2·a_5_5
  46. a_5_8·b_5_6 + a_5_7·b_5_6 + a_5_4·b_5_10 + a_5_4·b_5_6 + a_5_8·a_5_9 + a_5_7·a_5_9
       + a_5_7·a_5_8 + a_5_72 + a_5_4·a_5_7 + a_5_42 + a_5_3·a_5_4 + a_5_2·a_5_3
  47. b_5_62 + b_1_35·b_5_6 + b_1_35·a_5_9 + a_5_82 + a_5_52 + a_5_42 + a_5_32
       + a_5_22 + c_8_20·b_1_32
  48. a_5_3·b_5_6 + a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_8 + a_5_5·a_5_8 + a_5_42 + a_5_3·a_5_8
       + a_5_3·a_5_7 + a_5_3·a_5_5 + a_5_32 + a_5_2·a_5_3 + c_8_20·a_1_1·b_1_3
  49. a_5_4·b_5_6 + a_5_3·b_5_6 + a_1_2·b_1_34·b_5_6 + a_5_3·a_5_7 + a_1_2·b_1_34·a_5_9
       + c_8_20·a_1_2·b_1_3
  50. a_5_32 + c_8_20·a_1_12
  51. a_5_2·a_5_3 + c_8_20·a_1_0·a_1_1
  52. a_5_22 + c_8_20·a_1_02
  53. a_5_3·a_5_4 + a_5_32 + c_8_20·a_1_1·a_1_2
  54. a_5_42 + a_5_32 + c_8_20·a_1_22
  55. b_5_102 + b_5_62 + b_1_35·b_5_6 + b_1_35·a_5_9 + a_1_2·b_1_34·b_5_6 + a_5_72
       + a_5_52 + a_5_42 + a_1_2·b_1_34·a_5_9 + c_8_21·b_1_32
  56. a_5_8·b_5_10 + a_5_8·b_5_6 + a_5_7·b_5_6 + a_5_4·b_5_6 + a_5_3·b_5_6 + a_5_7·a_5_9
       + a_5_7·a_5_8 + a_5_72 + a_5_5·a_5_8 + a_5_42 + a_5_3·a_5_8 + a_5_3·a_5_4
       + c_8_21·a_1_1·b_1_3
  57. a_5_7·b_5_10 + a_5_4·b_5_6 + a_5_3·b_5_6 + a_1_2·b_1_34·b_5_6 + a_5_7·a_5_9 + a_5_4·a_5_7
       + a_1_2·b_1_34·a_5_9 + c_8_21·a_1_2·b_1_3
  58. a_5_82 + a_5_42 + a_5_32 + c_8_21·a_1_12
  59. a_5_5·a_5_8 + a_5_3·a_5_8 + a_5_3·a_5_5 + a_5_32 + a_5_2·a_5_3 + c_8_21·a_1_0·a_1_1
  60. a_5_52 + a_5_32 + a_5_22 + c_8_21·a_1_02
  61. a_5_7·a_5_8 + a_5_4·a_5_7 + a_5_3·a_5_4 + a_5_32 + c_8_21·a_1_1·a_1_2
  62. a_5_72 + a_5_42 + a_5_32 + c_8_21·a_1_22
  63. a_5_9·b_5_6 + a_5_8·b_5_6 + a_5_7·b_5_10 + a_5_7·b_5_6 + a_5_4·b_5_6 + a_5_3·b_5_6
       + b_1_3·a_9_18 + a_1_2·b_1_34·b_5_6 + a_5_7·a_5_9 + a_5_5·a_5_8 + a_5_52 + a_5_3·a_5_8
       + a_5_3·a_5_7 + a_5_3·a_5_5 + a_5_2·a_5_5
  64. a_5_7·a_5_8 + a_5_4·a_5_7 + a_5_32 + a_1_1·a_9_18
  65. a_5_2·a_5_3 + a_1_0·a_9_18
  66. a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_8 + a_5_72 + a_5_5·a_5_8 + a_5_42 + a_5_3·a_5_7
       + a_5_32 + a_1_2·a_9_18
  67. a_5_8·b_5_10 + a_5_8·b_5_6 + a_5_7·b_5_6 + a_5_4·b_5_6 + b_1_3·a_9_15
       + a_1_2·b_1_34·b_5_10 + a_5_82 + a_5_7·a_5_9 + a_5_42 + a_5_3·a_5_5
  68. a_5_82 + a_5_5·a_5_8 + a_5_42 + a_5_3·a_5_8 + a_5_2·a_5_3 + a_1_1·a_9_15
  69. a_5_5·a_5_8 + a_5_52 + a_5_3·a_5_8 + a_5_3·a_5_5 + a_5_2·a_5_5 + a_5_2·a_5_3 + a_5_22
       + a_1_0·a_9_15
  70. a_5_7·a_5_8 + a_5_4·a_5_7 + a_1_2·a_9_15
  71. a_5_9·b_5_6 + a_5_8·b_5_10 + a_5_8·b_5_6 + b_1_3·a_9_10 + b_1_35·a_5_9
       + a_1_2·b_1_34·b_5_10 + a_1_2·b_1_34·b_5_6 + a_5_8·a_5_9 + a_5_7·a_5_8 + a_5_52
       + a_5_42 + a_5_3·a_5_4 + a_5_32 + a_5_2·a_5_5 + a_5_2·a_5_3
  72. a_5_82 + a_5_42 + a_5_3·a_5_8 + a_1_1·a_9_10
  73. a_5_5·a_5_8 + a_5_3·a_5_8 + a_5_2·a_5_3 + a_1_0·a_9_10
  74. a_5_8·a_5_9 + a_5_82 + a_5_5·a_5_8 + a_5_4·a_5_7 + a_1_2·a_9_10 + a_1_2·b_1_34·a_5_9
  75. a_5_9·b_5_6 + a_5_3·b_5_6 + b_1_3·a_9_14 + a_1_2·b_1_34·b_5_10 + a_1_2·b_1_34·b_5_6
       + a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_9 + a_5_52 + a_5_4·a_5_7 + a_5_3·a_5_7 + a_5_3·a_5_5
       + a_5_3·a_5_4 + a_5_32 + a_5_2·a_5_5 + a_5_2·a_5_3
  76. a_5_5·a_5_8 + a_5_3·a_5_7 + a_5_3·a_5_4 + a_5_32 + a_5_2·a_5_3 + a_1_1·a_9_14
  77. a_5_52 + a_5_3·a_5_5 + a_5_2·a_5_5 + a_5_22 + a_1_0·a_9_14
  78. a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_8 + a_5_5·a_5_8 + a_5_4·a_5_7 + a_5_42 + a_5_3·a_5_7
       + a_5_32 + a_1_2·a_9_14
  79. a_5_9·b_5_10 + a_5_9·b_5_6 + a_5_8·b_5_6 + a_5_7·b_5_10 + a_5_7·b_5_6 + a_5_4·b_5_6
       + b_1_3·a_9_19 + b_1_35·a_5_9 + a_1_2·b_1_34·b_5_6 + a_5_8·a_5_9 + a_5_5·a_5_8 + a_5_52
       + a_5_4·a_5_7 + a_5_42 + a_5_3·a_5_5 + a_5_32 + a_5_2·a_5_3
  80. a_5_82 + a_5_5·a_5_8 + a_5_42 + a_5_3·a_5_8 + a_5_2·a_5_3 + a_1_1·a_9_19
  81. a_5_5·a_5_8 + a_5_52 + a_5_3·a_5_8 + a_5_3·a_5_5 + a_5_2·a_5_5 + a_5_2·a_5_3 + a_5_22
       + a_1_0·a_9_19
  82. a_5_8·a_5_9 + a_5_82 + a_5_7·a_5_9 + a_5_7·a_5_8 + a_5_72 + a_5_5·a_5_8 + a_5_42
       + a_5_3·a_5_7 + a_5_3·a_5_4 + a_1_2·a_9_19 + a_1_2·b_1_34·a_5_9
  83. b_5_6·b_5_10 + b_1_3·b_9_24 + b_1_35·b_5_6 + a_5_9·b_5_10 + a_5_9·b_5_6 + a_5_8·b_5_10
       + a_5_7·b_5_10 + b_1_35·a_5_9 + a_1_2·b_1_34·b_5_10 + a_5_7·a_5_9 + a_5_7·a_5_8
       + a_5_72 + a_5_52 + a_5_4·a_5_7 + a_5_42 + a_5_3·a_5_4 + a_5_32 + a_5_2·a_5_5
       + a_5_22 + a_1_2·b_1_34·a_5_9
  84. a_5_8·b_5_6 + a_5_4·b_5_6 + a_1_1·b_9_24 + a_5_5·a_5_8 + a_5_3·a_5_7 + a_5_3·a_5_5
       + a_5_2·a_5_3
  85. a_1_0·b_9_24 + a_5_5·a_5_8 + a_5_4·a_5_7 + a_5_3·a_5_5 + a_5_3·a_5_4 + a_5_32
       + a_5_2·a_5_5 + a_5_2·a_5_3 + a_5_22
  86. a_5_7·b_5_6 + a_1_2·b_9_24 + a_1_2·b_1_34·b_5_6 + a_5_7·a_5_9 + a_5_7·a_5_8 + a_5_72
       + a_5_42 + a_5_32 + a_1_2·b_1_34·a_5_9
  87. a_1_1·b_1_3·b_9_24 + a_1_02·a_9_15 + c_8_21·a_1_12·b_1_3 + c_8_20·a_1_1·a_1_2·b_1_3
