Schur Algebra S( 5 ,8) in characteristic 2

Field k

Finite field of size 2

The Module M

The module M is the direct sum of permutation module with point stabilizers being the Young subgroups corresponding to partitions of lenght at most 5. . The dimension of M is 18223 .

The dimensions of the irreducible submodules modules are 64, 40, 14, 8, 6, 1 .



The module M has radical filtration (Loewy series)
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2



The module M has socle filtration (socle series)
2, 2, 2, 2, 2, 2, 2, 2, 2, 2

3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6



The module M has simple direct summands:

60 copies of simple module number 1
1 copy of simple module number 6

The remaining indecomposable components of M have radical and socle filtrations as follows:

1). 3 direct summands of the form:


radical layers
1
1



socle layers
1
1


2). 6 direct summands of the form:


radical layers
6
5
6



socle layers
6
5
6


3). 10 direct summands of the form:


radical layers
3
5
4
5
3



socle layers
3
5
4
5
3


4). 2 direct summands of the form:


radical layers
5, 6
3, 6
5



socle layers
5
3, 6
5, 6


5). 7 direct summands of the form:


radical layers
5
3, 6
5, 6
3
5



socle layers
5
3
5, 6
3, 6
5


6). 1 direct summand of the form:


radical layers
5, 6
3, 4, 6
5, 5
3, 4
5



socle layers
5
3, 4
5, 5
3, 4, 6
5, 6


7). 3 direct summands of the form:


radical layers
6
2, 5
4, 6, 6
3, 6
5, 6
2
6
3
6
2
6



socle layers
6
2
6
3
6
2
5, 6
3, 6
4, 6, 6
2, 5
6


8). 2 direct summands of the form:


radical layers
3, 6
5, 5, 6
3, 4, 6
5, 5
3, 5
4, 6
5
3



socle layers
3
5
4, 6
3, 5
5, 5
3, 4, 6
5, 5, 6
3, 6


9). 12 direct summands of the form:


radical layers
5
3, 4, 6
5, 5, 6
2, 3, 3, 4
5, 5, 6
3, 4, 6
5



socle layers
5
3, 4, 6
5, 5, 6
2, 3, 3, 4
5, 5, 6
3, 4, 6
5


10). 3 direct summands of the form:


radical layers
3, 5
3, 4, 5, 6, 6
2, 3, 4, 5, 5
3, 4, 5, 5, 6
3, 3, 4, 5, 6
5, 6
2
6
3



socle layers
3
6
2
5, 6
3, 3, 4, 5, 6
3, 4, 5, 5, 6
2, 3, 4, 5, 5
3, 4, 5, 6, 6
3, 5


11). 10 direct summands of the form:


radical layers
2
4, 6
3, 6
3, 5, 6
2, 5, 6
2, 4, 6
3, 5, 6
3, 5, 6
2, 4, 6
2, 6
3, 6
3, 6
6
2



socle layers
2
6
3, 6
3, 6
2, 6
2, 4, 6
3, 5, 6
3, 5, 6
2, 4, 6
2, 5, 6
3, 5, 6
3, 6
4, 6
2


12). 9 direct summands of the form:


radical layers
3
5, 6
2, 3, 4
5, 5, 6
3, 3, 4, 5, 6
3, 4, 5, 6, 6
2, 5, 5
3, 4, 6
3, 5
6
2
6
3



socle layers
3
6
2
6
3, 5
3, 4, 6
2, 5, 5
3, 4, 5, 6, 6
3, 3, 4, 5, 6
5, 5, 6
2, 3, 4
5, 6
3


13). 2 direct summands of the form:


radical layers
5
3, 4, 6
5, 5, 6
2, 3, 3, 4, 5
3, 4, 5, 5, 6, 6
3, 4, 5, 5, 6, 6
2, 3, 3, 4, 5
5, 5, 6
3, 4, 6
5



socle layers
5
3, 4, 6
5, 5, 6
2, 3, 3, 4, 5
3, 4, 5, 5, 6, 6
3, 4, 5, 5, 6, 6
2, 3, 3, 4, 5
5, 5, 6
3, 4, 6
5


14). 1 direct summand of the form:


radical layers
4
2, 4, 5
3, 4, 5, 6
3, 4, 5, 6, 6
3, 5, 5, 6
2, 3, 3, 4, 5, 5
3, 4, 5, 5, 6, 6
3, 4, 5, 6, 6
2, 3, 4, 5
5
4



socle layers
4
5
2, 3, 4, 5
3, 4, 5, 6, 6
3, 4, 5, 5, 6, 6
2, 3, 3, 4, 5, 5
3, 5, 5, 6
3, 4, 5, 6, 6
3, 4, 5, 6
2, 4, 5
4


15). 2 direct summands of the form:


radical layers
3, 3, 6
2, 5, 5, 5, 6
2, 3, 4, 4, 4, 6, 6
3, 5, 5, 5, 6, 6
3, 3, 3, 3, 4, 5, 5, 6, 6
2, 4, 5, 5, 6, 6
2, 4, 5, 6
3, 3, 5, 6
3, 6
2, 6
2, 6
3, 6



socle layers
3, 6
2, 6
2, 6
3, 6
3, 3, 5, 6
2, 4, 5, 6
2, 4, 5, 5, 6, 6
3, 3, 3, 3, 4, 5, 5, 6, 6
3, 5, 5, 5, 6, 6
2, 3, 4, 4, 4, 6, 6
2, 5, 5, 5, 6
3, 3, 6


16). 1 direct summand of the form:


radical layers
2, 3, 4, 5, 6
2, 3, 4, 4, 5, 5, 6, 6, 6
2, 3, 3, 3, 4, 5, 5, 6, 6
3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6
2, 3, 3, 3, 4, 5, 5, 6, 6
2, 3, 4, 5, 5, 5, 6, 6
2, 3, 3, 4, 5, 6, 6
5, 6, 6
2, 3, 4
6, 6
2, 3



socle layers
2, 3
6, 6
2, 3, 4
5, 6, 6
2, 3, 3, 4, 5, 6, 6
2, 3, 4, 5, 5, 5, 6, 6
2, 3, 3, 3, 4, 5, 5, 6, 6
3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6
2, 3, 3, 3, 4, 5, 5, 6, 6
2, 3, 4, 4, 5, 5, 6, 6, 6
2, 3, 4, 5, 6


The Action Algebra

The action algebra A is the image of kG in the k-endomorphism ring of M. It's simple modules are the irreducible submodules of M.

The dimensions of the projective modules are 128, 384, 599, 384, 592, 867 .

The cartan matrix of A is



The determinant of the Cartan matrix is 2330.

