Cohomology of group number 1478 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 4.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 3.
  • It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 4.


Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 3.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    t8  −  t7  +  3·t6  +  t5  +  3·t4  +  5·t3  +  t2  +  2·t  +  1

    (t  +  1)2 · (t  −  1)4 · (t2  +  1)3
  • The a-invariants are -∞,-∞,-∞,-5,-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 19 minimal generators of maximal degree 5:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. b_1_2, an element of degree 1
  4. b_1_3, an element of degree 1
  5. a_3_3, a nilpotent element of degree 3
  6. a_3_5, a nilpotent element of degree 3
  7. b_3_6, an element of degree 3
  8. b_3_8, an element of degree 3
  9. b_3_9, an element of degree 3
  10. b_3_10, an element of degree 3
  11. b_3_11, an element of degree 3
  12. b_3_12, an element of degree 3
  13. c_4_21, a Duflot regular element of degree 4
  14. c_4_22, a Duflot regular element of degree 4
  15. c_4_23, a Duflot regular element of degree 4
  16. b_5_33, an element of degree 5
  17. b_5_34, an element of degree 5
  18. b_5_35, an element of degree 5
  19. b_5_36, an element of degree 5

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

Ring relations

There are 103 minimal relations of maximal degree 10:

  1. a_1_1·b_1_2 + a_1_12 + a_1_02
  2. b_1_2·b_1_3 + b_1_22 + a_1_1·b_1_3 + a_1_0·a_1_1 + a_1_02
  3. a_1_0·b_1_3 + a_1_0·b_1_2 + a_1_12 + a_1_0·a_1_1 + a_1_02
  4. a_1_0·a_1_12
  5. a_1_02·a_1_1 + a_1_03
  6. a_1_12·b_1_3 + a_1_03
  7. a_1_1·b_3_8 + a_1_1·b_3_6 + a_1_1·a_3_3 + a_1_0·a_3_3
  8. b_1_2·a_3_3 + a_1_0·b_3_8 + a_1_0·b_3_6 + a_1_1·a_3_3 + a_1_0·a_3_3
  9. b_1_3·b_3_8 + b_1_3·b_3_6 + b_1_2·b_3_8 + b_1_2·b_3_6 + b_1_3·a_3_3 + b_1_2·a_3_3
       + a_1_1·b_3_6 + a_1_1·b_1_33
  10. b_1_3·b_3_6 + b_1_2·b_3_9 + b_1_2·b_3_8 + b_1_24 + b_1_3·a_3_3 + b_1_2·a_3_3
       + a_1_1·b_1_33 + a_1_0·b_3_6
  11. b_1_3·b_3_6 + b_1_2·b_3_6 + b_1_3·a_3_3 + b_1_2·a_3_3 + a_1_1·b_3_9 + a_1_1·b_3_6
       + a_1_1·b_1_33 + a_1_0·a_3_3
  12. b_1_2·a_3_3 + a_1_1·b_3_6 + a_1_0·b_3_9 + a_1_0·b_1_23
  13. a_1_1·b_3_10 + a_1_1·b_3_6 + a_1_1·a_3_5 + a_1_1·a_3_3 + a_1_0·a_3_5
  14. b_1_2·a_3_5 + a_1_0·b_3_10 + a_1_0·b_3_6 + a_1_1·a_3_5 + a_1_0·a_3_5 + a_1_0·a_3_3
  15. b_1_3·b_3_10 + b_1_2·b_3_10 + b_1_3·a_3_3 + b_1_2·a_3_3 + a_1_1·b_1_33 + a_1_1·a_3_3
       + a_1_0·a_3_5
  16. b_1_2·b_3_11 + b_1_2·b_3_10 + b_1_3·a_3_3 + b_1_2·a_3_5 + b_1_2·a_3_3 + a_1_1·b_1_33
       + a_1_0·b_3_6 + a_1_0·b_1_23 + a_1_0·a_3_3
  17. b_1_3·a_3_3 + b_1_2·a_3_3 + a_1_1·b_3_11 + a_1_1·b_3_6 + a_1_1·b_1_33 + a_1_0·a_3_5
       + a_1_0·a_3_3
  18. b_1_2·a_3_5 + a_1_0·b_3_11 + a_1_0·b_3_6 + a_1_1·a_3_5 + a_1_1·a_3_3 + a_1_0·a_3_3
  19. b_1_3·b_3_6 + b_1_2·b_3_12 + b_1_2·b_3_8 + b_1_2·b_3_6 + b_1_24 + b_1_3·a_3_5
       + b_1_2·a_3_5 + b_1_2·a_3_3 + a_1_1·b_3_6 + a_1_0·b_3_6 + a_1_1·a_3_5 + a_1_1·a_3_3
       + a_1_0·a_3_3
  20. b_1_3·b_3_6 + b_1_2·b_3_6 + b_1_3·a_3_5 + b_1_2·a_3_5 + a_1_1·b_3_12 + a_1_1·a_3_5
       + a_1_1·a_3_3 + a_1_0·a_3_5
  21. b_1_2·a_3_3 + a_1_1·b_3_6 + a_1_0·b_3_12 + a_1_0·b_3_6 + a_1_0·b_1_23 + a_1_1·a_3_5
       + a_1_1·a_3_3
  22. a_1_12·a_3_3
  23. a_1_12·b_3_9 + a_1_0·a_1_1·a_3_5 + a_1_0·a_1_1·a_3_3 + a_1_02·a_3_5 + a_1_02·a_3_3
  24. a_1_12·b_3_11 + a_1_12·a_3_5 + a_1_0·a_1_1·a_3_5 + a_1_0·a_1_1·a_3_3 + a_1_02·a_3_3
  25. a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_10 + a_3_3·b_3_6 + a_3_32
  26. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_11 + b_3_6·b_3_11 + b_1_23·b_3_10
       + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_9 + a_3_3·b_3_8
       + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10 + a_3_3·a_3_5
  27. b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_11 + b_3_6·b_3_9 + b_3_62
       + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_11
       + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_11 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_22·b_3_8
  28. b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_3_62 + b_1_23·b_3_6 + a_3_5·b_3_12 + a_3_5·b_3_10 + a_3_5·b_3_9
       + a_3_3·b_3_11 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_0·b_1_22·b_3_10
       + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_52 + a_3_32
  29. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_6·b_3_12 + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_62 + b_1_23·b_3_10 + a_3_5·b_3_11 + a_3_5·b_3_9 + a_3_5·b_3_8
       + a_3_5·b_3_6 + a_3_3·b_3_6 + a_1_0·b_1_22·b_3_6 + a_3_52
  30. b_3_10·b_3_11 + b_3_102 + b_3_8·b_3_12 + b_3_8·b_3_9 + b_3_6·b_3_11 + b_3_6·b_3_10
       + b_3_6·b_3_8 + a_3_5·b_3_10 + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_8
  31. b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_11 + b_3_6·b_3_9 + b_3_62
       + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_11 + a_3_5·b_3_10
       + a_3_3·b_3_12 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_12 + a_1_0·b_1_22·b_3_8
       + a_3_52 + a_3_3·a_3_5 + a_3_32
  32. b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_6·b_3_10 + b_3_62 + b_1_26 + a_3_5·b_3_6 + a_3_3·b_3_9
       + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10
       + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5 + a_3_32 + c_4_21·b_1_22
       + c_4_21·a_1_0·b_1_2 + c_4_21·a_1_12
  33. b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6
       + b_1_26 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_8
       + a_1_0·b_1_22·b_3_6 + a_1_0·b_1_25 + a_3_32 + c_4_21·b_1_22 + c_4_21·a_1_0·a_1_1
       + c_4_21·a_1_02
  34. b_3_10·b_3_11 + b_3_102 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_11 + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_62 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_10 + a_3_5·b_3_8
       + a_3_5·b_3_6 + a_3_3·b_3_11 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10
       + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5 + c_4_21·a_1_1·b_1_3
  35. b_3_112 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_11
       + b_3_6·b_3_9 + b_1_33·b_3_11 + b_1_33·b_3_9 + b_1_23·b_3_10 + a_3_5·b_3_11
       + a_3_5·b_3_10 + a_3_3·b_3_12 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5
       + c_4_21·b_1_32
  36. b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_3_6·b_3_10 + b_3_62 + b_1_23·b_3_10
       + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_6 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6
       + a_1_1·b_1_32·b_3_9 + a_3_3·a_3_5 + a_3_32 + c_4_22·b_1_22 + c_4_21·a_1_0·b_1_2
  37. b_3_10·b_3_11 + b_3_102 + b_3_6·b_3_11 + b_3_6·b_3_10 + b_3_62 + b_1_23·b_3_10
       + b_1_26 + a_3_5·b_3_10 + a_3_3·b_3_9 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10
       + a_1_0·b_1_22·b_3_6 + a_1_0·b_1_25 + a_3_32 + c_4_21·b_1_22 + c_4_22·a_1_0·b_1_2
       + c_4_21·a_1_0·a_1_1
  38. b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_1_23·b_3_8 + b_1_23·b_3_6 + b_1_26 + a_3_5·b_3_6 + a_3_3·b_3_6