       + c_8_20·a_1_12·b_1_3 + c_8_21·a_1_02·a_1_1 + c_8_21·a_1_03 + c_8_20·a_1_1·a_1_22
       + c_8_20·a_1_12·a_1_2 + c_8_20·a_1_13 + c_8_20·a_1_0·a_1_12 + c_8_20·a_1_02·a_1_1
  88. a_1_22·b_9_24 + a_1_1·a_1_2·b_9_24 + a_1_12·b_9_24 + a_1_1·a_1_2·a_9_14
       + c_8_21·a_1_1·a_1_22 + c_8_21·a_1_12·a_1_2 + c_8_21·a_1_13
       + c_8_20·a_1_1·a_1_22 + c_8_20·a_1_13 + c_8_20·a_1_0·a_1_12
  89. a_5_3·a_9_18 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_1·a_5_4
  90. a_5_2·a_9_18 + c_8_20·a_1_0·a_5_3
  91. a_5_5·a_9_18 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  92. a_5_9·a_9_18 + a_5_7·a_9_18 + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_2·a_5_7
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  93. a_5_8·a_9_18 + a_1_2·b_1_34·a_9_18 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_7
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8
  94. a_5_4·a_9_18 + a_1_2·b_1_34·a_9_18 + c_8_21·a_1_2·a_5_4 + c_8_20·a_1_2·a_5_9
       + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4
  95. a_5_3·a_9_15 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_1·a_5_3
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  96. a_5_2·a_9_15 + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_0·a_5_5
  97. a_5_5·a_9_15 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5
       + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_2
  98. a_5_7·a_9_15 + c_8_21·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_7
  99. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_9·a_9_15 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6
       + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_1·a_5_7
       + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_0·a_5_5 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_2·a_5_4
       + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_0·a_5_2
  100. a_5_8·a_9_15 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_3
       + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_0·a_5_8
  101. b_5_10·a_9_15 + a_5_7·a_9_18 + c_8_21·a_1_2·b_1_35 + c_8_21·a_1_1·b_5_10
       + c_8_20·a_1_2·b_1_35 + c_8_20·a_1_1·b_5_10 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_8
       + c_8_21·a_1_1·a_5_7 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_2
       + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_3
       + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_3
  102. a_5_4·a_9_15 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  103. a_5_3·a_9_10 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_3
  104. a_5_2·a_9_10 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  105. a_5_5·a_9_10 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_20·a_1_1·a_5_8
       + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_3
  106. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_7·a_9_10 + a_5_7·a_9_18 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6
       + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_7
       + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_8
  107. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_9·a_9_10 + a_5_7·a_9_18 + a_1_2·b_1_34·a_9_18
       + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9
       + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6
       + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_1·a_5_7 + c_8_21·a_1_0·a_5_8
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  108. a_5_8·a_9_10 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_2·a_5_9
       + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7
       + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_1·a_5_3
  109. b_5_6·a_9_10 + b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_7·a_9_18 + a_1_2·b_1_34·a_9_18
       + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_21·a_1_1·b_5_6
       + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_3
       + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_0·a_5_8
       + c_8_20·a_1_0·a_5_3
  110. a_5_4·a_9_10 + c_8_21·a_1_1·a_5_4 + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_7
       + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_4
  111. a_5_3·a_9_14 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7
       + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  112. a_5_2·a_9_14 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5
       + c_8_20·a_1_0·a_5_3
  113. a_5_5·a_9_14 + c_8_21·a_1_0·a_5_5 + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2
       + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_1·a_5_3
       + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  114. a_5_7·a_9_14 + a_5_7·a_9_18 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_2·a_5_4
       + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4
  115. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_9·a_9_14 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6
       + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_4
       + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_1·a_5_8
       + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  116. a_5_8·a_9_14 + a_1_2·b_1_34·a_9_18 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_0·a_5_8
       + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_0·a_5_8
  117. b_5_10·a_9_14 + b_5_10·a_9_18 + c_8_21·a_1_2·b_5_10 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_21·a_1_1·b_5_6 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6
       + c_8_20·a_1_2·b_1_35 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_1·a_5_7
       + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_2
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_3
       + c_8_20·a_1_0·a_5_5
  118. b_5_6·a_9_14 + b_1_35·a_9_18 + a_5_7·a_9_18 + c_8_21·a_1_2·b_1_35
       + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_2·a_5_4
       + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5
       + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  119. a_5_4·a_9_14 + a_1_2·b_1_34·a_9_18 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_9
       + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  120. a_5_3·a_9_19 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_1·a_5_3
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  121. a_5_2·a_9_19 + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_0·a_5_5
  122. a_5_5·a_9_19 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5
       + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_2
  123. b_5_10·a_9_10 + b_5_10·a_9_18 + b_5_6·a_9_15 + b_1_35·a_9_19 + b_1_35·a_9_18
       + b_1_39·a_5_9 + a_1_2·b_1_34·a_9_18 + c_8_21·a_1_2·b_5_10 + c_8_21·a_1_2·b_1_35
       + c_8_21·a_1_1·b_5_10 + c_8_20·a_1_2·b_1_35 + c_8_20·a_1_1·b_5_10
       + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_8
       + c_8_21·a_1_1·a_5_7 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_5 + c_8_20·a_1_2·a_5_7
       + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  124. b_5_6·a_9_18 + b_1_35·a_9_18 + a_1_2·b_1_34·a_9_19 + a_1_2·b_1_34·a_9_18
       + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9
       + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6
       + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_0·a_5_8
  125. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_7·a_9_19 + a_5_7·a_9_18 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6
       + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_9
       + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_0·a_5_8
  126. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_9·a_9_19 + a_5_7·a_9_18 + a_1_2·b_1_38·a_5_9
       + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10
       + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_9
       + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_0·a_5_5 + c_8_21·a_1_0·a_5_2
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_2
  127. a_5_8·a_9_19 + a_5_7·a_9_18 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_8
       + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_1·a_5_8
       + c_8_20·a_1_0·a_5_8
  128. b_5_10·a_9_19 + b_5_10·a_9_10 + b_5_6·a_9_15 + b_5_6·a_9_18 + b_1_35·a_9_18
       + c_8_21·b_1_3·a_5_9 + c_8_21·a_1_2·b_5_10 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_1·b_5_10
       + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_2·b_1_35
       + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_2·a_5_4
       + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5 + c_8_21·a_1_0·a_5_2
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  129. b_5_10·a_9_18 + b_5_6·a_9_19 + b_5_6·a_9_18 + b_1_35·a_9_18 + a_1_2·b_1_38·b_5_6
       + a_5_7·a_9_18 + c_8_21·a_1_2·b_5_10 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35
       + c_8_21·a_1_1·b_5_6 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_2·b_1_35
       + c_8_20·a_1_1·b_5_10 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_3
       + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  130. a_5_7·a_9_18 + a_5_4·a_9_19 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_4
       + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_0·a_5_8
       + c_8_20·a_1_0·a_5_3
  131. a_5_3·b_9_24 + a_5_7·a_9_18 + a_1_2·b_1_34·a_9_18 + c_8_20·a_1_1·b_5_10
       + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_1·a_5_7
       + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_3
  132. a_5_2·b_9_24 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_1·a_5_8
       + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  133. a_5_5·b_9_24 + c_8_20·a_1_1·b_5_10 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_0·a_5_8
       + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_0·a_5_5
       + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  134. b_5_6·a_9_15 + b_5_6·a_9_18 + b_1_35·a_9_18 + a_1_2·b_1_34·b_9_24
       + a_1_2·b_1_38·b_5_6 + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_21·a_1_1·b_5_6 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10
       + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_1·b_5_10 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_3
       + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5 + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_4
       + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_0·a_5_5
       + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  135. b_5_6·a_9_15 + b_5_6·a_9_18 + a_5_7·b_9_24 + b_1_35·a_9_18 + c_8_21·a_1_2·b_1_35
       + c_8_21·a_1_1·b_5_6 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_1·b_5_10
       + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_7 + c_8_21·a_1_1·a_5_3
       + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  136. b_5_10·a_9_18 + a_5_9·b_9_24 + b_1_35·a_9_18 + a_1_2·b_1_38·b_5_6 + a_5_7·a_9_18
       + a_1_2·b_1_34·a_9_18 + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_10 + c_8_21·a_1_2·b_5_6
       + c_8_21·a_1_2·b_1_35 + c_8_21·a_1_1·b_5_6 + c_8_20·a_1_2·b_5_10 + c_8_20·a_1_2·b_5_6
       + c_8_20·a_1_2·b_1_35 + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_9
       + c_8_21·a_1_1·a_5_7 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_2
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  137. b_5_6·a_9_15 + b_5_6·a_9_18 + a_5_8·b_9_24 + b_1_35·a_9_18 + a_1_2·b_1_38·b_5_6
       + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9
       + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_2·b_1_35 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_4
       + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_5 + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_7
       + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4
       + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  138. b_5_10·b_9_24 + b_1_35·b_9_24 + b_1_39·b_5_6 + b_5_10·a_9_18 + b_5_6·a_9_15
       + b_1_35·a_9_18 + b_1_39·a_5_9 + a_1_2·b_1_38·b_5_10 + a_1_2·b_1_34·a_9_18
       + c_8_21·b_1_3·b_5_6 + c_8_20·b_1_3·b_5_6 + c_8_21·b_1_3·a_5_9 + c_8_21·a_1_2·b_1_35
       + c_8_21·a_1_1·b_5_10 + c_8_21·a_1_1·b_5_6 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_1·b_5_6
       + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5
       + c_8_21·a_1_0·a_5_3 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_0·a_5_8
       + c_8_20·a_1_0·a_5_3
  139. b_5_6·b_9_24 + b_1_35·b_9_24 + b_5_10·a_9_18 + b_5_6·a_9_15 + b_1_35·a_9_18
       + a_1_2·b_1_38·b_5_10 + a_1_2·b_1_38·b_5_6 + a_5_7·a_9_18 + c_8_20·b_1_3·b_5_10
       + c_8_20·b_1_36 + c_8_21·a_1_2·b_5_10 + c_8_21·a_1_1·b_5_6 + c_8_20·b_1_3·a_5_9
       + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_7 + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_0·a_5_5
       + c_8_21·a_1_0·a_5_3 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_7
       + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_1·a_5_3 + c_8_20·a_1_0·a_5_8
       + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  140. b_5_6·a_9_15 + b_5_6·a_9_18 + a_5_4·b_9_24 + b_1_35·a_9_18 + a_1_2·b_1_38·b_5_6
       + a_1_2·b_1_38·a_5_9 + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_21·a_1_1·b_5_6
       + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_2·b_1_35 + c_8_21·a_1_2·a_5_4
       + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_5
       + c_8_20·a_1_2·a_5_7 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_0·a_5_8
       + c_8_20·a_1_0·a_5_5 + c_8_20·a_1_0·a_5_2
  141. b_5_10·a_9_10 + b_5_6·a_9_18 + b_1_3·a_13_29 + a_5_7·a_9_18 + c_8_21·a_1_2·b_1_35
       + c_8_21·a_1_1·b_5_10 + c_8_21·a_1_1·b_5_6 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10
       + c_8_20·a_1_2·b_1_35 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_9 + c_8_21·a_1_2·a_5_4
       + c_8_21·a_1_1·a_5_8 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_8 + c_8_21·a_1_0·a_5_3
       + c_8_20·a_1_2·a_5_9 + c_8_20·a_1_2·a_5_4 + c_8_20·a_1_1·a_5_4 + c_8_20·a_1_1·a_5_3
       + c_8_20·a_1_0·a_5_8
  142. a_1_1·a_13_29 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_21·a_1_0·a_5_3
       + c_8_20·a_1_1·a_5_8 + c_8_20·a_1_1·a_5_7 + c_8_20·a_1_0·a_5_8
  143. a_1_0·a_13_29 + c_8_21·a_1_0·a_5_2 + c_8_20·a_1_0·a_5_8 + c_8_20·a_1_0·a_5_5
       + c_8_20·a_1_0·a_5_3 + c_8_20·a_1_0·a_5_2
  144. b_5_6·a_9_18 + b_1_35·a_9_18 + a_5_7·a_9_18 + a_1_2·a_13_29 + a_1_2·b_1_34·a_9_18
       + c_8_21·a_1_2·b_5_6 + c_8_21·a_1_2·b_1_35 + c_8_20·b_1_3·a_5_9 + c_8_20·a_1_2·b_5_10
       + c_8_20·a_1_2·b_5_6 + c_8_20·a_1_1·b_5_10 + c_8_20·a_1_1·b_5_6 + c_8_21·a_1_2·a_5_7