The blocks of A consist of the following irreducible modules:

The radical and socle filtrations of the projective modules for A are the following:


Projective module number 1


radical layers
1
1



socle layers
1
1



Projective module number 2


radical layers
2
4, 6
3, 6
3, 5, 6
2, 5, 6
2, 4, 6
3, 5, 6
3, 5, 6
2, 4, 6
2, 6
3, 6
3, 6
6
2



socle layers
2
6
3, 6
3, 6
2, 6
2, 4, 6
3, 5, 6
3, 5, 6
2, 4, 6
2, 5, 6
3, 5, 6
3, 6
4, 6
2



Projective module number 3


radical layers
3
3, 5, 6
2, 3, 4, 5, 6
2, 3, 4, 5, 5, 6
3, 3, 4, 5, 5, 5, 6, 6
3, 3, 3, 4, 4, 5, 5, 6, 6, 6
2, 3, 4, 5, 5, 5, 6, 6
2, 3, 4, 5, 6
3, 4, 5, 6
3, 6
2, 6
2, 6
3



socle layers
3
6
2, 3
6, 6
2, 3, 5
3, 4, 6, 6
2, 3, 5, 5, 5
3, 3, 4, 4, 5, 6, 6, 6
2, 3, 3, 4, 5, 5, 5, 6
3, 4, 5, 5, 5, 6, 6, 6
2, 3, 3, 3, 4, 5, 6
4, 5, 5, 6, 6
2, 3, 4



Projective module number 4


radical layers
4
2, 4, 5
3, 4, 5, 6
3, 4, 5, 6, 6
3, 5, 5, 6
2, 3, 3, 4, 5, 5
3, 4, 5, 5, 6, 6
3, 4, 5, 6, 6
2, 3, 4, 5
5
4



socle layers
4
5
2, 3, 4, 5
3, 4, 5, 6, 6
3, 4, 5, 5, 6, 6
2, 3, 3, 4, 5, 5
3, 5, 5, 6
3, 4, 5, 6, 6
3, 4, 5, 6
2, 4, 5
4



Projective module number 5


radical layers
5
3, 4, 5, 6
3, 4, 5, 5, 6, 6
2, 3, 3, 4, 5, 5, 5, 6
2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6
3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6
2, 3, 3, 3, 4, 4, 5, 5, 6, 6
2, 3, 4, 5, 5, 5, 6
3, 4, 5, 6
4, 5



socle layers
5
3, 4, 5, 6
3, 4, 5, 5, 6, 6
2, 3, 3, 4, 5, 5, 5, 6
2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6
3, 3, 4, 5, 5, 5, 5, 6, 6, 6
2, 3, 3, 3, 4, 4, 5, 5, 6, 6
3, 4, 5, 5, 5, 6, 6
2, 3, 4, 4, 5, 6
4, 5



Projective module number 6


radical layers
6
2, 3, 5, 6
2, 3, 4, 5, 5, 6, 6, 6
2, 3, 4, 4, 5, 6, 6, 6, 6
2, 3, 3, 4, 5, 5, 6, 6, 6
2, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6
2, 3, 3, 4, 4, 5, 5, 6, 6, 6
2, 3, 4, 4, 5, 6, 6, 6
2, 3, 5, 6, 6
2, 3, 6, 6
2, 3, 6, 6
2, 3, 6, 6
2



socle layers
6
3, 6
2, 3, 6
2, 2, 6, 6
2, 3, 6, 6
3, 3, 5, 5, 6, 6
2, 3, 5, 5, 6, 6
2, 2, 4, 4, 4, 6, 6, 6
2, 3, 3, 4, 5, 5, 5, 6, 6, 6, 6
3, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6
2, 3, 3, 4, 5, 6, 6, 6
2, 4, 4, 4, 5, 6, 6, 6, 6
2, 2, 3, 5, 6


The degrees of the splitting fields are 1, 1, 1, 1, 1, 1 .

The Basic Algebra H of the Schur Algebra



The dimension of H is 958 .

The dimensions of the irreducible H-modules are 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 .

The Simple modules for H correspond to the following direct summands of the module M.


The degrees of the splitting fields are 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 .

The dimensions of the projective modules of H are 2, 64, 34, 27, 66, 33, 19, 3, 42, 98, 60, 33, 130, 78, 8, 52, 158, 51 .

The cartan matrix of H is



The determinant of the Cartan matrix is 1.

The blocks of H consist of the following irreducible modules:

The radical and socle filtrations of the projective modules for H are the following:


Projective module number 1


radical layers
1
8



socle layers
1
8



Projective module number 2


radical layers
2
6, 10, 13, 14, 17
2, 11, 16, 17, 18
5, 9, 10, 10, 12, 13, 14
2, 4, 7, 13, 16, 17, 17, 17
3, 5, 6, 9, 10, 10, 11, 13, 14, 17
2, 4, 11, 13, 16, 17, 18
10, 10, 12, 13, 13, 14
2, 5, 11, 16, 17, 17
6, 10, 13, 14, 17
2, 5, 18
14



socle layers
2
6, 10
2, 16, 17, 17
10, 10, 12, 13
2, 4, 11, 14, 16, 17
5, 6, 9, 10, 10, 13, 14, 17
2, 4, 5, 7, 13, 16, 17, 17
9, 10, 10, 11, 12, 13, 13, 18
2, 11, 11, 13, 14, 16, 17, 17
3, 5, 6, 10, 13, 13, 14, 17, 18
2, 5, 14, 17
14, 18



Projective module number 3


radical layers
3
13, 17
3, 5, 9, 18
13, 13, 14, 17, 17
3, 3, 10, 18
2, 17
5, 9, 14, 17
13, 13, 17, 18
3, 10
17
5, 9
13, 17
3



socle layers
3
13, 17
5, 9
17
3, 10
13, 13, 17, 18
5, 9, 14, 17
2, 17
3, 3, 10, 18
13, 13, 14, 17, 17
3, 5, 9, 18
13, 17
3



Projective module number 4


radical layers
4
10, 13
11, 16, 17
10, 12, 13
2, 5, 16, 17
6, 10, 14, 17
2, 4, 18
10, 13, 14
11, 17
13
5



socle layers
4
10
16, 17
10, 12, 13
11, 16, 17
2, 10, 13
4, 5, 6
2, 13, 17
10, 11
13, 14, 14, 17
5, 18