       + a_1_0·b_1_22·b_3_10 + a_3_3·a_3_5 + a_3_32 + c_4_21·b_1_22 + c_4_21·a_1_0·b_1_2
       + c_4_22·a_1_12 + c_4_21·a_1_0·a_1_1
  39. b_3_10·b_3_11 + b_3_102 + b_3_6·b_3_11 + b_3_6·b_3_10 + b_3_62 + b_1_23·b_3_10
       + b_1_26 + a_3_5·b_3_10 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_25 + c_4_21·b_1_22
       + c_4_22·a_1_0·a_1_1
  40. b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_6·b_3_10 + b_3_62 + b_1_26 + a_3_5·b_3_6 + a_3_3·b_3_9
       + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10
       + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5 + c_4_21·b_1_22
       + c_4_21·a_1_0·b_1_2 + c_4_22·a_1_02
  41. b_3_6·b_3_11 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_8 + b_3_62 + b_1_23·b_3_6
       + a_3_5·b_3_8 + a_3_3·b_3_11 + a_3_3·b_3_6 + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5 + a_3_32
       + c_4_22·a_1_1·b_1_3
  42. b_3_92 + b_1_33·b_3_11 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6 + b_1_26
       + a_3_5·b_3_11 + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_12 + a_3_3·b_3_11
       + a_3_3·b_3_9 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_52 + a_3_3·a_3_5
       + c_4_22·b_1_32
  43. b_3_122 + b_3_102 + b_3_82 + b_3_6·b_3_11 + b_3_6·b_3_10 + b_1_33·b_3_11
       + b_1_33·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_6 + b_1_26 + a_3_5·b_3_8 + a_3_3·b_3_11
       + a_3_3·b_3_9 + a_3_3·b_3_8 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_8
       + a_1_0·b_1_22·b_3_6 + a_1_0·b_1_25 + a_3_52 + a_3_3·a_3_5 + c_4_23·b_1_22
       + c_4_21·b_1_22 + c_4_21·a_1_0·b_1_2 + c_4_21·a_1_0·a_1_1
  44. b_3_10·b_3_12 + b_3_9·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_11 + b_3_6·b_3_9
       + b_3_62 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_11 + a_3_5·b_3_8 + a_3_5·b_3_6
       + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_1_0·b_1_25 + a_3_52 + a_3_32
       + c_4_23·a_1_0·b_1_2 + c_4_21·a_1_0·b_1_2 + c_4_21·a_1_0·a_1_1
  45. b_3_122 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_6·b_3_11 + b_3_6·b_3_9
       + b_1_33·b_3_11 + b_1_33·b_3_9 + b_1_23·b_3_10 + b_1_26 + a_3_5·b_3_8 + a_3_5·b_3_6
       + a_3_3·b_3_11 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + c_4_21·b_1_22
       + c_4_23·a_1_12
  46. b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_9 + b_3_82
       + b_3_6·b_3_10 + b_3_6·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6 + b_1_26
       + a_3_5·b_3_11 + a_3_5·b_3_8 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6
       + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5
       + a_3_32 + c_4_21·b_1_22 + c_4_21·a_1_0·b_1_2 + c_4_23·a_1_0·a_1_1
  47. b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_9 + b_3_62 + b_1_23·b_3_8 + b_1_23·b_3_6
       + a_3_3·b_3_9 + a_3_3·b_3_8 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_8
       + a_1_0·b_1_22·b_3_6 + a_3_52 + c_4_23·a_1_02 + c_4_21·a_1_0·a_1_1
  48. b_3_10·b_3_11 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_11 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_8 + b_3_62 + b_1_2·b_5_33 + b_1_23·b_3_10 + b_1_23·b_3_6 + b_1_26
       + a_3_5·b_3_6 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10
       + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_3·a_3_5 + a_3_32 + c_4_21·b_1_22
       + c_4_23·a_1_1·b_1_3
  49. b_3_122 + b_3_10·b_3_12 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_6·b_3_9 + b_3_62
       + b_1_33·b_3_11 + b_1_33·b_3_9 + a_3_5·b_3_11 + a_3_5·b_3_10 + a_3_5·b_3_6 + a_3_3·b_3_11
       + a_3_3·b_3_9 + a_3_3·b_3_8 + a_1_1·b_5_33 + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_8
       + a_3_3·a_3_5 + a_3_32 + c_4_23·a_1_1·b_1_3 + c_4_21·a_1_0·b_1_2 + c_4_21·a_1_0·a_1_1
  50. b_3_122 + b_3_10·b_3_12 + b_3_9·b_3_10 + b_3_82 + b_3_6·b_3_10 + b_1_33·b_3_11
       + b_1_33·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_11
       + a_3_5·b_3_6 + a_3_3·b_3_11 + a_3_3·b_3_6 + a_1_0·b_5_33 + a_1_0·b_1_22·b_3_8
       + a_1_0·b_1_22·b_3_6 + a_3_52 + a_3_3·a_3_5 + c_4_21·a_1_0·b_1_2
  51. b_3_122 + b_3_9·b_3_11 + b_3_9·b_3_10 + b_3_82 + b_3_6·b_3_8 + b_1_3·b_5_33
       + b_1_33·b_3_11 + b_1_33·b_3_9 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_11
       + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_3·b_3_12 + a_3_3·b_3_11 + a_3_3·b_3_9 + a_3_3·b_3_6
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_25 + a_3_52 + a_3_32
       + c_4_23·b_1_32 + c_4_23·a_1_1·b_1_3
  52. b_3_122 + b_3_10·b_3_12 + b_3_8·b_3_9 + b_3_6·b_3_10 + b_3_62 + b_1_33·b_3_11
       + b_1_33·b_3_9 + b_1_2·b_5_34 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_11
       + a_3_5·b_3_10 + a_3_5·b_3_8 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_25 + c_4_23·a_1_1·b_1_3
       + c_4_21·a_1_0·a_1_1
  53. b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_8 + b_3_62 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_26
       + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_11 + a_1_1·b_5_34 + a_1_1·b_1_32·b_3_9
       + a_1_0·b_1_22·b_3_10 + a_3_52 + c_4_21·b_1_22 + c_4_23·a_1_1·b_1_3
       + c_4_21·a_1_0·b_1_2 + c_4_21·a_1_0·a_1_1
  54. b_3_122 + b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82
       + b_3_6·b_3_10 + b_3_62 + b_1_33·b_3_11 + b_1_33·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_8
       + b_1_23·b_3_6 + b_1_26 + a_3_5·b_3_10 + a_3_3·b_3_11 + a_3_3·b_3_9 + a_3_3·b_3_8
       + a_1_1·b_1_32·b_3_9 + a_1_0·b_5_34 + a_3_52 + a_3_3·a_3_5 + a_3_32 + c_4_21·b_1_22
  55. b_3_122 + b_3_112 + b_3_10·b_3_12 + b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_92
       + b_3_8·b_3_10 + b_3_6·b_3_11 + b_3_6·b_3_10 + b_3_6·b_3_8 + b_3_62 + b_1_3·b_5_34
       + b_1_23·b_3_10 + a_3_5·b_3_11 + a_3_5·b_3_9 + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_12
       + a_3_3·b_3_11 + a_3_3·b_3_9 + a_3_3·b_3_6 + a_3_52 + a_3_3·a_3_5 + a_3_32
       + c_4_23·b_1_32
  56. b_3_122 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_3_6·b_3_9 + b_3_62
       + b_1_33·b_3_11 + b_1_33·b_3_9 + b_1_2·b_5_35 + b_1_26 + a_3_5·b_3_11 + a_3_5·b_3_9
       + a_3_5·b_3_6 + a_3_3·b_3_11 + a_3_3·b_3_9 + a_3_3·b_3_8 + a_3_3·b_3_6
       + a_1_1·b_1_32·b_3_9 + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_25 + a_3_32
       + c_4_21·b_1_22 + c_4_23·a_1_1·b_1_3 + c_4_21·a_1_0·a_1_1
  57. b_3_10·b_3_12 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_6·b_3_8 + b_3_62
       + b_1_23·b_3_8 + b_1_26 + a_3_5·b_3_9 + a_3_5·b_3_6 + a_1_1·b_5_35
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_6 + a_1_0·b_1_25 + a_3_52 + a_3_3·a_3_5
       + c_4_21·b_1_22 + c_4_23·a_1_1·b_1_3
  58. b_3_122 + b_3_10·b_3_11 + b_3_102 + b_3_82 + b_3_62 + b_1_33·b_3_11 + b_1_33·b_3_9
       + b_1_23·b_3_8 + b_1_23·b_3_6 + b_1_26 + a_3_5·b_3_8 + a_3_3·b_3_11 + a_1_0·b_5_35
       + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_1_0·b_1_25 + a_3_52 + a_3_32
       + c_4_21·b_1_22 + c_4_21·a_1_0·b_1_2
  59. b_3_122 + b_3_11·b_3_12 + b_3_9·b_3_12 + b_3_9·b_3_11 + b_1_3·b_5_35 + b_1_33·b_3_11
       + b_1_33·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_26 + a_3_5·b_3_10 + a_3_5·b_3_6