       + c_8_21·a_1_2·a_5_4 + c_8_21·a_1_1·a_5_4 + c_8_21·a_1_1·a_5_3 + c_8_20·a_1_1·a_5_7
       + c_8_20·a_1_0·a_5_8
  145. a_9_182 + a_1_2·b_1_38·a_9_18 + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_212·a_1_22
       + c_8_202·a_1_22 + c_8_202·a_1_12
  146. a_9_152 + c_8_212·a_1_12 + c_8_212·a_1_02 + c_8_20·c_8_21·a_1_02
       + c_8_202·a_1_12 + c_8_202·a_1_02
  147. a_9_102 + a_1_2·b_1_38·a_9_18 + a_1_2·b_1_312·a_5_9 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_212·a_1_12 + c_8_20·c_8_21·a_1_12 + c_8_202·a_1_22 + c_8_202·a_1_12
  148. a_9_18·a_9_10 + c_8_21·a_1_2·a_9_18 + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_21·a_1_1·a_9_14
       + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_20·a_1_1·a_9_14 + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_22 + c_8_212·a_1_1·a_1_2
       + c_8_212·a_1_12 + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_202·a_1_22
       + c_8_202·a_1_1·a_1_2 + c_8_202·a_1_12
  149. a_9_15·a_9_14 + a_9_18·a_9_10 + a_9_18·a_9_15 + c_8_21·a_1_2·a_9_18
       + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_21·a_1_1·a_9_10 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_22 + c_8_212·a_1_12 + c_8_212·a_1_0·a_1_1
       + c_8_212·a_1_02 + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_12
       + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_20·c_8_21·a_1_02 + c_8_202·a_1_22
       + c_8_202·a_1_0·a_1_1 + c_8_202·a_1_02
  150. a_9_142 + a_1_2·b_1_38·a_9_18 + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_22 + c_8_20·c_8_21·a_1_12 + c_8_20·c_8_21·a_1_02
       + c_8_202·a_1_22 + c_8_202·a_1_02
  151. a_9_10·a_9_14 + a_9_15·a_9_10 + a_9_18·a_9_14 + a_9_18·a_9_10 + a_1_2·b_1_38·a_9_18
       + c_8_21·a_1_2·a_9_14 + c_8_21·a_1_2·a_9_18 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_22 + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12
       + c_8_202·a_1_22 + c_8_202·a_1_1·a_1_2
  152. a_9_15·a_9_10 + a_9_18·a_9_15 + a_1_2·b_1_38·a_9_19 + a_1_2·b_1_38·a_9_18
       + a_1_2·b_1_312·a_5_9 + c_8_21·a_1_1·a_9_10 + c_8_20·a_1_1·a_9_10
       + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_0·a_1_1
       + c_8_20·c_8_21·a_1_12 + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_202·a_1_1·a_1_2
       + c_8_202·a_1_12 + c_8_202·a_1_0·a_1_1
  153. a_9_10·a_9_14 + a_9_15·a_9_10 + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10
       + c_8_21·a_1_0·a_9_10 + c_8_20·a_1_2·a_9_19 + c_8_20·a_1_2·a_9_14 + c_8_20·a_1_2·a_9_18
       + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·c_8_21·a_1_22 + c_8_202·a_1_22
       + c_8_202·a_1_12
  154. a_9_192 + a_1_2·b_1_38·a_9_18 + a_1_2·b_1_312·a_5_9 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_212·a_1_12 + c_8_212·a_1_02 + c_8_20·c_8_21·a_1_02 + c_8_202·a_1_12
       + c_8_202·a_1_02
  155. a_9_15·a_9_19 + a_9_15·a_9_10 + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_21·a_1_1·a_9_10
       + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_1·a_9_10 + c_8_212·a_1_12
       + c_8_212·a_1_0·a_1_1 + c_8_212·a_1_02 + c_8_20·c_8_21·a_1_0·a_1_1
       + c_8_20·c_8_21·a_1_02 + c_8_202·a_1_12 + c_8_202·a_1_0·a_1_1 + c_8_202·a_1_02
  156. a_9_14·a_9_19 + a_9_10·a_9_14 + a_9_18·a_9_10 + a_9_18·a_9_15 + a_1_2·b_1_38·a_9_18
       + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10 + c_8_20·a_1_2·a_9_14
       + c_8_20·a_1_2·a_9_18 + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_1·a_9_10
       + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_12 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_12 + c_8_20·c_8_21·a_1_02
       + c_8_202·a_1_1·a_1_2 + c_8_202·a_1_12 + c_8_202·a_1_02
  157. a_9_10·a_9_19 + a_9_10·a_9_14 + a_9_15·a_9_10 + a_1_2·b_1_38·a_9_18
       + a_1_2·b_1_312·a_5_9 + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_0·a_9_10
       + c_8_20·a_1_2·a_9_14 + c_8_20·a_1_2·a_9_18 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_20·a_1_1·a_9_10 + c_8_212·a_1_0·a_1_1 + c_8_20·c_8_21·a_1_22
       + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_202·a_1_22
       + c_8_202·a_1_1·a_1_2 + c_8_202·a_1_12 + c_8_202·a_1_0·a_1_1
  158. a_9_10·a_9_14 + a_9_15·a_9_10 + a_9_18·a_9_19 + a_9_18·a_9_15 + a_1_2·b_1_38·a_9_18
       + c_8_21·a_1_2·a_9_19 + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10
       + c_8_20·a_1_2·a_9_14 + c_8_20·a_1_2·a_9_18 + c_8_212·a_1_1·a_1_2
       + c_8_20·c_8_21·a_1_22 + c_8_202·a_1_22 + c_8_202·a_1_1·a_1_2 + c_8_202·a_1_12
  159. b_9_242 + b_1_313·b_5_6 + b_1_313·a_5_9 + a_1_2·b_1_312·b_5_6
       + a_1_2·b_1_38·a_9_18 + c_8_21·b_1_35·b_5_6 + c_8_20·b_1_35·b_5_6 + c_8_20·b_1_310
       + c_8_21·b_1_35·a_5_9 + c_8_20·b_1_35·a_5_9 + c_8_20·a_1_2·b_1_34·b_5_6
       + c_8_20·a_1_2·b_1_39 + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_20·c_8_21·b_1_32 + c_8_202·b_1_32 + c_8_212·a_1_12