Projective module number 5


radical layers
5
13, 14, 17
3, 10, 11, 18
2, 13, 17
4, 5, 5, 6, 9, 14, 17
2, 10, 13, 13, 13, 14, 17, 17, 18
3, 10, 10, 11, 11, 14, 16, 17, 18
10, 12, 13, 13, 17, 17
2, 5, 5, 5, 9, 16, 17
6, 10, 13, 14, 17, 17
2, 3, 4, 18
10, 13, 14
11, 17
13
5



socle layers
5
13
11, 17
10, 13, 14
2, 4
6, 10, 17
2, 5, 5, 9, 16, 17
10, 12, 13, 13, 17, 17
10, 10, 11, 11, 14, 16, 17
2, 10, 13, 13, 14, 17, 17
3, 4, 5, 5, 6, 9, 18
2, 13, 13, 14, 17, 17
3, 5, 10, 11, 18, 18
13, 13, 14, 14, 17, 17
3, 5, 18



Projective module number 6


radical layers
6
2, 11, 12
6, 7, 10, 13, 14, 17
11, 12, 16, 17
5, 6, 9, 10
2, 4, 13
10, 13, 14, 17
11, 16, 17
10, 13
2, 5
14



socle layers
6
2
10, 12
11, 16, 17
6, 10, 13, 14, 17
2, 4, 5, 7
9, 10, 12, 13
11, 11, 16, 17
6, 10, 13, 13, 14, 17
2, 5
14



Projective module number 7


radical layers
7
9, 11, 12
6, 13, 16, 17
10, 15
2, 16
12, 14
7, 17
9, 11
13



socle layers
7
12
16
9, 15
16, 17
10, 11, 12
6, 7, 13, 17
2, 9, 11
13, 14



Projective module number 8


radical layers
8
1
8



socle layers
8
1
8



Projective module number 9


radical layers
9
7, 13, 17
3, 9, 10, 11, 12
2, 13, 16, 17, 17
5, 6, 9, 10, 14, 15, 17
2, 13, 13, 16, 17, 18
3, 10, 12, 14
7, 17, 17
5, 9, 9, 11
13, 13, 17
3



socle layers
9
17
7, 10
12, 13, 17
5, 9, 16
2, 9, 15, 17
3, 10, 16, 17
10, 11, 12, 13, 13, 14, 17, 17
3, 5, 6, 7, 9, 13, 17, 18
2, 9, 11, 13, 17
3, 13, 14



Projective module number 10


radical layers
10
2, 4, 16, 17
5, 6, 9, 10, 10, 12, 13, 14, 17
2, 2, 4, 7, 11, 13, 13, 16, 16, 17, 17, 17, 18
3, 6, 9, 10, 10, 10, 10, 10, 11, 11, 12, 13, 13, 14, 14, 17
2, 2, 4, 5, 11, 13, 13, 16, 16, 17, 17, 17, 17, 18
5, 5, 6, 9, 10, 10, 10, 12, 13, 13, 14, 14, 17
2, 2, 4, 5, 11, 13, 16, 17, 17, 17, 18
3, 6, 10, 10, 13, 13, 14, 14, 17
2, 5, 11, 17, 18
13, 14
5



socle layers
10
2, 4
6, 10, 16, 17
2, 5, 9, 10, 12, 16, 17
2, 4, 10, 12, 13, 13, 16, 17, 17, 17
6, 10, 10, 10, 10, 11, 11, 16, 17
2, 2, 4, 7, 10, 13, 13, 13, 14, 16, 17, 17, 17, 17
4, 5, 5, 6, 9, 9, 10, 10, 11, 12, 13, 13
2, 2, 11, 11, 13, 13, 14, 14, 16, 17, 17
3, 5, 5, 6, 10, 10, 11, 13, 13, 14, 17, 18, 18
2, 5, 13, 13, 14, 14, 14, 17, 17, 17
3, 5, 14, 18, 18



Projective module number 11


radical layers
11
6, 7, 13
2, 4, 5, 9, 11, 11, 12
6, 10, 13, 13, 13, 14, 14, 16, 17, 17
10, 10, 11, 15, 16, 17, 18
2, 10, 12, 13, 16, 17
2, 5, 5, 12, 14, 16, 17
6, 7, 10, 14, 17, 17
2, 4, 9, 11, 18
10, 13, 13, 14
11, 17
13
5



socle layers
11
13
4
6, 10
2, 5, 7, 16, 17
10, 12, 12, 13, 17
10, 11, 11, 14, 16, 16, 17
2, 9, 10, 13, 13, 14, 15, 17
4, 5, 5, 6, 16, 17
2, 10, 11, 12, 13, 17
6, 7, 10, 11, 13, 17, 18
2, 9, 11, 13, 14, 14, 17
5, 13, 14, 18



Projective module number 12


radical layers
12
6, 7, 16, 17
9, 10, 11, 12, 15
2, 4, 6, 13, 16
10, 12, 13, 14, 17
7, 11, 16, 17, 17
9, 10, 11, 13
2, 5, 13
14



socle layers
12
16, 17
6, 10
2, 4, 7, 15
9, 10, 12, 13, 16
11, 11, 12, 16, 17
6, 7, 10, 13, 13, 14, 17, 17
2, 5, 9, 11
13, 14



Projective module number 13


radical layers
13
2, 3, 4, 5, 9, 11
6, 7, 10, 13, 13, 13, 13, 13, 14, 14, 17, 17, 17
2, 3, 3, 4, 5, 9, 10, 10, 11, 11, 11, 12, 16, 17, 18, 18
2, 10, 10, 12, 13, 13, 13, 13, 14, 14, 16, 17, 17, 17, 17
2, 5, 5, 5, 6, 9, 9, 10, 10, 11, 14, 15, 16, 16, 17, 17, 17, 18
2, 6, 10, 10, 12, 13, 13, 13, 13, 14, 16, 17, 17, 17, 17, 18
2, 2, 3, 3, 4, 5, 5, 10, 12, 14, 16, 17, 18
6, 7, 10, 10, 13, 14, 14, 17, 17, 17
2, 4, 5, 9, 9, 11, 11, 17, 18
10, 13, 13, 13, 13, 14, 17
3, 5, 11, 17
13
5



socle layers
13
11
13
2, 4, 4, 5, 9
6, 10, 10, 17
2, 3, 5, 7, 10, 16, 16, 17, 17, 17
10, 10, 12, 12, 12, 13, 13, 13, 13, 13, 17, 17
5, 9, 10, 10, 11, 11, 11, 14, 14, 16, 16, 16, 17, 17
2, 2, 2, 9, 10, 10, 13, 13, 13, 14, 14, 15, 17, 17, 17, 17
3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 9, 10, 16, 17, 18
2, 2, 10, 11, 12, 13, 13, 13, 13, 14, 17, 17, 17, 17
3, 5, 6, 7, 9, 10, 10, 11, 11, 13, 13, 17, 18, 18, 18
2, 9, 11, 13, 13, 13, 14, 14, 14, 14, 17, 17, 17, 17
3, 3, 5, 5, 13, 14, 18, 18