       + a_3_3·b_3_12 + a_3_3·b_3_11 + a_1_0·b_1_22·b_3_8 + a_1_0·b_1_22·b_3_6 + a_3_52
       + a_3_3·a_3_5 + c_4_23·b_1_32
  60. b_3_10·b_3_12 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_6·b_3_8 + b_3_62 + b_1_2·b_5_36
       + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_26 + a_3_5·b_3_11 + a_3_5·b_3_10 + a_3_5·b_3_8
       + a_3_3·b_3_12 + a_3_3·b_3_11 + a_3_3·b_3_8 + a_1_1·b_1_32·b_3_9 + a_3_52
       + c_4_23·a_1_1·b_1_3
  61. b_3_122 + b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9
       + b_3_6·b_3_11 + b_3_6·b_3_8 + b_1_33·b_3_11 + b_1_33·b_3_9 + b_1_23·b_3_6
       + a_3_5·b_3_10 + a_3_5·b_3_6 + a_3_3·b_3_12 + a_3_3·b_3_9 + a_1_1·b_5_36 + a_1_0·b_1_25
       + a_3_52 + a_3_3·a_3_5 + a_3_32 + c_4_23·a_1_1·b_1_3
  62. b_3_122 + b_3_10·b_3_12 + b_3_9·b_3_10 + b_3_82 + b_3_6·b_3_10 + b_1_33·b_3_11
       + b_1_33·b_3_9 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_6 + a_3_5·b_3_11
       + a_3_5·b_3_10 + a_3_3·b_3_11 + a_3_3·b_3_8 + a_3_3·b_3_6 + a_1_0·b_5_36
       + a_1_0·b_1_22·b_3_10 + a_1_0·b_1_22·b_3_6 + a_3_52 + a_3_3·a_3_5
  63. b_3_122 + b_3_11·b_3_12 + b_3_10·b_3_12 + b_3_102 + b_3_9·b_3_11 + b_3_92
       + b_3_8·b_3_10 + b_3_82 + b_3_6·b_3_10 + b_3_62 + b_1_3·b_5_36 + b_1_33·b_3_12
       + a_3_5·b_3_8 + a_3_5·b_3_6 + a_3_3·b_3_12 + a_3_3·b_3_9 + a_1_1·b_1_32·b_3_9
       + a_3_3·a_3_5 + a_3_32 + c_4_23·b_1_32 + c_4_23·a_1_1·b_1_3
  64. a_1_12·b_5_33 + a_1_02·b_5_34 + a_1_0·a_3_3·a_3_5 + c_4_22·a_1_03
  65. a_3_3·b_5_33 + a_1_1·b_1_34·b_3_11 + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_8
       + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_1·b_1_33
       + c_4_23·a_1_0·b_3_9 + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_6 + c_4_21·a_1_1·b_3_9
       + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6 + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_1·a_3_3
       + c_4_23·a_1_0·a_3_5
  66. b_3_8·b_5_33 + b_1_23·b_5_34 + b_1_25·b_3_8 + b_1_25·b_3_6 + a_1_1·b_1_34·b_3_11
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_34 + a_1_0·b_1_22·b_5_33
       + a_1_0·b_1_24·b_3_8 + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·b_1_2·b_3_8
       + c_4_22·b_1_2·b_3_6 + c_4_21·b_1_2·b_3_6 + c_4_23·a_1_1·b_3_9 + c_4_23·a_1_0·b_3_9
       + c_4_23·a_1_0·b_3_6 + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_0·b_1_23
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6
       + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_3
  67. b_3_8·b_5_33 + b_1_23·b_5_34 + b_1_25·b_3_8 + b_1_25·b_3_6 + a_3_3·b_5_34
       + a_1_1·b_1_34·b_3_11 + a_1_0·b_1_24·b_3_8 + c_4_23·b_1_2·b_3_8 + c_4_22·b_1_2·b_3_6
       + c_4_21·b_1_2·b_3_6 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_1·b_3_9 + c_4_23·a_1_1·b_1_33
       + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_9
       + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_23 + c_4_21·a_1_1·b_3_11
       + c_4_21·a_1_1·b_1_33 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_3
  68. b_3_11·b_5_34 + b_3_10·b_5_34 + b_3_9·b_5_33 + b_3_8·b_5_33 + b_1_23·b_5_34 + b_1_28
       + a_3_5·b_5_33 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_11 + a_1_0·b_1_22·b_5_33
       + a_1_0·b_1_24·b_3_8 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_21·b_1_3·b_3_11 + c_4_21·b_1_2·b_3_10
       + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_9
       + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_9 + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_0·a_3_5 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5
  69. b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_8·b_5_33 + b_3_6·b_5_33 + b_1_33·b_5_33
       + b_1_35·b_3_11 + b_1_25·b_3_10 + b_1_25·b_3_8 + b_1_25·b_3_6 + b_1_28 + a_3_5·b_5_34
       + a_3_5·b_5_33 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_11 + a_1_1·b_1_34·b_3_9
       + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_34
       + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6 + c_4_22·b_1_34
       + c_4_22·b_1_2·b_3_6 + c_4_22·b_1_24 + c_4_21·b_1_3·b_3_9 + c_4_23·a_1_1·b_3_11
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_6 + c_4_23·a_1_0·b_1_23
       + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_1·b_1_33 + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_11
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_1_23
       + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_3
  70. b_3_10·b_5_33 + b_3_8·b_5_33 + b_3_6·b_5_34 + b_1_25·b_3_8 + b_1_28
       + a_1_1·b_1_34·b_3_11 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_22·b_1_2·b_3_6
       + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_24 + c_4_23·a_1_0·b_3_10
       + c_4_23·a_1_0·b_3_8 + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_5
       + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5
  71. b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_9·b_5_34 + b_3_6·b_5_33 + b_1_35·b_3_11
       + b_1_23·b_5_34 + b_1_25·b_3_10 + b_1_25·b_3_6 + a_1_1·b_1_32·b_5_33
       + a_1_1·b_1_34·b_3_12 + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_11
       + c_4_23·b_1_3·b_3_9 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_24
       + c_4_22·b_1_3·b_3_9 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_10 + c_4_22·b_1_2·b_3_8
       + c_4_22·b_1_24 + c_4_21·b_1_2·b_3_8 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_1·b_3_9
       + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_12
       + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_3_9 + c_4_22·a_1_0·b_3_6 + c_4_21·a_1_1·b_1_33
       + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_3
       + c_4_23·a_1_0·a_3_5 + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_3
  72. b_3_10·b_5_33 + b_3_8·b_5_34 + b_3_6·b_5_33 + b_1_23·b_5_34 + b_1_28
       + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_11 + a_1_1·b_1_34·b_3_9
       + a_1_0·b_1_24·b_3_8 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_6 + c_4_22·b_1_2·b_3_10
       + c_4_22·b_1_2·b_3_6 + c_4_22·b_1_24 + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_6
       + c_4_21·b_1_24 + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_6
       + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_3_9 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_5
  73. b_3_10·b_5_34 + b_3_10·b_5_33 + b_3_8·b_5_33 + b_3_6·b_5_33 + b_1_23·b_5_35
       + b_1_23·b_5_34 + b_1_25·b_3_6 + b_1_28 + a_1_1·b_1_34·b_3_11 + a_1_1·b_1_34·b_3_9
       + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_24
       + c_4_22·b_1_2·b_3_6 + c_4_22·b_1_24 + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_24
       + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8 + c_4_23·a_1_0·b_3_6
       + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_1·b_1_33 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3
       + c_4_22·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_3
  74. b_3_6·b_5_33 + b_1_23·b_5_34 + b_1_23·b_5_33 + b_1_28 + a_1_1·b_1_32·b_5_33
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_35 + a_1_0·b_1_27 + c_4_23·b_1_2·b_3_6