       + c_8_20·c_8_21·a_1_22 + c_8_20·c_8_21·a_1_12 + c_8_20·c_8_21·a_1_02
  160. a_9_15·b_9_24 + a_1_2·b_1_38·b_9_24 + a_1_2·b_1_312·b_5_6 + a_9_10·a_9_14
       + a_9_15·a_9_10 + a_1_2·b_1_312·a_5_9 + c_8_21·a_1_2·b_1_34·b_5_6
       + c_8_21·a_1_1·b_9_24 + c_8_20·a_1_2·b_1_34·b_5_6 + c_8_20·a_1_1·b_9_24
       + c_8_21·a_1_2·a_9_14 + c_8_21·a_1_2·a_9_18 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_0·a_9_15 + c_8_20·a_1_2·a_9_14 + c_8_20·a_1_0·a_9_10
       + c_8_20·a_1_0·a_9_15 + c_8_212·a_1_22 + c_8_212·a_1_12 + c_8_212·a_1_0·a_1_1
       + c_8_212·a_1_02 + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_12
       + c_8_20·c_8_21·a_1_02 + c_8_202·a_1_22 + c_8_202·a_1_1·a_1_2
       + c_8_202·a_1_0·a_1_1 + c_8_202·a_1_02
  161. a_9_19·b_9_24 + a_9_14·b_9_24 + b_1_39·a_9_18 + a_1_2·b_1_38·b_9_24 + a_9_10·a_9_14
       + a_9_15·a_9_10 + a_9_18·a_9_10 + a_9_18·a_9_15 + a_1_2·b_1_38·a_9_18
       + c_8_21·b_1_3·a_9_18 + c_8_21·a_1_2·b_1_39 + c_8_21·a_1_1·b_9_24
       + c_8_20·b_1_3·a_9_18 + c_8_20·a_1_2·b_1_34·b_5_10 + c_8_20·a_1_2·b_1_39
       + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_0·a_9_10
       + c_8_212·a_1_2·b_1_3 + c_8_20·c_8_21·a_1_2·b_1_3 + c_8_212·a_1_12
       + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_12 + c_8_202·a_1_1·a_1_2
       + c_8_202·a_1_12 + c_8_202·a_1_0·a_1_1
  162. a_9_10·b_9_24 + a_9_10·a_9_14 + a_9_18·a_9_10 + c_8_21·a_1_1·b_9_24
       + c_8_20·b_1_3·a_9_19 + c_8_20·b_1_3·a_9_18 + c_8_20·a_1_2·b_9_24
       + c_8_20·a_1_2·b_1_34·b_5_10 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_20·c_8_21·a_1_2·b_1_3 + c_8_202·a_1_2·b_1_3 + c_8_202·a_1_1·b_1_3
       + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_0·a_1_1 + c_8_20·c_8_21·a_1_12
       + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_202·a_1_22
  163. a_9_19·b_9_24 + a_9_18·b_9_24 + b_1_39·a_9_18 + a_1_2·b_1_38·b_9_24 + a_9_18·a_9_15
       + a_1_2·b_1_38·a_9_18 + c_8_21·b_1_3·a_9_18 + c_8_21·a_1_2·b_9_24
       + c_8_21·a_1_2·b_1_39 + c_8_21·a_1_1·b_9_24 + c_8_20·b_1_3·a_9_18
       + c_8_20·a_1_2·b_9_24 + c_8_20·a_1_2·b_1_39 + c_8_21·a_1_2·a_9_14
       + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10 + c_8_21·a_1_0·a_9_15 + c_8_20·a_1_2·a_9_18
       + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_0·a_9_15 + c_8_212·a_1_2·b_1_3
       + c_8_20·c_8_21·a_1_1·b_1_3 + c_8_202·a_1_2·b_1_3 + c_8_202·a_1_1·b_1_3
       + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12 + c_8_212·a_1_0·a_1_1 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_02 + c_8_202·a_1_1·a_1_2
       + c_8_202·a_1_0·a_1_1 + c_8_202·a_1_02
  164. a_9_18·a_9_10 + a_5_3·a_13_29 + c_8_21·a_1_2·a_9_18 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10
       + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_22
       + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12 + c_8_202·a_1_22 + c_8_202·a_1_12
       + c_8_202·a_1_0·a_1_1
  165. a_5_2·a_13_29 + c_8_20·a_1_0·a_9_10 + c_8_20·a_1_0·a_9_15 + c_8_202·a_1_02
  166. a_9_18·a_9_10 + a_5_5·a_13_29 + c_8_21·a_1_2·a_9_18 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10 + c_8_21·a_1_0·a_9_15
       + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_0·a_9_15 + c_8_212·a_1_22
       + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12 + c_8_212·a_1_0·a_1_1 + c_8_212·a_1_02
       + c_8_202·a_1_22 + c_8_202·a_1_12 + c_8_202·a_1_0·a_1_1 + c_8_202·a_1_02
  167. a_9_19·b_9_24 + b_1_35·a_13_29 + b_1_39·a_9_19 + b_1_313·a_5_9 + a_1_2·b_1_312·b_5_6
       + a_9_10·a_9_14 + a_9_18·a_9_15 + a_1_2·b_1_312·a_5_9 + c_8_21·b_1_3·a_9_18
       + c_8_21·a_1_2·b_1_34·b_5_6 + c_8_21·a_1_2·b_1_39 + c_8_21·a_1_1·b_9_24
       + c_8_20·b_1_3·a_9_19 + c_8_20·a_1_2·b_1_34·b_5_10 + c_8_20·a_1_2·b_1_34·b_5_6
       + c_8_20·a_1_2·b_1_39 + c_8_20·a_1_1·b_9_24 + c_8_21·a_1_2·a_9_14
       + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10
       + c_8_21·a_1_0·a_9_15 + c_8_20·a_1_0·a_9_10 + c_8_20·a_1_0·a_9_15
       + c_8_212·a_1_2·b_1_3 + c_8_20·c_8_21·a_1_2·b_1_3 + c_8_202·a_1_1·b_1_3
       + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_20·c_8_21·a_1_02
       + c_8_202·a_1_22 + c_8_202·a_1_12 + c_8_202·a_1_02
  168. a_9_15·a_9_10 + a_1_2·b_1_34·a_13_29 + a_1_2·b_1_38·a_9_18 + c_8_21·a_1_1·a_9_10
       + c_8_20·a_1_1·a_9_10 + c_8_212·a_1_0·a_1_1 + c_8_20·c_8_21·a_1_0·a_1_1
       + c_8_202·a_1_0·a_1_1
  169. a_9_18·a_9_15 + a_5_7·a_13_29 + c_8_21·a_1_2·a_9_14 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_21·a_1_1·a_9_14 + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10 + c_8_20·a_1_2·a_9_14
       + c_8_20·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_1·a_1_2
       + c_8_212·a_1_12 + c_8_20·c_8_21·a_1_22 + c_8_20·c_8_21·a_1_1·a_1_2
       + c_8_202·a_1_22 + c_8_202·a_1_1·a_1_2 + c_8_202·a_1_12