Projective module number 14


radical layers
14
2, 5, 18
6, 10, 13, 13, 14, 14, 17, 17
2, 3, 11, 11, 16, 17, 18, 18
5, 9, 10, 10, 12, 13, 13, 14
2, 4, 5, 7, 13, 16, 17, 17, 17
3, 5, 6, 9, 10, 10, 11, 13, 14, 14, 17, 17
2, 4, 11, 13, 16, 17, 18, 18
10, 10, 12, 13, 13, 14
2, 5, 11, 16, 17, 17
6, 10, 13, 14, 17
2, 5, 18
14



socle layers
14
2, 5
6, 10, 13
2, 11, 16, 17, 17
10, 10, 12, 13, 13, 14, 18
2, 4, 11, 14, 16, 17, 17
5, 5, 6, 9, 10, 10, 13, 14, 17
2, 4, 5, 7, 13, 16, 17, 17
3, 9, 10, 10, 11, 12, 13, 13, 14, 18, 18
2, 11, 11, 13, 14, 16, 17, 17, 17
3, 5, 6, 10, 13, 13, 14, 17, 18, 18
2, 5, 14, 17
14, 18



Projective module number 15


radical layers
15
16
12
7, 17
9, 11
13



socle layers
15
16
12
7, 17
9, 11
13



Projective module number 16


radical layers
16
10, 12, 15
2, 4, 7, 16, 16, 17
6, 9, 10, 10, 11, 12, 13, 14, 17
2, 4, 7, 11, 13, 16, 17, 17, 18
9, 10, 10, 11, 12, 13, 13, 14
2, 5, 11, 13, 16, 17, 17
6, 10, 13, 14, 17
2, 5, 18
14



socle layers
16
10, 12
2, 4, 16, 17
6, 10, 10
2, 4, 7, 13, 15, 16, 17, 17
9, 10, 10, 11, 12, 13, 16
2, 11, 11, 12, 13, 14, 16, 17
5, 6, 7, 10, 13, 13, 14, 17, 17, 18
2, 5, 9, 11, 14, 17
13, 14, 18



Projective module number 17


radical layers
17
2, 3, 5, 9, 10, 12, 18
2, 4, 6, 7, 10, 13, 13, 13, 14, 14, 16, 17, 17, 17, 17, 17, 17
3, 3, 5, 6, 9, 9, 10, 10, 10, 11, 11, 13, 14, 15, 16, 17, 17, 18, 18, 18
2, 2, 2, 4, 5, 9, 10, 11, 12, 13, 13, 13, 13, 16, 16, 17, 17, 17, 18
2, 3, 4, 5, 5, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 13, 14, 14, 14, 17, 17, 17
2, 3, 5, 6, 7, 10, 11, 13, 13, 13, 13, 14, 14, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18
3, 5, 5, 6, 9, 9, 10, 10, 10, 11, 11, 13, 14, 16, 17, 17, 18, 18
2, 2, 4, 5, 10, 13, 13, 13, 17, 17, 18
2, 3, 5, 5, 9, 10, 13, 14, 14
11, 13, 14, 17, 17, 17
3, 13, 18
5



socle layers
17
10
2, 2, 4, 5, 9
6, 10, 10, 13, 17, 17
2, 5, 9, 10, 11, 12, 16, 16, 17, 17, 18
3, 10, 10, 12, 13, 13, 13, 13, 14, 14, 16, 17, 17, 17, 17, 17, 17
2, 4, 5, 5, 6, 9, 10, 10, 10, 11, 11, 13, 16, 17, 17
2, 2, 2, 4, 5, 7, 9, 10, 10, 13, 13, 13, 14, 15, 17, 17, 17
3, 3, 4, 5, 5, 6, 9, 9, 10, 10, 11, 12, 13, 16, 16, 17, 18, 18, 18
2, 10, 11, 11, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 16, 17, 17, 17, 17, 17, 17, 17
2, 3, 3, 3, 5, 5, 5, 6, 7, 9, 10, 10, 11, 13, 13, 14, 17, 17, 18, 18, 18, 18
2, 5, 9, 11, 13, 13, 13, 14, 14, 14, 17, 17, 17, 17
3, 3, 5, 13, 14, 18, 18



Projective module number 18


radical layers
18
14, 17
2, 3, 5, 18, 18
10, 13, 13, 14, 14, 17, 17, 17
3, 11, 16, 17, 18, 18, 18
5, 9, 10, 13
2, 4, 5, 13, 17
3, 10, 13, 14, 14, 17, 17
11, 16, 17, 18, 18
10, 13
2, 5
14, 17
18



socle layers
18
14, 17
2, 5
10, 13
11, 16, 17, 18, 18
3, 10, 13, 14, 14, 17, 17
2, 4, 5, 13, 17
5, 9, 10, 13
3, 11, 16, 17, 18, 18, 18
10, 13, 13, 14, 14, 17, 17, 17
2, 3, 5, 18, 18
14, 17
18


A presentation for H is the quotient of a polynomial ring P in noncommuting variables

The generators designated by a subscripted 'b' are generators for subspaces determined by primitive idempotents. The generators given by subscripted 'z' are generators for the radical.

A Groebner basis for the ideal of relation consists of the elements:


The ideal of relations is not generated by the elements of degree at most 2. The following relation were not contained in the ideal generated by the relations of degree 2:

z_8*z_54*z_56*z_52*z_27*z_51 + z_7*z_36*z_8*z_51 + z_8*z_50*z_11*z_39 ,
z_8*z_54*z_56*z_54*z_56*z_54 + z_8*z_54*z_55*z_43 + z_8*z_54*z_56*z_54 ,
z_29*z_19*z_33*z_47*z_44*z_46 + z_30*z_37*z_9*z_27*z_53 + z_28*z_16 ,
z_33*z_47*z_44*z_46*z_32*z_18 + z_34*z_52*z_25*z_10*z_40 + z_31*z_15 ,
z_40*z_29*z_19*z_33*z_47*z_44 + z_39*z_23*z_52*z_26 ,
z_40*z_30*z_37*z_9*z_27*z_53 + z_39*z_23*z_53 + z_40*z_28*z_16 + z_40*z_29*z_19 ,
z_40*z_30*z_37*z_9*z_27*z_54 + z_35*z_5*z_43 + z_35*z_6*z_54 ,
z_43*z_56*z_54*z_56*z_54*z_55 + z_42*z_13*z_50*z_12 ,
z_46*z_34*z_52*z_25*z_10*z_40 + z_46*z_31*z_15 ,
z_54*z_56*z_54*z_56*z_54*z_55 ,
z_3*z_27*z_50*z_12*z_42 + z_3*z_27*z_50 + z_4*z_38 ,
z_4*z_37*z_9*z_27*z_52 + z_6*z_53*z_34*z_52 + z_3*z_27*z_52 + z_4*z_37*z_9 ,
z_4*z_37*z_9*z_27*z_53 + z_2*z_16 + z_6*z_53 ,
z_4*z_37*z_9*z_27*z_54 + z_3*z_27*z_54 + z_5*z_43 + z_6*z_54 ,
z_4*z_40*z_30*z_37*z_9 + z_6*z_48*z_3 ,
z_4*z_40*z_30*z_37*z_10 + z_2*z_14*z_4 + z_4*z_37*z_10 + z_4*z_38*z_11 + z_4*z_40*z_30 + z_6*z_48*z_4 + z_6*z_51*z_22 ,
z_6*z_52*z_26*z_45*z_25 ,
z_6*z_52*z_26*z_45*z_27 ,
z_6*z_53*z_31*z_15*z_30 + z_6*z_48*z_4 ,
z_6*z_53*z_32*z_18*z_30 + z_2*z_14*z_4 + z_4*z_37*z_10 + z_4*z_40*z_30 + z_5*z_42*z_11 + z_6*z_51*z_22 ,
z_6*z_53*z_34*z_48*z_5 + z_3*z_27*z_50*z_12 + z_4*z_35*z_5 + z_5*z_42*z_12 + z_6*z_48*z_5 ,
z_6*z_53*z_34*z_52*z_25 + z_4*z_40*z_30*z_37 ,
z_6*z_53*z_34*z_52*z_26 + z_2*z_16*z_33 + z_6*z_53*z_33 ,
z_6*z_53*z_34*z_52*z_27 + z_6*z_48*z_3*z_27 ,
z_8*z_51*z_23*z_49*z_7 + z_7*z_36*z_7 + z_7*z_38*z_11 + z_8*z_51*z_22 ,
z_8*z_51*z_23*z_49*z_8 + z_8*z_54*z_56*z_52*z_27 + z_8*z_54*z_56*z_54*z_56 ,
z_8*z_51*z_23*z_52*z_27 + z_8*z_54*z_56*z_52*z_27 + z_7*z_36*z_8 + z_7*z_38*z_13 + z_8*z_50*z_13 ,
z_8*z_54*z_55*z_43*z_56 + z_8*z_54*z_56*z_54*z_56 + z_7*z_38*z_13 + z_8*z_50*z_13 ,
z_8*z_54*z_56*z_48*z_3 + z_8*z_54*z_56*z_52 ,
z_8*z_54*z_56*z_48*z_5 + z_8*z_54*z_56*z_54*z_55 ,
z_8*z_54*z_56*z_49*z_8 + z_8*z_54*z_56*z_52*z_27 ,
z_8*z_54*z_56*z_52*z_26 ,
z_9*z_27*z_48*z_4*z_40 + z_10*z_40*z_28*z_15 ,
z_9*z_27*z_52*z_25*z_10 + z_9*z_27*z_48*z_4 ,
z_9*z_27*z_52*z_27*z_50 + z_9*z_27*z_50 + z_10*z_38 ,
z_9*z_27*z_52*z_27*z_52 ,
z_9*z_27*z_53*z_34*z_48 ,
z_9*z_27*z_53*z_34*z_51 ,
z_9*z_27*z_53*z_34*z_52 + z_9*z_27*z_52 ,
z_10*z_38*z_13*z_52*z_27 + z_9*z_27*z_52*z_27 ,
z_10*z_40*z_28*z_15*z_30 + z_9*z_27*z_48*z_4 + z_10*z_35*z_4 ,
z_11*z_35*z_3*z_27*z_50 + z_13*z_54*z_56*z_50 + z_11*z_38 ,
z_11*z_35*z_3*z_27*z_52 + z_13*z_52*z_26*z_45 + z_12*z_41*z_3 + z_13*z_48*z_3 ,
z_12*z_42*z_11*z_40*z_30 + z_11*z_39*z_22 + z_12*z_41*z_4 + z_13*z_48*z_4 + z_13*z_49*z_7 ,
z_12*z_42*z_13*z_48*z_2 + z_13*z_48*z_6*z_53*z_31 ,
z_12*z_42*z_13*z_48*z_3 ,
z_12*z_42*z_13*z_48*z_4 + z_11*z_38*z_11 ,
z_12*z_42*z_13*z_48*z_5 + z_12*z_41*z_5 + z_13*z_48*z_5 + z_13*z_50*z_12 ,
z_12*z_42*z_13*z_48*z_6 + z_13*z_50*z_13 ,
z_13*z_48*z_6*z_51*z_22 + z_13*z_54*z_56*z_50*z_11 + z_12*z_41*z_4 + z_13*z_48*z_4 ,
z_13*z_52*z_26*z_45*z_25 + z_11*z_37 ,
z_13*z_52*z_26*z_45*z_27 + z_13*z_48*z_3*z_27 + z_11*z_35*z_6 + z_12*z_42*z_13 + z_13*z_54*z_56 ,
z_13*z_52*z_27*z_50*z_11 + z_13*z_54*z_56*z_50*z_11 + z_12*z_41*z_4 + z_13*z_49*z_7 ,
z_13*z_52*z_27*z_50*z_12 + z_12*z_41*z_5 + z_13*z_50*z_12 + z_13*z_54*z_55 ,
z_13*z_52*z_27*z_50*z_13 + z_13*z_48*z_3*z_27 + z_11*z_39*z_23 + z_12*z_42*z_13 + z_13*z_48*z_6 + z_13*z_49*z_8 + z_13*z_50*z_13 ,
z_13*z_54*z_55*z_43*z_56 + z_13*z_49*z_8 + z_13*z_54*z_56 ,
z_13*z_54*z_56*z_49*z_7 ,
z_13*z_54*z_56*z_49*z_8 ,