       + c_4_23·b_1_24 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_11
       + c_4_23·a_1_1·b_3_9 + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_8
       + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_1_33
       + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6 + c_4_22·a_1_0·b_1_23
       + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_1_23
       + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_0·a_3_5
  75. a_3_5·b_5_33 + a_3_3·b_5_35 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_11
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_10
       + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_9
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_6 + c_4_22·a_1_1·b_3_11
       + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_23 + c_4_21·a_1_1·b_3_12
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_3
  76. b_3_11·b_5_33 + b_3_10·b_5_35 + b_3_9·b_5_33 + b_3_8·b_5_33 + b_1_33·b_5_33
       + b_1_35·b_3_9 + b_1_23·b_5_34 + b_1_25·b_3_10 + b_1_28 + a_1_1·b_1_34·b_3_12
       + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_11
       + c_4_23·b_1_3·b_3_9 + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8
       + c_4_23·b_1_2·b_3_6 + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_34
       + c_4_22·b_1_2·b_3_10 + c_4_22·b_1_24 + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_34
       + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_12
       + c_4_22·a_1_1·b_3_9 + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_1_23
       + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_8
       + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_0·a_3_5 + c_4_22·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_3
  77. b_3_9·b_5_33 + b_1_35·b_3_11 + b_1_35·b_3_9 + b_1_25·b_3_10 + a_3_5·b_5_35
       + a_3_5·b_5_33 + a_1_1·b_1_34·b_3_12 + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_24·b_3_8
       + a_1_0·b_1_24·b_3_6 + c_4_23·b_1_3·b_3_9 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_2·b_3_10
       + c_4_22·b_1_2·b_3_6 + c_4_21·b_1_34 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_6
       + c_4_23·a_1_1·b_3_9 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_6 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_0·b_3_10 + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9
       + c_4_23·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3
       + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_3
  78. b_3_12·b_5_35 + b_3_12·b_5_33 + b_3_10·b_5_33 + b_3_8·b_5_33 + b_1_35·b_3_9
       + b_1_23·b_5_33 + b_1_25·b_3_10 + b_1_28 + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_24·b_3_10
       + a_1_0·b_1_24·b_3_6 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_22·b_1_34
       + c_4_22·b_1_2·b_3_6 + c_4_22·b_1_24 + c_4_21·b_1_34 + c_4_21·b_1_2·b_3_6
       + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_1·b_3_9
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_3_11
       + c_4_22·a_1_0·b_3_6 + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33
       + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_3
       + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_0·a_3_5
  79. b_3_10·b_5_34 + b_3_10·b_5_33 + b_3_9·b_5_33 + b_3_6·b_5_35 + b_1_35·b_3_11
       + b_1_35·b_3_9 + b_1_23·b_5_33 + b_1_25·b_3_10 + a_1_1·b_1_34·b_3_12
       + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_2·b_3_10
       + c_4_22·b_1_2·b_3_6 + c_4_22·b_1_24 + c_4_21·b_1_34 + c_4_21·b_1_2·b_3_8
       + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_6
       + c_4_22·a_1_1·b_3_9 + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_9
       + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6 + c_4_22·a_1_0·b_1_23 + c_4_21·a_1_1·b_3_12
       + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_10
       + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6 + c_4_21·a_1_0·b_1_23
       + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_5
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_3
  80. b_3_12·b_5_34 + b_3_12·b_5_33 + b_3_11·b_5_33 + b_3_10·b_5_34 + b_3_9·b_5_35
       + b_3_8·b_5_33 + b_1_33·b_5_33 + b_1_35·b_3_9 + b_1_23·b_5_34 + b_1_25·b_3_10
       + b_1_28 + a_3_5·b_5_33 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_12 + a_1_0·b_1_27
       + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_3·b_3_9 + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_8
       + c_4_23·b_1_2·b_3_6 + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_34
       + c_4_22·b_1_24 + c_4_21·b_1_3·b_3_12 + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_34
       + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_11
       + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_23 + c_4_21·a_1_1·b_3_11
       + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_0·a_3_5
       + c_4_22·a_1_1·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_3
       + c_4_21·a_1_0·a_3_5
  81. b_3_11·b_5_33 + b_3_10·b_5_34 + b_3_10·b_5_33 + b_3_8·b_5_35 + b_1_33·b_5_33
       + b_1_35·b_3_11 + b_1_23·b_5_34 + b_1_25·b_3_6 + a_1_1·b_1_34·b_3_11
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_24·b_3_8
       + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_6
       + c_4_23·b_1_24 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_6 + c_4_21·b_1_3·b_3_9
       + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_6 + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_11
       + c_4_23·a_1_1·b_3_9 + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_3_12
       + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6 + c_4_23·a_1_0·a_3_5 + c_4_21·a_1_1·a_3_3
  82. b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_9·b_5_33 + b_3_8·b_5_33 + b_3_6·b_5_33
       + b_1_33·b_5_33 + b_1_35·b_3_9 + b_1_25·b_3_8 + b_1_25·b_3_6 + b_1_28 + a_3_5·b_5_33
       + a_1_1·b_1_32·b_5_35 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_12
       + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_6 + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6
       + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_10 + c_4_22·b_1_24
       + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_34 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_6
       + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_10
       + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_8 + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8
       + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_5 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_3
  83. b_3_12·b_5_33 + b_3_11·b_5_35 + b_3_10·b_5_34 + b_3_6·b_5_33 + b_1_33·b_5_35
       + b_1_35·b_3_11 + b_1_23·b_5_34 + b_1_25·b_3_8 + a_1_1·b_1_32·b_5_33
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_24·b_3_10 + c_4_23·b_1_3·b_3_12
       + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6
       + c_4_23·b_1_24 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_6 + c_4_21·b_1_3·b_3_12
       + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_2·b_3_10 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_9
       + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_9
       + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_1_33
       + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_9
       + c_4_21·a_1_0·b_3_8 + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_5 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_3
  84. b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_9·b_5_33 + b_3_8·b_5_33 + b_3_6·b_5_33
       + b_1_33·b_5_33 + b_1_35·b_3_9 + b_1_25·b_3_8 + b_1_25·b_3_6 + b_1_28 + a_3_5·b_5_33
       + a_3_3·b_5_36 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_11 + a_1_1·b_1_34·b_3_9
       + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_6 + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6
       + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_10 + c_4_22·b_1_24
       + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_34 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_6
       + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_1·b_1_33
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_6 + c_4_23·a_1_0·b_1_23
       + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_3_9 + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6 + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_1_33
       + c_4_21·a_1_0·b_3_6 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3
  85. b_3_10·b_5_36 + b_3_9·b_5_33 + b_3_6·b_5_33 + b_1_35·b_3_11 + b_1_35·b_3_9
       + b_1_25·b_3_8 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_12 + a_1_1·b_1_34·b_3_11
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_10
       + a_1_0·b_1_24·b_3_8 + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_2·b_3_6 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_2·b_3_6 + c_4_21·b_1_34
       + c_4_21·b_1_2·b_3_6 + c_4_23·a_1_1·b_1_33 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_8
       + c_4_22·a_1_1·b_3_12 + c_4_22·a_1_1·b_3_9 + c_4_22·a_1_1·b_1_33
       + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_1_23
       + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_3
       + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_3
  86. b_3_12·b_5_34 + b_3_12·b_5_33 + b_3_11·b_5_36 + b_3_11·b_5_35 + b_3_11·b_5_33
       + b_3_10·b_5_33 + b_3_6·b_5_33 + b_1_35·b_3_11 + b_1_23·b_5_33 + b_1_25·b_3_10
       + b_1_25·b_3_8 + b_1_28 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_12
       + a_1_1·b_1_34·b_3_11 + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_33
       + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_12
       + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_10 + c_4_22·b_1_2·b_3_8
       + c_4_22·b_1_24 + c_4_21·b_1_3·b_3_12 + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_2·b_3_10
       + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_9 + c_4_23·a_1_1·b_1_33
       + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_6 + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_0·b_3_10
       + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_1_23 + c_4_21·a_1_1·b_3_12
       + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_3_6 + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_5 + c_4_21·a_1_0·a_3_3
  87. b_3_9·b_5_33 + b_3_8·b_5_33 + b_3_6·b_5_33 + b_1_35·b_3_11 + b_1_35·b_3_9
       + b_1_23·b_5_33 + b_1_25·b_3_10 + b_1_25·b_3_8 + b_1_25·b_3_6 + b_1_28 + a_3_5·b_5_36
       + a_1_1·b_1_34·b_3_12 + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_33
       + a_1_0·b_1_24·b_3_8 + c_4_23·b_1_3·b_3_9 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6
       + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_2·b_3_10 + c_4_21·b_1_34
       + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_8
       + c_4_23·a_1_0·b_3_6 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_21·a_1_1·b_3_12
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_1_23
       + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_5
       + c_4_22·a_1_1·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3 + c_4_21·a_1_1·a_3_5
  88. b_3_12·b_5_36 + b_3_12·b_5_34 + b_3_11·b_5_35 + b_3_9·b_5_33 + b_3_6·b_5_33
       + b_1_35·b_3_9 + b_1_25·b_3_10 + b_1_25·b_3_6 + a_1_1·b_1_34·b_3_12
       + a_1_1·b_1_34·b_3_11 + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_24·b_3_8
       + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_8
       + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12
       + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_9 + c_4_23·a_1_0·b_3_6
       + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6 + c_4_21·a_1_1·b_3_12
       + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_1·b_1_33
       + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_0·a_3_3 + c_4_21·a_1_0·a_3_3
  89. b_3_8·b_5_33 + b_3_6·b_5_36 + b_3_6·b_5_33 + b_1_25·b_3_8 + a_3_5·b_5_33
       + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27
       + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_6
       + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_8
       + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_3_9
       + c_4_22·a_1_0·b_1_23 + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_9
       + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_1_23 + c_4_23·a_1_1·a_3_5
       + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3
       + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5
  90. b_3_12·b_5_34 + b_3_11·b_5_35 + b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_9·b_5_36
       + b_3_9·b_5_33 + b_1_35·b_3_11 + b_1_23·b_5_34 + b_1_25·b_3_8 + b_1_25·b_3_6 + b_1_28
       + a_1_1·b_1_34·b_3_12 + a_1_1·b_1_34·b_3_11 + a_1_1·b_1_34·b_3_9
       + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_12 + c_4_23·b_1_2·b_3_10
       + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_12 + c_4_22·b_1_3·b_3_9 + c_4_22·b_1_34
       + c_4_22·b_1_2·b_3_10 + c_4_22·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_6
       + c_4_23·a_1_0·b_3_10 + c_4_22·a_1_1·b_3_9 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_1_23
       + c_4_21·a_1_1·b_3_12 + c_4_21·a_1_1·b_3_11 + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_0·b_3_10
       + c_4_21·a_1_0·b_3_6 + c_4_23·a_1_1·a_3_5 + c_4_22·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5
       + c_4_21·a_1_0·a_3_3
  91. b_3_9·b_5_33 + b_3_8·b_5_36 + b_3_8·b_5_33 + b_1_35·b_3_11 + b_1_35·b_3_9
       + b_1_23·b_5_34 + b_1_23·b_5_33 + b_1_25·b_3_10 + b_1_25·b_3_8 + b_1_28
       + a_3_5·b_5_33 + a_1_1·b_1_32·b_5_33 + a_1_1·b_1_34·b_3_12 + a_1_1·b_1_34·b_3_11
       + a_1_1·b_1_34·b_3_9 + a_1_0·b_1_22·b_5_33 + a_1_0·b_1_24·b_3_10
       + a_1_0·b_1_24·b_3_8 + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27 + c_4_23·b_1_3·b_3_9
       + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_11 + c_4_22·b_1_2·b_3_10
       + c_4_22·b_1_2·b_3_8 + c_4_22·b_1_24 + c_4_21·b_1_34 + c_4_21·b_1_2·b_3_8
       + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_1·b_1_33
       + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_12
       + c_4_22·a_1_1·b_3_11 + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_1_23