  170. a_9_10·a_9_14 + a_9_18·a_9_10 + a_9_18·a_9_15 + a_5_9·a_13_29 + c_8_21·a_1_2·a_9_14
       + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10
       + c_8_21·a_1_0·a_9_15 + c_8_20·a_1_2·a_9_18 + c_8_20·a_1_1·a_9_10 + c_8_20·a_1_0·a_9_10
       + c_8_20·a_1_0·a_9_15 + c_8_212·a_1_12 + c_8_212·a_1_0·a_1_1 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_22 + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_202·a_1_22
       + c_8_202·a_1_12 + c_8_202·a_1_02
  171. a_9_10·a_9_14 + a_9_15·a_9_10 + a_5_8·a_13_29 + a_1_2·b_1_38·a_9_18
       + c_8_21·a_1_0·a_9_10 + c_8_20·a_1_2·a_9_18 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_212·a_1_12 + c_8_212·a_1_0·a_1_1 + c_8_202·a_1_1·a_1_2 + c_8_202·a_1_12
  172. a_9_19·b_9_24 + b_5_10·a_13_29 + a_1_2·b_1_38·b_9_24 + a_9_15·a_9_10
       + a_1_2·b_1_38·a_9_18 + c_8_21·b_1_35·a_5_9 + c_8_21·a_1_2·b_9_24
       + c_8_21·a_1_1·b_9_24 + c_8_20·b_1_3·a_9_19 + c_8_20·b_1_3·a_9_18
       + c_8_20·b_1_35·a_5_9 + c_8_20·a_1_2·b_9_24 + c_8_20·a_1_2·b_1_34·b_5_10
       + c_8_20·a_1_2·b_1_39 + c_8_21·a_1_2·a_9_19 + c_8_21·a_1_2·b_1_34·a_5_9
       + c_8_21·a_1_1·a_9_10 + c_8_21·a_1_0·a_9_10 + c_8_21·a_1_0·a_9_15 + c_8_20·a_1_2·a_9_14
       + c_8_20·a_1_1·a_9_10 + c_8_202·a_1_1·b_1_3 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_12 + c_8_20·c_8_21·a_1_02 + c_8_202·a_1_22
       + c_8_202·a_1_0·a_1_1
  173. b_5_6·a_13_29 + b_1_39·a_9_18 + a_9_10·a_9_14 + a_9_15·a_9_10 + a_9_18·a_9_15
       + c_8_21·a_1_2·b_1_39 + c_8_20·b_1_3·a_9_19 + c_8_20·b_1_3·a_9_18
       + c_8_20·a_1_2·b_9_24 + c_8_20·a_1_2·b_1_34·b_5_10 + c_8_20·a_1_1·b_9_24
       + c_8_21·a_1_0·a_9_10 + c_8_21·a_1_0·a_9_15 + c_8_20·a_1_2·b_1_34·a_5_9
       + c_8_20·a_1_0·a_9_10 + c_8_20·c_8_21·a_1_1·b_1_3 + c_8_202·a_1_1·b_1_3
       + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12 + c_8_212·a_1_02
       + c_8_20·c_8_21·a_1_0·a_1_1 + c_8_202·a_1_12 + c_8_202·a_1_0·a_1_1
  174. a_9_10·a_9_14 + a_9_15·a_9_10 + a_9_18·a_9_10 + a_5_4·a_13_29 + a_1_2·b_1_38·a_9_18
       + c_8_21·a_1_2·a_9_18 + c_8_21·a_1_2·b_1_34·a_5_9 + c_8_20·a_1_2·a_9_18
       + c_8_20·a_1_0·a_9_10 + c_8_212·a_1_22 + c_8_212·a_1_1·a_1_2 + c_8_212·a_1_12
       + c_8_20·c_8_21·a_1_1·a_1_2 + c_8_202·a_1_22 + c_8_202·a_1_1·a_1_2
       + c_8_202·a_1_0·a_1_1
  175. b_9_24·a_13_29 + b_1_39·a_13_29 + b_1_313·a_9_19 + b_1_313·a_9_18 + b_1_317·a_5_9
       + a_1_2·b_1_312·b_9_24 + a_1_2·b_1_316·b_5_6 + a_1_2·b_1_38·a_13_29
       + a_1_2·b_1_316·a_5_9 + c_8_21·a_1_2·b_1_38·b_5_6 + c_8_20·b_1_39·a_5_9
       + c_8_20·a_1_2·b_1_38·b_5_10 + c_8_21·a_1_2·a_13_29 + c_8_20·a_1_2·b_1_34·a_9_19
       + c_8_20·c_8_21·b_1_3·a_5_9 + c_8_20·c_8_21·a_1_2·b_5_6
       + c_8_20·c_8_21·a_1_2·b_1_35 + c_8_20·c_8_21·a_1_1·b_5_10
       + c_8_20·c_8_21·a_1_1·b_5_6 + c_8_202·b_1_3·a_5_9 + c_8_202·a_1_2·b_5_6
       + c_8_202·a_1_2·b_1_35 + c_8_202·a_1_1·b_5_6 + c_8_212·a_1_2·a_5_4
       + c_8_212·a_1_0·a_5_3 + c_8_20·c_8_21·a_1_2·a_5_9 + c_8_20·c_8_21·a_1_2·a_5_7
       + c_8_20·c_8_21·a_1_1·a_5_8 + c_8_20·c_8_21·a_1_0·a_5_8 + c_8_20·c_8_21·a_1_0·a_5_5
       + c_8_20·c_8_21·a_1_0·a_5_3 + c_8_202·a_1_2·a_5_9 + c_8_202·a_1_2·a_5_7
       + c_8_202·a_1_2·a_5_4 + c_8_202·a_1_1·a_5_8 + c_8_202·a_1_1·a_5_4
       + c_8_202·a_1_1·a_5_3 + c_8_202·a_1_0·a_5_8 + c_8_202·a_1_0·a_5_3
  176. b_9_24·a_13_29 + b_1_39·a_13_29 + b_1_313·a_9_19 + b_1_313·a_9_18 + b_1_317·a_5_9
       + a_1_2·b_1_312·b_9_24 + a_1_2·b_1_316·b_5_6 + a_9_19·a_13_29 + a_1_2·b_1_38·a_13_29
       + a_1_2·b_1_312·a_9_19 + c_8_21·a_1_2·b_1_38·b_5_6 + c_8_20·b_1_39·a_5_9
       + c_8_20·a_1_2·b_1_38·b_5_10 + c_8_21·a_1_2·b_1_38·a_5_9
       + c_8_20·a_1_2·b_1_34·a_9_18 + c_8_20·c_8_21·b_1_3·a_5_9 + c_8_20·c_8_21·a_1_2·b_5_6
       + c_8_20·c_8_21·a_1_2·b_1_35 + c_8_20·c_8_21·a_1_1·b_5_10
       + c_8_20·c_8_21·a_1_1·b_5_6 + c_8_202·b_1_3·a_5_9 + c_8_202·a_1_2·b_5_6
       + c_8_202·a_1_2·b_1_35 + c_8_202·a_1_1·b_5_6 + c_8_212·a_1_0·a_5_2
       + c_8_20·c_8_21·a_1_2·a_5_9 + c_8_20·c_8_21·a_1_2·a_5_4 + c_8_20·c_8_21·a_1_1·a_5_4
       + c_8_20·c_8_21·a_1_1·a_5_3 + c_8_20·c_8_21·a_1_0·a_5_8 + c_8_20·c_8_21·a_1_0·a_5_5
       + c_8_20·c_8_21·a_1_0·a_5_3 + c_8_202·a_1_2·a_5_9 + c_8_202·a_1_2·a_5_7
       + c_8_202·a_1_2·a_5_4 + c_8_202·a_1_1·a_5_7 + c_8_202·a_1_1·a_5_4
       + c_8_202·a_1_1·a_5_3 + c_8_202·a_1_0·a_5_8 + c_8_202·a_1_0·a_5_5
       + c_8_202·a_1_0·a_5_2
  177. a_9_15·a_13_29 + a_1_2·b_1_38·a_13_29 + a_1_2·b_1_312·a_9_19 + a_1_2·b_1_316·a_5_9
       + c_8_21·a_1_2·b_1_34·a_9_18 + c_8_21·a_1_2·b_1_38·a_5_9
       + c_8_20·a_1_2·b_1_34·a_9_18 + c_8_20·a_1_2·b_1_38·a_5_9 + c_8_212·a_1_1·a_5_4
       + c_8_212·a_1_1·a_5_3 + c_8_212·a_1_0·a_5_3 + c_8_212·a_1_0·a_5_2
       + c_8_20·c_8_21·a_1_1·a_5_8 + c_8_20·c_8_21·a_1_1·a_5_7 + c_8_20·c_8_21·a_1_1·a_5_4
       + c_8_20·c_8_21·a_1_1·a_5_3 + c_8_202·a_1_1·a_5_8 + c_8_202·a_1_1·a_5_7