z_13*z_54*z_56*z_50*z_12 + z_13*z_50*z_12 ,
z_13*z_54*z_56*z_50*z_13 + z_13*z_49*z_8 + z_13*z_54*z_56 ,
z_13*z_54*z_56*z_54*z_55 + z_13*z_50*z_12 ,
z_13*z_54*z_56*z_54*z_56 + z_13*z_49*z_8 + z_13*z_54*z_56 ,
z_16*z_31*z_14*z_3*z_27 + z_16*z_34*z_52*z_27 ,
z_16*z_34*z_52*z_27*z_50 + z_14*z_5*z_42 + z_15*z_30*z_38 ,
z_22*z_35*z_3*z_27*z_50 + z_23*z_52*z_27*z_50 + z_22*z_38 ,
z_22*z_35*z_3*z_27*z_52 ,
z_23*z_49*z_8*z_51*z_22 + z_22*z_38*z_11 + z_23*z_49*z_7 ,
z_23*z_49*z_8*z_54*z_56 + z_22*z_35*z_6 + z_23*z_49*z_8 ,
z_23*z_52*z_27*z_50*z_11 + z_23*z_49*z_7 ,
z_23*z_52*z_27*z_50*z_12 + z_23*z_48*z_5 ,
z_23*z_52*z_27*z_50*z_13 + z_22*z_35*z_6 + z_22*z_38*z_13 + z_23*z_49*z_8 ,
z_23*z_52*z_27*z_51*z_22 + z_22*z_35*z_4 + z_22*z_38*z_11 ,
z_23*z_52*z_27*z_51*z_23 + z_22*z_38*z_13 ,
z_23*z_53*z_33*z_47*z_44 + z_23*z_52*z_26 ,
z_23*z_53*z_34*z_52*z_25 ,
z_23*z_53*z_34*z_52*z_26 ,
z_23*z_53*z_34*z_52*z_27 + z_21*z_19*z_34 + z_23*z_53*z_34 ,
z_24*z_6*z_51*z_22*z_38 + z_27*z_50*z_13*z_50 ,
z_25*z_10*z_38*z_13*z_52 + z_27*z_50*z_13*z_52 + z_27*z_51*z_23*z_52 + z_27*z_52*z_26*z_45 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_25*z_10*z_40*z_28*z_15 + z_27*z_48*z_4*z_40 + z_27*z_53*z_31*z_15 ,
z_26*z_45*z_24*z_4*z_38 + z_27*z_50*z_13*z_50 + z_27*z_52*z_27*z_50 + z_24*z_4*z_38 + z_24*z_5*z_42 ,
z_26*z_45*z_24*z_5*z_43 + z_24*z_5*z_43 + z_24*z_6*z_54 + z_27*z_54 ,
z_26*z_45*z_24*z_6*z_54 + z_27*z_54*z_56*z_54 + z_24*z_5*z_43 + z_24*z_6*z_54 + z_27*z_54 ,
z_26*z_45*z_25*z_10*z_40 + z_27*z_50*z_11*z_40 + z_27*z_53*z_32*z_18 + z_24*z_4*z_40 ,
z_27*z_50*z_11*z_40*z_30 + z_24*z_6*z_48*z_4 + z_24*z_6*z_51*z_22 + z_25*z_10*z_40*z_30 + z_26*z_45*z_25*z_10 + z_27*z_50*z_11 + z_27*z_51*z_22 + z_24*z_4 ,
z_27*z_50*z_12*z_42*z_11 + z_25*z_10*z_35*z_4 ,
z_27*z_50*z_12*z_42*z_12 + z_27*z_48*z_5 + z_27*z_50*z_12 ,
z_27*z_50*z_13*z_52*z_27 + z_24*z_3*z_27 + z_25*z_9*z_27 + z_26*z_45*z_27 + z_27*z_52*z_27 + z_27*z_54*z_56 ,
z_27*z_51*z_23*z_49*z_7 + z_24*z_6*z_48*z_4 + z_24*z_6*z_51*z_22 ,
z_27*z_51*z_23*z_49*z_8 + z_27*z_54*z_56 ,
z_27*z_51*z_23*z_52*z_27 + z_24*z_6*z_52*z_27 + z_24*z_6*z_54*z_56 + z_25*z_10*z_38*z_13 + z_24*z_3*z_27 + z_25*z_9*z_27 + z_27*z_48*z_6 + z_27*z_50*z_13 + z_27*z_51*z_23 ,
z_27*z_52*z_24*z_5*z_42 + z_27*z_50*z_12*z_42 + z_27*z_50*z_13*z_50 + z_27*z_52*z_27*z_50 ,
z_27*z_52*z_24*z_6*z_54 ,
z_27*z_52*z_25*z_10*z_35 + z_27*z_53*z_34*z_48 ,
z_27*z_52*z_25*z_10*z_38 + z_27*z_50*z_12*z_42 + z_27*z_50*z_13*z_50 + z_27*z_52*z_27*z_50 ,
z_27*z_52*z_25*z_10*z_40 + z_27*z_53*z_31*z_15 ,
z_27*z_52*z_26*z_45*z_25 + z_24*z_4*z_37 ,
z_27*z_52*z_26*z_45*z_27 + z_24*z_6*z_54*z_56 + z_25*z_10*z_38*z_13 + z_27*z_48*z_6 + z_27*z_50*z_13 + z_27*z_51*z_23 ,
z_27*z_52*z_27*z_50*z_11 + z_25*z_10*z_35*z_4 ,
z_27*z_52*z_27*z_50*z_12 + z_24*z_5*z_42*z_12 + z_25*z_10*z_38*z_12 + z_27*z_48*z_5 + z_27*z_50*z_12 ,
z_27*z_52*z_27*z_50*z_13 + z_27*z_54*z_56 ,
z_27*z_52*z_27*z_52*z_26 ,
z_27*z_52*z_27*z_52*z_27 + z_24*z_6*z_54*z_56 + z_25*z_10*z_38*z_13 + z_27*z_48*z_6 + z_27*z_50*z_13 + z_27*z_51*z_23 ,
z_27*z_53*z_31*z_15*z_30 + z_27*z_52*z_24*z_4 ,
z_27*z_53*z_32*z_18*z_30 + z_24*z_6*z_48*z_4 + z_24*z_6*z_51*z_22 + z_25*z_10*z_35*z_4 + z_25*z_10*z_40*z_30 + z_26*z_45*z_25*z_10 + z_27*z_52*z_25*z_10 + z_27*z_48*z_4 + z_27*z_50*z_11 + z_27*z_51*z_22 + z_24*z_4 ,
z_27*z_53*z_32*z_19*z_31 + z_26*z_45*z_24*z_2 + z_27*z_53*z_31 ,
z_27*z_53*z_34*z_48*z_5 + z_24*z_5*z_42*z_12 + z_25*z_10*z_38*z_12 ,