       + c_4_21·a_1_1·b_3_9 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_8
       + c_4_21·a_1_0·b_3_6 + c_4_23·a_1_1·a_3_5 + c_4_23·a_1_1·a_3_3 + c_4_23·a_1_0·a_3_3
       + c_4_22·a_1_1·a_3_3 + c_4_21·a_1_1·a_3_5 + c_4_21·a_1_0·a_3_5
  92. b_3_11·b_5_33 + b_3_10·b_5_33 + b_3_8·b_5_33 + b_1_33·b_5_33 + b_1_35·b_3_11
       + b_1_23·b_5_34 + b_1_23·b_5_33 + b_1_25·b_3_10 + b_1_25·b_3_8 + b_1_25·b_3_6
       + a_3_5·b_5_33 + a_1_1·b_1_32·b_5_36 + a_1_1·b_1_34·b_3_12 + a_1_0·b_1_22·b_5_33
       + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_24·b_3_8 + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27
       + c_4_23·b_1_3·b_3_11 + c_4_23·b_1_34 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8
       + c_4_23·b_1_24 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_6 + c_4_22·b_1_24
       + c_4_21·b_1_3·b_3_9 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_24 + c_4_23·a_1_1·b_3_12
       + c_4_23·a_1_1·b_3_11 + c_4_23·a_1_0·b_3_10 + c_4_23·a_1_0·b_3_9 + c_4_22·a_1_1·b_3_11
       + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_9 + c_4_22·a_1_0·b_3_8 + c_4_22·a_1_0·b_3_6
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_1_23
       + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_3 + c_4_22·a_1_0·a_3_5 + c_4_22·a_1_0·a_3_3
       + c_4_21·a_1_0·a_3_3
  93. b_3_12·b_5_34 + b_3_10·b_5_33 + b_3_6·b_5_33 + b_1_33·b_5_36 + b_1_33·b_5_33
       + b_1_35·b_3_12 + b_1_35·b_3_9 + b_1_23·b_5_33 + b_1_25·b_3_8 + a_3_5·b_5_33
       + a_1_1·b_1_34·b_3_12 + a_1_1·b_1_34·b_3_11 + a_1_0·b_1_22·b_5_33
       + a_1_0·b_1_24·b_3_10 + a_1_0·b_1_24·b_3_8 + a_1_0·b_1_24·b_3_6 + a_1_0·b_1_27
       + c_4_23·b_1_3·b_3_12 + c_4_23·b_1_2·b_3_10 + c_4_23·b_1_2·b_3_8 + c_4_23·b_1_2·b_3_6
       + c_4_23·b_1_24 + c_4_22·b_1_3·b_3_12 + c_4_22·b_1_34 + c_4_22·b_1_2·b_3_10
       + c_4_22·b_1_2·b_3_8 + c_4_22·b_1_2·b_3_6 + c_4_21·b_1_3·b_3_12 + c_4_21·b_1_2·b_3_10
       + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_6 + c_4_23·a_1_1·b_3_12 + c_4_23·a_1_1·b_3_11
       + c_4_23·a_1_0·b_3_8 + c_4_23·a_1_0·b_1_23 + c_4_22·a_1_1·b_3_12
       + c_4_22·a_1_1·b_1_33 + c_4_22·a_1_0·b_3_10 + c_4_22·a_1_0·b_3_9 + c_4_21·a_1_1·b_3_9
       + c_4_21·a_1_1·b_1_33 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6
       + c_4_23·a_1_0·a_3_5 + c_4_23·a_1_0·a_3_3 + c_4_22·a_1_1·a_3_5 + c_4_21·a_1_1·a_3_5
       + c_4_21·a_1_1·a_3_3 + c_4_21·a_1_0·a_3_5
  94. b_5_332 + b_1_35·b_5_33 + b_1_37·b_3_11 + b_1_37·b_3_9 + b_1_25·b_5_34
       + b_1_27·b_3_10 + b_1_27·b_3_8 + b_1_210 + a_1_1·b_1_34·b_5_33
       + a_1_1·b_1_36·b_3_11 + a_1_1·b_1_36·b_3_9 + a_1_0·b_1_24·b_5_34
       + a_1_0·b_1_24·b_5_33 + a_1_0·b_1_26·b_3_8 + c_4_23·b_1_36 + c_4_22·b_1_33·b_3_11
       + c_4_22·b_1_33·b_3_9 + c_4_22·b_1_23·b_3_8 + c_4_22·b_1_23·b_3_6
       + c_4_21·b_1_33·b_3_11 + c_4_21·b_1_36 + c_4_21·b_1_23·b_3_10
       + c_4_21·b_1_23·b_3_8 + c_4_21·b_1_23·b_3_6 + c_4_23·a_1_0·b_1_25
       + c_4_22·a_1_1·b_1_32·b_3_12 + c_4_22·a_1_1·b_1_32·b_3_9
       + c_4_22·a_1_0·b_1_22·b_3_10 + c_4_22·a_1_0·b_1_22·b_3_6
       + c_4_21·a_1_1·b_1_32·b_3_12 + c_4_21·a_1_1·b_1_32·b_3_11
       + c_4_21·a_1_1·b_1_32·b_3_9 + c_4_21·a_1_1·b_1_35 + c_4_21·a_1_0·b_1_22·b_3_8
       + c_4_21·a_1_0·b_1_22·b_3_6 + c_4_232·b_1_32 + c_4_21·c_4_22·b_1_32
       + c_4_212·b_1_22 + c_4_232·a_1_12 + c_4_232·a_1_02 + c_4_222·a_1_12
       + c_4_222·a_1_02 + c_4_212·a_1_02
  95. b_5_342 + b_1_37·b_3_11 + b_1_37·b_3_9 + b_1_25·b_5_34 + b_1_27·b_3_6
       + a_1_1·b_1_36·b_3_12 + a_1_1·b_1_36·b_3_9 + a_1_0·b_1_24·b_5_35
       + a_1_0·b_1_26·b_3_10 + a_1_0·b_1_26·b_3_8 + c_4_23·b_1_23·b_3_8
       + c_4_23·b_1_23·b_3_6 + c_4_22·b_1_23·b_3_10 + c_4_22·b_1_23·b_3_8 + c_4_21·b_1_36
       + c_4_23·a_1_0·b_1_22·b_3_10 + c_4_23·a_1_0·b_1_22·b_3_8
       + c_4_23·a_1_0·b_1_22·b_3_6 + c_4_23·a_1_0·b_1_25 + c_4_22·a_1_0·b_1_25
       + c_4_232·b_1_32 + c_4_232·b_1_22 + c_4_22·c_4_23·b_1_22 + c_4_222·b_1_32
       + c_4_222·b_1_22 + c_4_212·b_1_32 + c_4_212·b_1_22 + c_4_232·a_1_12
       + c_4_22·c_4_23·a_1_12 + c_4_21·c_4_23·a_1_02 + c_4_21·c_4_22·a_1_12
       + c_4_21·c_4_22·a_1_02 + c_4_212·a_1_12
  96. b_5_362 + b_1_35·b_5_33 + b_1_37·b_3_11 + b_1_37·b_3_9 + b_1_25·b_5_33
       + b_1_27·b_3_10 + a_1_1·b_1_34·b_5_35 + a_1_1·b_1_36·b_3_12 + a_1_1·b_1_36·b_3_9
       + a_1_0·b_1_26·b_3_8 + c_4_23·b_1_36 + c_4_23·b_1_26 + c_4_22·b_1_33·b_3_11
       + c_4_22·b_1_33·b_3_9 + c_4_22·b_1_23·b_3_10 + c_4_22·b_1_23·b_3_8
       + c_4_22·b_1_23·b_3_6 + c_4_21·b_1_33·b_3_9 + c_4_21·b_1_23·b_3_8
       + c_4_21·b_1_23·b_3_6 + c_4_21·b_1_26 + c_4_22·a_1_1·b_1_32·b_3_12
       + c_4_22·a_1_1·b_1_32·b_3_9 + c_4_22·a_1_1·b_1_35 + c_4_22·a_1_0·b_1_22·b_3_10
       + c_4_22·a_1_0·b_1_22·b_3_6 + c_4_22·a_1_0·b_1_25 + c_4_21·a_1_1·b_1_32·b_3_12
       + c_4_21·a_1_1·b_1_32·b_3_9 + c_4_21·a_1_0·b_1_22·b_3_6 + c_4_232·b_1_32
       + c_4_232·b_1_22 + c_4_222·b_1_32 + c_4_21·c_4_22·b_1_32
       + c_4_21·c_4_22·b_1_22 + c_4_22·c_4_23·a_1_02 + c_4_21·c_4_23·a_1_12
       + c_4_21·c_4_22·a_1_02 + c_4_212·a_1_12
  97. b_5_35·b_5_36 + b_5_352 + b_5_34·b_5_36 + b_5_342 + b_1_37·b_3_9
       + b_1_22·b_3_6·b_5_34 + b_1_25·b_5_34 + b_1_27·b_3_8 + b_1_27·b_3_6 + b_1_210
       + a_1_1·b_1_3·b_3_9·b_5_35 + a_1_1·b_1_34·b_5_33 + a_1_1·b_1_36·b_3_9
       + c_4_23·b_1_3·b_5_35 + c_4_23·b_1_33·b_3_11 + c_4_23·b_1_2·b_5_35 + c_4_23·b_1_26
       + c_4_22·b_1_3·b_5_35 + c_4_22·b_1_3·b_5_33 + c_4_22·b_1_36 + c_4_22·b_1_2·b_5_34
       + c_4_22·b_1_2·b_5_33 + c_4_22·b_1_23·b_3_10 + c_4_22·b_1_23·b_3_8 + c_4_22·b_1_26
       + c_4_21·b_1_3·b_5_36 + c_4_21·b_1_36 + c_4_21·b_1_23·b_3_10 + c_4_21·b_1_23·b_3_8
       + c_4_23·a_1_1·b_5_35 + c_4_23·a_1_1·b_1_32·b_3_12 + c_4_23·a_1_1·b_1_32·b_3_11
       + c_4_23·a_1_1·b_1_35 + c_4_23·a_1_0·b_5_34 + c_4_23·a_1_0·b_1_22·b_3_10
       + c_4_23·a_1_0·b_1_25 + c_4_22·a_1_1·b_1_32·b_3_11 + c_4_22·a_1_0·b_1_22·b_3_10
       + c_4_22·a_1_0·b_1_22·b_3_8 + c_4_21·a_1_1·b_5_36 + c_4_21·a_1_0·b_5_33
       + c_4_21·a_1_0·b_1_22·b_3_10 + c_4_21·a_1_0·b_1_22·b_3_6 + c_4_23·a_3_3·a_3_5
       + c_4_232·b_1_32 + c_4_22·c_4_23·b_1_32 + c_4_21·c_4_23·b_1_22
       + c_4_212·b_1_32 + c_4_212·b_1_22 + c_4_22·c_4_23·a_1_1·b_1_3
       + c_4_22·c_4_23·a_1_0·b_1_2 + c_4_222·a_1_1·b_1_3 + c_4_21·c_4_23·a_1_1·b_1_3
       + c_4_21·c_4_23·a_1_0·b_1_2 + c_4_21·c_4_22·a_1_0·b_1_2 + c_4_212·a_1_0·b_1_2
       + c_4_232·a_1_12 + c_4_232·a_1_0·a_1_1 + c_4_232·a_1_02
       + c_4_22·c_4_23·a_1_0·a_1_1 + c_4_22·c_4_23·a_1_02 + c_4_222·a_1_0·a_1_1
       + c_4_222·a_1_02 + c_4_21·c_4_22·a_1_0·a_1_1
  98. b_5_352 + b_5_33·b_5_34 + b_1_35·b_5_33 + b_1_37·b_3_11 + b_1_37·b_3_9
       + b_1_22·b_3_6·b_5_34 + b_1_25·b_5_35 + b_1_25·b_5_33 + b_1_27·b_3_6
       + a_1_1·b_1_3·b_3_9·b_5_35 + a_1_1·b_1_34·b_5_33 + a_1_1·b_1_36·b_3_11
       + a_1_0·b_1_26·b_3_6 + a_1_0·b_1_29 + c_4_23·b_1_3·b_5_33 + c_4_23·b_1_33·b_3_11
       + c_4_23·b_1_36 + c_4_23·b_1_2·b_5_34 + c_4_23·b_1_2·b_5_33 + c_4_22·b_1_3·b_5_33
       + c_4_22·b_1_2·b_5_35 + c_4_22·b_1_23·b_3_10 + c_4_22·b_1_23·b_3_6