       + c_8_202·a_1_0·a_5_5 + c_8_202·a_1_0·a_5_3 + c_8_202·a_1_0·a_5_2
  178. a_9_14·a_13_29 + a_1_2·b_1_312·a_9_18 + c_8_21·a_1_2·b_1_34·a_9_18
       + c_8_21·a_1_2·b_1_38·a_5_9 + c_8_20·a_1_2·a_13_29 + c_8_20·a_1_2·b_1_34·a_9_18
       + c_8_212·a_1_0·a_5_2 + c_8_20·c_8_21·a_1_2·a_5_7 + c_8_20·c_8_21·a_1_1·a_5_7
       + c_8_20·c_8_21·a_1_1·a_5_4 + c_8_202·a_1_0·a_5_8 + c_8_202·a_1_0·a_5_5
       + c_8_202·a_1_0·a_5_3 + c_8_202·a_1_0·a_5_2
  179. a_9_10·a_13_29 + a_1_2·b_1_38·a_13_29 + a_1_2·b_1_312·a_9_18
       + c_8_21·a_1_2·b_1_34·a_9_18 + c_8_21·a_1_2·b_1_38·a_5_9
       + c_8_20·a_1_2·b_1_34·a_9_19 + c_8_20·a_1_2·b_1_38·a_5_9 + c_8_212·a_1_1·a_5_4
       + c_8_212·a_1_1·a_5_3 + c_8_212·a_1_0·a_5_3 + c_8_20·c_8_21·a_1_2·a_5_9
       + c_8_20·c_8_21·a_1_2·a_5_7 + c_8_20·c_8_21·a_1_2·a_5_4 + c_8_20·c_8_21·a_1_1·a_5_8
       + c_8_20·c_8_21·a_1_1·a_5_7 + c_8_20·c_8_21·a_1_1·a_5_3 + c_8_202·a_1_2·a_5_9
       + c_8_202·a_1_2·a_5_4 + c_8_202·a_1_1·a_5_8 + c_8_202·a_1_1·a_5_7
       + c_8_202·a_1_0·a_5_8
  180. b_9_24·a_13_29 + b_1_39·a_13_29 + b_1_313·a_9_19 + b_1_313·a_9_18 + b_1_317·a_5_9
       + a_1_2·b_1_312·b_9_24 + a_1_2·b_1_316·b_5_6 + a_9_18·a_13_29 + a_1_2·b_1_38·a_13_29
       + a_1_2·b_1_312·a_9_18 + a_1_2·b_1_316·a_5_9 + c_8_21·a_1_2·b_1_38·b_5_6
       + c_8_20·b_1_39·a_5_9 + c_8_20·a_1_2·b_1_38·b_5_10 + c_8_20·a_1_2·b_1_34·a_9_18
       + c_8_20·c_8_21·b_1_3·a_5_9 + c_8_20·c_8_21·a_1_2·b_5_6
       + c_8_20·c_8_21·a_1_2·b_1_35 + c_8_20·c_8_21·a_1_1·b_5_10
       + c_8_20·c_8_21·a_1_1·b_5_6 + c_8_202·b_1_3·a_5_9 + c_8_202·a_1_2·b_5_6
       + c_8_202·a_1_2·b_1_35 + c_8_202·a_1_1·b_5_6 + c_8_212·a_1_2·a_5_4
       + c_8_212·a_1_0·a_5_3 + c_8_20·c_8_21·a_1_2·a_5_4 + c_8_20·c_8_21·a_1_1·a_5_8
       + c_8_20·c_8_21·a_1_1·a_5_7 + c_8_20·c_8_21·a_1_0·a_5_8 + c_8_20·c_8_21·a_1_0·a_5_5
       + c_8_202·a_1_2·a_5_7 + c_8_202·a_1_1·a_5_7 + c_8_202·a_1_1·a_5_4
       + c_8_202·a_1_1·a_5_3 + c_8_202·a_1_0·a_5_3
  181. a_13_292 + a_1_2·b_1_316·a_9_18 + c_8_21·a_1_2·b_1_38·a_9_18
       + c_8_21·a_1_2·b_1_312·a_5_9 + c_8_20·a_1_2·b_1_38·a_9_18
       + c_8_20·c_8_21·a_1_2·b_1_34·a_5_9 + c_8_202·a_1_2·b_1_34·a_5_9
       + c_8_20·c_8_212·a_1_22 + c_8_20·c_8_212·a_1_02 + c_8_202·c_8_21·a_1_22
       + c_8_202·c_8_21·a_1_12 + c_8_202·c_8_21·a_1_02

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

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 26.
  • 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_8_20, a Duflot regular element of degree 8
    2. c_8_21, a Duflot regular element of degree 8
    3. b_1_32, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 13, 15].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

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

Restriction maps

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

  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. b_1_3 → 0, an element of degree 1
  5. a_5_2 → 0, an element of degree 5
  6. a_5_3 → 0, an element of degree 5
  7. a_5_4 → 0, an element of degree 5
  8. a_5_5 → 0, an element of degree 5
  9. a_5_7 → 0, an element of degree 5
  10. a_5_8 → 0, an element of degree 5
  11. a_5_9 → 0, an element of degree 5
  12. b_5_6 → 0, an element of degree 5
  13. b_5_10 → 0, an element of degree 5
  14. c_8_20 → c_1_08, an element of degree 8
  15. c_8_21 → c_1_18, an element of degree 8
  16. a_9_18 → 0, an element of degree 9
  17. a_9_15 → 0, an element of degree 9
  18. a_9_10 → 0, an element of degree 9
  19. a_9_14 → 0, an element of degree 9
  20. a_9_19 → 0, an element of degree 9
  21. b_9_24 → 0, an element of degree 9
  22. a_13_29 → 0, an element of degree 13

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 → 0, an element of degree 1
  4. b_1_3 → c_1_2, an element of degree 1
  5. a_5_2 → 0, an element of degree 5
  6. a_5_3 → 0, an element of degree 5
  7. a_5_4 → 0, an element of degree 5
  8. a_5_5 → 0, an element of degree 5
  9. a_5_7 → 0, an element of degree 5
  10. a_5_8 → 0, an element of degree 5
  11. a_5_9 → 0, an element of degree 5
  12. b_5_6 → c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  13. b_5_10 → c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  14. c_8_20 → c_1_02·c_1_26 + c_1_08, an element of degree 8
  15. c_8_21 → c_1_14·c_1_24 + c_1_18 + c_1_02·c_1_26 + c_1_04·c_1_24, an element of degree 8
  16. a_9_18 → 0, an element of degree 9
  17. a_9_15 → 0, an element of degree 9
  18. a_9_10 → 0, an element of degree 9
  19. a_9_14 → 0, an element of degree 9
  20. a_9_19 → 0, an element of degree 9
  21. b_9_24 → c_1_02·c_1_27 + c_1_02·c_1_12·c_1_25 + c_1_02·c_1_14·c_1_23
       + c_1_04·c_1_12·c_1_23 + c_1_04·c_1_14·c_1_2 + c_1_08·c_1_2, an element of degree 9
  22. a_13_29 → 0, an element of degree 13

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