z_27*z_53*z_34*z_51*z_22 + z_24*z_6*z_48*z_4 + z_24*z_6*z_51*z_22 + z_25*z_10*z_35*z_4 + z_25*z_10*z_40*z_30 + z_26*z_45*z_25*z_10 + z_27*z_52*z_25*z_10 + z_27*z_48*z_4 + z_27*z_50*z_11 + z_27*z_51*z_22 + z_24*z_4 ,
z_27*z_53*z_34*z_51*z_23 + z_27*z_52*z_24*z_6 ,
z_27*z_53*z_34*z_52*z_25 + z_27*z_52*z_25 ,
z_27*z_53*z_34*z_52*z_26 + z_24*z_3*z_26 + z_25*z_9*z_26 + z_26*z_45*z_26 + z_27*z_52*z_26 + z_27*z_53*z_33 ,
z_27*z_53*z_34*z_52*z_27 + z_24*z_6*z_52*z_27 + z_24*z_6*z_54*z_56 + z_25*z_10*z_38*z_13 + z_26*z_45*z_27 + z_27*z_48*z_6 + z_27*z_50*z_13 + z_27*z_51*z_23 + z_27*z_52*z_27 + z_27*z_54*z_56 ,
z_27*z_54*z_56*z_54*z_55 ,
z_27*z_54*z_56*z_54*z_56 ,
z_30*z_35*z_3*z_27*z_50 + z_30*z_35*z_5*z_42 ,
z_30*z_35*z_3*z_27*z_52 + z_30*z_38*z_11*z_35*z_3 ,
z_30*z_35*z_6*z_52*z_24 + z_30*z_38*z_11*z_35 + z_30*z_38*z_13*z_48 ,
z_30*z_37*z_9*z_27*z_52 + z_30*z_35*z_6*z_52 ,
z_30*z_38*z_11*z_40*z_30 + z_30*z_39*z_22*z_35*z_4 + z_28*z_15*z_30 + z_30*z_35*z_4 + z_30*z_37*z_10 + z_30*z_38*z_11 + z_30*z_39*z_22 ,
z_30*z_38*z_12*z_42*z_12 + z_30*z_38*z_13*z_54*z_55 + z_30*z_39*z_22*z_35*z_5 ,
z_30*z_38*z_13*z_48*z_2 + z_28*z_16*z_31 ,
z_30*z_38*z_13*z_48*z_3 ,
z_30*z_38*z_13*z_48*z_4 + z_30*z_39*z_22*z_35*z_4 + z_28*z_15*z_30 + z_30*z_35*z_4 ,
z_30*z_38*z_13*z_52*z_27 + z_30*z_35*z_3*z_27 + z_29*z_19*z_34 + z_30*z_39*z_23 ,
z_30*z_38*z_13*z_54*z_56 ,
z_30*z_39*z_22*z_35*z_3 ,
z_30*z_39*z_22*z_35*z_6 ,
z_30*z_39*z_23*z_52*z_26 ,
z_30*z_39*z_23*z_52*z_27 + z_29*z_19*z_34 + z_30*z_39*z_23 ,
z_33*z_47*z_44*z_46*z_34 + z_31*z_14*z_3*z_27 + z_34*z_52*z_27 ,
z_34*z_52*z_25*z_10*z_35 + z_34*z_48 ,
z_34*z_52*z_25*z_10*z_38 + z_34*z_52*z_27*z_50 ,
z_34*z_52*z_26*z_45*z_25 ,
z_34*z_52*z_26*z_45*z_27 ,
z_34*z_52*z_27*z_50*z_11 ,
z_34*z_52*z_27*z_50*z_12 + z_34*z_48*z_5 ,
z_34*z_52*z_27*z_50*z_13 ,
z_35*z_3*z_27*z_50*z_12 + z_36*z_8*z_54*z_55 + z_38*z_12*z_42*z_12 + z_38*z_13*z_48*z_5 + z_39*z_22*z_35*z_5 ,
z_36*z_8*z_54*z_55*z_43 + z_35*z_5*z_43 + z_35*z_6*z_54 ,
z_36*z_8*z_54*z_56*z_48 ,
z_36*z_8*z_54*z_56*z_49 + z_35*z_6*z_49 ,
z_36*z_8*z_54*z_56*z_52 ,
z_36*z_8*z_54*z_56*z_54 + z_35*z_5*z_43 + z_35*z_6*z_54 ,
z_37*z_9*z_27*z_52*z_25 + z_40*z_30*z_35*z_4*z_37 + z_35*z_4*z_37 ,
z_37*z_9*z_27*z_52*z_27 + z_40*z_30*z_37*z_9*z_27 + z_35*z_6*z_52*z_27 + z_38*z_13*z_52*z_27 + z_39*z_23*z_52*z_27 + z_35*z_3*z_27 ,
z_37*z_9*z_27*z_53*z_33 + z_40*z_30*z_37*z_9*z_26 + z_39*z_23*z_52*z_26 + z_40*z_28*z_16*z_33 + z_35*z_3*z_26 ,
z_37*z_9*z_27*z_53*z_34 + z_40*z_30*z_37*z_9*z_27 + z_36*z_8*z_54*z_56 + z_38*z_13*z_54*z_56 + z_39*z_23*z_49*z_8 + z_39*z_23*z_52*z_27 + z_40*z_30*z_38*z_13 + z_40*z_30*z_39*z_23 + z_35*z_6 + z_36*z_8 ,
z_38*z_11*z_35*z_3*z_27 + z_40*z_30*z_37*z_9*z_27 + z_35*z_6*z_52*z_27 + z_38*z_13*z_52*z_27 + z_38*z_13*z_54*z_56 + z_39*z_22*z_35*z_6 + z_39*z_23*z_52*z_27 + z_35*z_3*z_27 ,
z_38*z_13*z_48*z_2*z_15 + z_37*z_10*z_40 + z_38*z_11*z_40 + z_40*z_29*z_18 ,
z_38*z_13*z_48*z_3*z_26 ,
z_38*z_13*z_48*z_3*z_27 + z_38*z_13*z_54*z_56 + z_39*z_22*z_35*z_6 ,
z_38*z_13*z_48*z_4*z_38 + z_39*z_23*z_52*z_27*z_50 + z_35*z_3*z_27*z_50 + z_35*z_4*z_38 + z_38*z_11*z_38 + z_39*z_22*z_38 ,
z_38*z_13*z_48*z_4*z_40 + z_37*z_10*z_40 + z_38*z_11*z_40 + z_40*z_29*z_18 ,
z_38*z_13*z_48*z_6*z_51 + z_36*z_8*z_51 + z_38*z_11*z_39 ,
z_38*z_13*z_48*z_6*z_52 + z_38*z_11*z_35*z_3 + z_38*z_13*z_48*z_3 ,
z_38*z_13*z_48*z_6*z_53 ,
z_38*z_13*z_49*z_7*z_36 + z_39*z_23*z_52*z_27*z_49 + z_36*z_7*z_36 + z_38*z_13*z_49 + z_39*z_23*z_49 ,