       + c_4_21·b_1_3·b_5_33 + c_4_21·b_1_36 + c_4_21·b_1_2·b_5_34 + c_4_21·b_1_2·b_5_33
       + c_4_21·b_1_23·b_3_10 + c_4_21·b_1_23·b_3_8 + c_4_23·a_1_1·b_5_35
       + c_4_23·a_1_1·b_5_33 + c_4_23·a_1_1·b_1_32·b_3_12 + c_4_23·a_1_0·b_5_34
       + c_4_23·a_1_0·b_1_22·b_3_10 + c_4_23·a_1_0·b_1_22·b_3_8 + c_4_23·a_1_0·b_1_25
       + c_4_22·a_1_1·b_5_36 + c_4_22·a_1_1·b_5_35 + c_4_22·a_1_1·b_1_32·b_3_11
       + c_4_22·a_1_1·b_1_32·b_3_9 + c_4_22·a_1_1·b_1_35 + c_4_22·a_1_0·b_5_35
       + c_4_22·a_1_0·b_1_22·b_3_8 + c_4_22·a_1_0·b_1_22·b_3_6 + c_4_21·a_1_1·b_5_36
       + c_4_21·a_1_1·b_5_35 + c_4_21·a_1_1·b_5_33 + c_4_21·a_1_1·b_1_32·b_3_12
       + c_4_21·a_1_0·b_1_22·b_3_8 + c_4_23·a_3_3·a_3_5 + c_4_22·a_3_3·a_3_5
       + c_4_21·a_3_3·a_3_5 + c_4_232·b_1_32 + c_4_21·c_4_23·b_1_22
       + c_4_21·c_4_22·b_1_32 + c_4_21·c_4_22·b_1_22 + c_4_22·c_4_23·a_1_1·b_1_3
       + c_4_22·c_4_23·a_1_0·b_1_2 + c_4_222·a_1_1·b_1_3 + c_4_21·c_4_22·a_1_1·b_1_3
       + c_4_212·a_1_1·b_1_3 + c_4_22·c_4_23·a_1_12 + c_4_22·c_4_23·a_1_02
       + c_4_222·a_1_12 + c_4_222·a_1_02 + c_4_21·c_4_23·a_1_12
       + c_4_21·c_4_23·a_1_0·a_1_1 + c_4_21·c_4_23·a_1_02 + c_4_21·c_4_22·a_1_12
       + c_4_21·c_4_22·a_1_02 + c_4_212·a_1_12 + c_4_212·a_1_0·a_1_1
  99. b_5_35·b_5_36 + b_5_34·b_5_36 + b_5_33·b_5_35 + b_5_332 + b_1_32·b_3_9·b_5_35
       + b_1_35·b_5_35 + b_1_35·b_5_33 + b_1_22·b_3_6·b_5_34 + b_1_25·b_5_33
       + b_1_27·b_3_10 + b_1_27·b_3_8 + a_1_1·b_1_34·b_5_35 + a_1_1·b_1_34·b_5_33
       + a_1_1·b_1_36·b_3_11 + a_1_0·b_1_24·b_5_33 + a_1_0·b_1_26·b_3_10
       + a_1_0·b_1_26·b_3_6 + a_1_0·b_1_29 + c_4_23·b_1_3·b_5_33 + c_4_23·b_1_33·b_3_11
       + c_4_23·b_1_33·b_3_9 + c_4_23·b_1_2·b_5_35 + c_4_23·b_1_23·b_3_10
       + c_4_22·b_1_3·b_5_36 + c_4_22·b_1_3·b_5_35 + c_4_22·b_1_33·b_3_12
       + c_4_22·b_1_33·b_3_11 + c_4_22·b_1_33·b_3_9 + c_4_22·b_1_2·b_5_34
       + c_4_22·b_1_23·b_3_8 + c_4_22·b_1_23·b_3_6 + c_4_22·b_1_26 + c_4_21·b_1_3·b_5_35
       + c_4_21·b_1_2·b_5_34 + c_4_21·b_1_23·b_3_8 + c_4_21·b_1_26
       + c_4_23·a_1_1·b_1_32·b_3_12 + c_4_23·a_1_1·b_1_32·b_3_11
       + c_4_23·a_1_1·b_1_32·b_3_9 + c_4_23·a_1_1·b_1_35 + c_4_23·a_1_0·b_5_35
       + c_4_23·a_1_0·b_5_34 + c_4_23·a_1_0·b_5_33 + c_4_23·a_1_0·b_1_22·b_3_8
       + c_4_22·a_1_1·b_5_33 + c_4_22·a_1_0·b_5_34 + c_4_22·a_1_0·b_5_33
       + c_4_22·a_1_0·b_1_22·b_3_8 + c_4_22·a_1_0·b_1_22·b_3_6 + c_4_22·a_1_0·b_1_25
       + c_4_21·a_1_1·b_5_36 + c_4_21·a_1_1·b_5_35 + c_4_21·a_1_1·b_5_33
       + c_4_21·a_1_1·b_1_32·b_3_12 + c_4_21·a_1_1·b_1_32·b_3_9 + c_4_21·a_1_1·b_1_35
       + c_4_21·a_1_0·b_1_22·b_3_10 + c_4_21·a_1_0·b_1_22·b_3_8 + c_4_23·a_3_3·a_3_5
       + c_4_21·a_3_3·a_3_5 + c_4_232·b_1_32 + c_4_232·b_1_22 + c_4_22·c_4_23·b_1_32
       + c_4_22·c_4_23·b_1_22 + c_4_222·b_1_22 + c_4_21·c_4_23·b_1_22
       + c_4_212·b_1_22 + c_4_232·a_1_1·b_1_3 + c_4_22·c_4_23·a_1_1·b_1_3
       + c_4_21·c_4_23·a_1_1·b_1_3 + c_4_21·c_4_23·a_1_0·b_1_2 + c_4_21·c_4_22·a_1_1·b_1_3
       + c_4_21·c_4_22·a_1_0·b_1_2 + c_4_232·a_1_12 + c_4_22·c_4_23·a_1_12
       + c_4_22·c_4_23·a_1_0·a_1_1 + c_4_22·c_4_23·a_1_02 + c_4_222·a_1_12
       + c_4_21·c_4_23·a_1_0·a_1_1 + c_4_21·c_4_22·a_1_12 + c_4_21·c_4_22·a_1_0·a_1_1
       + c_4_212·a_1_02
  100. b_5_35·b_5_36 + b_5_352 + b_5_33·b_5_36 + b_5_33·b_5_35 + b_5_332
       + b_1_32·b_3_9·b_5_35 + b_1_35·b_5_33 + b_1_37·b_3_11 + b_1_37·b_3_9
       + b_1_22·b_3_6·b_5_34 + b_1_25·b_5_33 + a_1_1·b_1_34·b_5_35 + a_1_1·b_1_36·b_3_11
       + a_1_0·b_1_2·b_3_6·b_5_34 + a_1_0·b_1_24·b_5_33 + a_1_0·b_1_26·b_3_10
       + a_1_0·b_1_26·b_3_6 + c_4_23·b_1_33·b_3_9 + c_4_23·b_1_36 + c_4_23·b_1_2·b_5_35
       + c_4_23·b_1_2·b_5_33 + c_4_23·b_1_23·b_3_10 + c_4_23·b_1_23·b_3_8
       + c_4_23·b_1_23·b_3_6 + c_4_23·b_1_26 + c_4_22·b_1_3·b_5_35 + c_4_22·b_1_3·b_5_33
       + c_4_22·b_1_23·b_3_10 + c_4_22·b_1_23·b_3_6 + c_4_21·b_1_33·b_3_11
       + c_4_21·b_1_33·b_3_9 + c_4_21·b_1_36 + c_4_21·b_1_2·b_5_35 + c_4_21·b_1_2·b_5_34
       + c_4_21·b_1_23·b_3_8 + c_4_21·b_1_23·b_3_6 + c_4_23·a_1_1·b_5_36
       + c_4_23·a_1_1·b_5_35 + c_4_23·a_1_0·b_5_35 + c_4_23·a_1_0·b_1_22·b_3_8
       + c_4_23·a_1_0·b_1_22·b_3_6 + c_4_22·a_1_1·b_5_35 + c_4_22·a_1_1·b_5_33
       + c_4_22·a_1_1·b_1_32·b_3_9 + c_4_22·a_1_1·b_1_35 + c_4_22·a_1_0·b_1_22·b_3_10
       + c_4_22·a_1_0·b_1_25 + c_4_21·a_1_1·b_5_33 + c_4_21·a_1_1·b_1_32·b_3_11
       + c_4_21·a_1_1·b_1_32·b_3_9 + c_4_21·a_1_0·b_5_34 + c_4_21·a_1_0·b_5_33
       + c_4_21·a_1_0·b_1_22·b_3_6 + c_4_22·a_3_3·a_3_5 + c_4_232·b_1_32
       + c_4_21·c_4_22·b_1_32 + c_4_212·b_1_22 + c_4_232·a_1_0·b_1_2
       + c_4_22·c_4_23·a_1_1·b_1_3 + c_4_21·c_4_23·a_1_1·b_1_3 + c_4_21·c_4_23·a_1_0·b_1_2
       + c_4_21·c_4_22·a_1_1·b_1_3 + c_4_21·c_4_22·a_1_0·b_1_2 + c_4_212·a_1_1·b_1_3
       + c_4_212·a_1_0·b_1_2 + c_4_232·a_1_12 + c_4_232·a_1_0·a_1_1
       + c_4_22·c_4_23·a_1_02 + c_4_222·a_1_02 + c_4_21·c_4_23·a_1_12
       + c_4_21·c_4_23·a_1_02 + c_4_21·c_4_22·a_1_12 + c_4_21·c_4_22·a_1_0·a_1_1
       + c_4_21·c_4_22·a_1_02 + c_4_212·a_1_0·a_1_1 + c_4_212·a_1_02
  101. b_5_34·b_5_36 + b_5_34·b_5_35 + b_5_342 + b_5_33·b_5_35 + b_1_35·b_5_35
       + b_1_35·b_5_33 + b_1_25·b_5_35 + b_1_25·b_5_34 + b_1_25·b_5_33 + b_1_27·b_3_10
       + b_1_27·b_3_8 + b_1_27·b_3_6 + b_1_210 + a_1_1·b_1_34·b_5_35 + a_1_1·b_1_36·b_3_9
       + a_1_0·b_1_2·b_3_6·b_5_34 + a_1_0·b_1_26·b_3_8 + a_1_0·b_1_29 + c_4_23·b_1_3·b_5_36
       + c_4_23·b_1_3·b_5_33 + c_4_23·b_1_2·b_5_35 + c_4_23·b_1_2·b_5_34 + c_4_23·b_1_2·b_5_33
       + c_4_23·b_1_23·b_3_8 + c_4_23·b_1_23·b_3_6 + c_4_23·b_1_26 + c_4_22·b_1_3·b_5_35
       + c_4_22·b_1_3·b_5_33 + c_4_22·b_1_2·b_5_34 + c_4_22·b_1_23·b_3_10
       + c_4_22·b_1_23·b_3_8 + c_4_22·b_1_23·b_3_6 + c_4_21·b_1_33·b_3_11
       + c_4_21·b_1_33·b_3_9 + c_4_21·b_1_2·b_5_35 + c_4_21·b_1_2·b_5_34
       + c_4_23·a_1_1·b_5_33 + c_4_23·a_1_0·b_5_35 + c_4_23·a_1_0·b_5_33
       + c_4_23·a_1_0·b_1_22·b_3_10 + c_4_23·a_1_0·b_1_22·b_3_6 + c_4_22·a_1_1·b_5_33
       + c_4_22·a_1_1·b_1_32·b_3_12 + c_4_22·a_1_1·b_1_32·b_3_11
       + c_4_22·a_1_1·b_1_32·b_3_9 + c_4_22·a_1_0·b_5_35 + c_4_22·a_1_0·b_1_22·b_3_6
       + c_4_22·a_1_0·b_1_25 + c_4_21·a_1_1·b_5_33 + c_4_21·a_1_1·b_1_32·b_3_12
       + c_4_21·a_1_1·b_1_35 + c_4_21·a_1_0·b_5_34 + c_4_21·a_1_0·b_1_22·b_3_10
       + c_4_21·a_1_0·b_1_22·b_3_8 + c_4_212·b_1_32 + c_4_212·b_1_22
       + c_4_232·a_1_0·b_1_2 + c_4_22·c_4_23·a_1_1·b_1_3 + c_4_222·a_1_1·b_1_3
       + c_4_21·c_4_23·a_1_1·b_1_3 + c_4_21·c_4_23·a_1_0·b_1_2 + c_4_21·c_4_22·a_1_0·b_1_2
       + c_4_232·a_1_12 + c_4_232·a_1_0·a_1_1 + c_4_232·a_1_02 + c_4_22·c_4_23·a_1_12
       + c_4_222·a_1_0·a_1_1 + c_4_222·a_1_02 + c_4_21·c_4_23·a_1_12
       + c_4_21·c_4_23·a_1_0·a_1_1 + c_4_21·c_4_23·a_1_02 + c_4_21·c_4_22·a_1_0·a_1_1
       + c_4_212·a_1_02
  102. b_5_352 + b_5_342 + b_5_332 + b_1_35·b_5_33 + b_1_37·b_3_9 + b_1_25·b_5_35
       + b_1_25·b_5_33 + b_1_27·b_3_10 + b_1_27·b_3_8 + b_1_27·b_3_6 + b_1_210
       + a_1_1·b_1_34·b_5_36 + a_1_1·b_1_34·b_5_35 + a_1_1·b_1_36·b_3_11
       + a_1_1·b_1_36·b_3_9 + a_1_0·b_1_26·b_3_10 + a_1_0·b_1_26·b_3_6 + c_4_23·b_1_36
       + c_4_23·b_1_23·b_3_10 + c_4_23·b_1_23·b_3_8 + c_4_23·b_1_23·b_3_6
       + c_4_22·b_1_33·b_3_11 + c_4_22·b_1_33·b_3_9 + c_4_22·b_1_36 + c_4_22·b_1_23·b_3_6
       + c_4_21·b_1_33·b_3_11 + c_4_21·b_1_33·b_3_9 + c_4_21·b_1_36 + c_4_21·b_1_23·b_3_6
       + c_4_21·b_1_26 + c_4_23·a_1_1·b_1_35 + c_4_23·a_1_0·b_1_22·b_3_10
       + c_4_23·a_1_0·b_1_22·b_3_8 + c_4_23·a_1_0·b_1_22·b_3_6
       + c_4_22·a_1_1·b_1_32·b_3_11 + c_4_22·a_1_0·b_1_22·b_3_10
       + c_4_22·a_1_0·b_1_22·b_3_6 + c_4_21·a_1_1·b_1_32·b_3_11 + c_4_21·a_1_1·b_1_35
       + c_4_21·a_1_0·b_1_22·b_3_10 + c_4_21·a_1_0·b_1_22·b_3_6 + c_4_21·a_1_0·b_1_25
       + c_4_232·b_1_32 + c_4_232·b_1_22 + c_4_22·c_4_23·b_1_22 + c_4_222·b_1_32
       + c_4_222·b_1_22 + c_4_21·c_4_23·b_1_22 + c_4_212·b_1_32
       + c_4_22·c_4_23·a_1_02 + c_4_222·a_1_12 + c_4_21·c_4_22·a_1_12
       + c_4_212·a_1_12 + c_4_212·a_1_02
  103. b_5_352 + b_5_34·b_5_35 + b_5_332 + b_1_32·b_3_9·b_5_35 + b_1_35·b_5_36
       + b_1_35·b_5_35 + b_1_37·b_3_12 + b_1_37·b_3_11 + b_1_25·b_5_33 + b_1_27·b_3_10
       + b_1_27·b_3_6 + a_1_1·b_1_3·b_3_9·b_5_35 + a_1_1·b_1_34·b_5_35
       + a_1_1·b_1_34·b_5_33 + a_1_0·b_1_26·b_3_10 + a_1_0·b_1_26·b_3_8
       + c_4_23·b_1_3·b_5_35 + c_4_23·b_1_33·b_3_11 + c_4_23·b_1_33·b_3_9
       + c_4_23·b_1_2·b_5_35 + c_4_23·b_1_2·b_5_34 + c_4_23·b_1_2·b_5_33 + c_4_22·b_1_3·b_5_35
       + c_4_22·b_1_33·b_3_12 + c_4_22·b_1_33·b_3_9 + c_4_22·b_1_36 + c_4_22·b_1_2·b_5_33
       + c_4_22·b_1_26 + c_4_21·b_1_3·b_5_35 + c_4_21·b_1_33·b_3_12 + c_4_21·b_1_33·b_3_11
       + c_4_21·b_1_36 + c_4_21·b_1_2·b_5_35 + c_4_21·b_1_23·b_3_10 + c_4_21·b_1_23·b_3_8
       + c_4_21·b_1_26 + c_4_23·a_1_1·b_5_33 + c_4_23·a_1_1·b_1_32·b_3_12
       + c_4_23·a_1_1·b_1_32·b_3_11 + c_4_23·a_1_1·b_1_35 + c_4_23·a_1_0·b_5_34
       + c_4_23·a_1_0·b_5_33 + c_4_23·a_1_0·b_1_22·b_3_6 + c_4_23·a_1_0·b_1_25
       + c_4_22·a_1_1·b_5_35 + c_4_22·a_1_1·b_5_33 + c_4_22·a_1_1·b_1_32·b_3_11
       + c_4_22·a_1_0·b_5_33 + c_4_22·a_1_0·b_1_22·b_3_10 + c_4_21·a_1_1·b_5_35
       + c_4_21·a_1_1·b_1_32·b_3_12 + c_4_21·a_1_0·b_1_22·b_3_8
       + c_4_21·a_1_0·b_1_22·b_3_6 + c_4_21·a_1_0·b_1_25 + c_4_22·a_3_3·a_3_5
       + c_4_232·b_1_22 + c_4_21·c_4_22·b_1_22 + c_4_212·b_1_22
       + c_4_22·c_4_23·a_1_1·b_1_3 + c_4_22·c_4_23·a_1_0·b_1_2 + c_4_21·c_4_23·a_1_1·b_1_3
       + c_4_21·c_4_23·a_1_0·b_1_2 + c_4_21·c_4_22·a_1_1·b_1_3 + c_4_21·c_4_22·a_1_0·b_1_2
       + c_4_232·a_1_02 + c_4_22·c_4_23·a_1_12 + c_4_22·c_4_23·a_1_02
       + c_4_222·a_1_12 + c_4_21·c_4_23·a_1_12 + c_4_21·c_4_23·a_1_02
       + c_4_21·c_4_22·a_1_12 + c_4_21·c_4_22·a_1_0·a_1_1 + c_4_21·c_4_22·a_1_02
       + c_4_212·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 10.
  • 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_21, a Duflot regular element of degree 4
    2. c_4_22, a Duflot regular element of degree 4
    3. c_4_23, a Duflot regular element of degree 4
    4. b_1_32, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 7, 10].
  • 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 3

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_20, an element of degree 1
  4. b_1_30, an element of degree 1
  5. a_3_30, an element of degree 3
  6. a_3_50, an element of degree 3
  7. b_3_60, an element of degree 3
  8. b_3_80, an element of degree 3
  9. b_3_90, an element of degree 3
  10. b_3_100, an element of degree 3
  11. b_3_110, an element of degree 3
  12. b_3_120, an element of degree 3
  13. c_4_21c_1_24 + c_1_14, an element of degree 4
  14. c_4_22c_1_14, an element of degree 4
  15. c_4_23c_1_24 + c_1_04, an element of degree 4
  16. b_5_330, an element of degree 5
  17. b_5_340, an element of degree 5
  18. b_5_350, an element of degree 5
  19. b_5_360, an element of degree 5

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

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_20, an element of degree 1
  4. b_1_3c_1_3, an element of degree 1
  5. a_3_30, an element of degree 3
  6. a_3_50, an element of degree 3
  7. b_3_60, an element of degree 3
  8. b_3_80, an element of degree 3
  9. b_3_9c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  10. b_3_100, an element of degree 3
  11. b_3_11c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  12. b_3_12c_1_2·c_1_32, an element of degree 3
  13. c_4_21c_1_22·c_1_32 + c_1_24 + c_1_12·c_1_32 + c_1_14, an element of degree 4
  14. c_4_22c_1_22·c_1_32 + c_1_1·c_1_33 + c_1_14, an element of degree 4
  15. c_4_23c_1_24 + c_1_02·c_1_32 + c_1_04, an element of degree 4
  16. b_5_33c_1_24·c_1_3 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_33 + c_1_12·c_1_22·c_1_3
       + c_1_14·c_1_3 + c_1_02·c_1_33 + c_1_04·c_1_3, an element of degree 5
  17. b_5_34c_1_22·c_1_33 + c_1_02·c_1_33 + c_1_04·c_1_3, an element of degree 5
  18. b_5_35c_1_23·c_1_32 + c_1_24·c_1_3 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_33
       + c_1_12·c_1_22·c_1_3 + c_1_14·c_1_3 + c_1_02·c_1_33 + c_1_04·c_1_3, an element of degree 5
  19. b_5_36c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_23·c_1_32 + c_1_24·c_1_3
       + c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_02·c_1_33 + c_1_04·c_1_3, an element of degree 5

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

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_2c_1_3, an element of degree 1
  4. b_1_3c_1_3, an element of degree 1
  5. a_3_30, an element of degree 3
  6. a_3_50, an element of degree 3
  7. b_3_6c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  8. b_3_8c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32, an element of degree 3
  9. b_3_9c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32, an element of degree 3
  10. b_3_10c_1_33 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  11. b_3_11c_1_33 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  12. b_3_12c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32, an element of degree 3
  13. c_4_21c_1_34 + c_1_22·c_1_32 + c_1_24 + c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33
       + c_1_02·c_1_32, an element of degree 4
  14. c_4_22c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_02·c_1_32, an element of degree 4
  15. c_4_23c_1_34 + c_1_2·c_1_33 + c_1_24 + c_1_1·c_1_33 + c_1_12·c_1_32 + c_1_04, an element of degree 4
  16. b_5_33c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_0·c_1_2·c_1_33 + c_1_0·c_1_22·c_1_32
       + c_1_0·c_1_1·c_1_33 + c_1_0·c_1_12·c_1_32 + c_1_02·c_1_33 + c_1_04·c_1_3, an element of degree 5
  17. b_5_34c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_0·c_1_2·c_1_33 + c_1_0·c_1_22·c_1_32
       + c_1_0·c_1_1·c_1_33 + c_1_0·c_1_12·c_1_32 + c_1_02·c_1_1·c_1_32
       + c_1_02·c_1_12·c_1_3 + c_1_03·c_1_32, an element of degree 5
  18. b_5_35c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_1·c_1_34 + c_1_14·c_1_3 + c_1_02·c_1_33
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_1·c_1_32
       + c_1_02·c_1_12·c_1_3 + c_1_04·c_1_3, an element of degree 5
  19. b_5_36c_1_12·c_1_33 + c_1_14·c_1_3 + c_1_02·c_1_33, an element of degree 5


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