z_38*z_13*z_52*z_27*z_50 + z_39*z_23*z_52*z_27*z_50 + z_35*z_5*z_42 + z_36*z_8*z_50 + z_39*z_22*z_38 ,
z_38*z_13*z_54*z_55*z_43 + z_39*z_23*z_49*z_8*z_54 + z_37*z_9*z_27*z_54 ,
z_38*z_13*z_54*z_56*z_49 + z_39*z_23*z_52*z_27*z_49 ,
z_38*z_13*z_54*z_56*z_50 + z_39*z_23*z_52*z_27*z_50 + z_35*z_3*z_27*z_50 + z_35*z_4*z_38 + z_38*z_11*z_38 + z_39*z_22*z_38 ,
z_38*z_13*z_54*z_56*z_54 + z_39*z_23*z_49*z_8*z_54 ,
z_39*z_22*z_35*z_3*z_27 + z_40*z_30*z_35*z_3*z_27 + z_40*z_30*z_37*z_9*z_27 + z_38*z_13*z_52*z_27 + z_38*z_13*z_54*z_56 + z_39*z_22*z_35*z_6 + z_39*z_23*z_52*z_27 + z_35*z_3*z_27 ,
z_39*z_23*z_49*z_7*z_36 + z_35*z_6*z_49 + z_36*z_7*z_36 + z_38*z_13*z_49 + z_39*z_23*z_49 ,
z_39*z_23*z_49*z_8*z_51 + z_36*z_8*z_51 + z_38*z_11*z_39 ,
z_39*z_23*z_52*z_27*z_51 + z_35*z_6*z_51 + z_38*z_11*z_39 ,
z_40*z_29*z_19*z_31*z_15 + z_39*z_21*z_18 + z_40*z_29*z_18 ,
z_40*z_30*z_35*z_5*z_42 + z_35*z_3*z_27*z_50 + z_35*z_5*z_42 ,
z_40*z_30*z_35*z_6*z_51 + z_39*z_21*z_17 + z_40*z_30*z_39 ,
z_40*z_30*z_35*z_6*z_52 + z_35*z_3*z_27*z_52 + z_38*z_11*z_35*z_3 + z_39*z_22*z_35*z_3 ,
z_40*z_30*z_38*z_11*z_35 + z_35*z_6*z_52*z_24 + z_37*z_10*z_35 + z_38*z_11*z_35 + z_39*z_22*z_35 + z_39*z_23*z_48 ,
z_40*z_30*z_38*z_11*z_38 + z_35*z_3*z_27*z_50 + z_35*z_4*z_38 + z_38*z_11*z_38 ,
z_40*z_30*z_38*z_12*z_42 + z_35*z_3*z_27*z_50 + z_35*z_4*z_38 + z_36*z_8*z_50 + z_38*z_11*z_38 + z_39*z_22*z_38 ,
z_40*z_30*z_38*z_13*z_48 + z_35*z_6*z_52*z_24 + z_38*z_11*z_35 + z_38*z_13*z_48 ,
z_40*z_30*z_38*z_13*z_52 + z_40*z_30*z_39*z_23*z_52 + z_35*z_3*z_27*z_52 + z_37*z_9*z_27*z_52 + z_38*z_11*z_35*z_3 + z_39*z_22*z_35*z_3 + z_35*z_6*z_52 ,
z_40*z_30*z_38*z_13*z_54 + z_35*z_6*z_54 + z_36*z_8*z_54 ,
z_40*z_30*z_39*z_22*z_35 + z_39*z_23*z_48 ,
z_41*z_6*z_52*z_26*z_45 + z_42*z_13*z_48*z_6*z_52 + z_42*z_11*z_35*z_3 + z_41*z_6*z_52 + z_42*z_13*z_52 ,
z_41*z_6*z_53*z_31*z_15 + z_42*z_13*z_48*z_4*z_40 ,
z_41*z_6*z_53*z_32*z_18 + z_42*z_13*z_48*z_4*z_40 + z_43*z_56*z_50*z_11*z_40 + z_41*z_2*z_15 + z_41*z_4*z_40 ,
z_42*z_12*z_42*z_11*z_40 + z_42*z_13*z_48*z_4*z_40 + z_41*z_2*z_15 + z_41*z_4*z_40 ,
z_42*z_12*z_42*z_13*z_48 + z_41*z_6*z_48 + z_42*z_11*z_35 + z_42*z_12*z_41 ,
z_42*z_13*z_48*z_2*z_15 + z_42*z_13*z_48*z_4*z_40 ,
z_42*z_13*z_48*z_3*z_26 + z_41*z_6*z_52*z_26 + z_42*z_13*z_52*z_26 ,
z_42*z_13*z_48*z_3*z_27 + z_42*z_11*z_39*z_23 + z_42*z_12*z_42*z_13 + z_42*z_13*z_48*z_6 + z_43*z_56*z_49*z_8 ,
z_42*z_13*z_48*z_4*z_38 + z_42*z_13*z_50 ,
z_42*z_13*z_48*z_6*z_51 ,
z_42*z_13*z_48*z_6*z_53 + z_41*z_2*z_16 + z_41*z_6*z_53 ,
z_42*z_13*z_52*z_26*z_45 + z_42*z_13*z_48*z_3 + z_41*z_6*z_52 + z_42*z_13*z_52 ,
z_42*z_13*z_52*z_27*z_50 + z_41*z_5*z_42 + z_42*z_13*z_50 + z_43*z_56*z_50 ,
z_43*z_56*z_49*z_8*z_54 + z_43*z_56*z_54*z_56*z_54 + z_42*z_12*z_43 + z_43*z_55*z_43 + z_43*z_56*z_54 ,
z_43*z_56*z_50*z_13*z_49 + z_42*z_13*z_49 + z_43*z_56*z_49 ,
z_43*z_56*z_50*z_13*z_54 + z_42*z_13*z_54 + z_43*z_55*z_43 + z_43*z_56*z_54 ,
z_43*z_56*z_54*z_55*z_42 + z_42*z_13*z_50 ,
z_43*z_56*z_54*z_55*z_43 + z_42*z_13*z_54 + z_43*z_55*z_43 + z_43*z_56*z_54 ,
z_43*z_56*z_54*z_56*z_49 + z_42*z_13*z_49 + z_43*z_56*z_49 ,
z_43*z_56*z_54*z_56*z_50 + z_42*z_13*z_50 ,
z_43*z_56*z_54*z_56*z_52 ,
z_44*z_46*z_34*z_51*z_23 ,
z_45*z_24*z_6*z_54*z_56 + z_45*z_27*z_50*z_13 ,
z_45*z_25*z_10*z_40*z_28 + z_45*z_24*z_2 + z_46*z_31 ,
z_45*z_25*z_10*z_40*z_30 + z_46*z_34*z_52*z_25*z_10 + z_45*z_27*z_51*z_22 + z_45*z_24*z_4 ,
z_45*z_27*z_50*z_12*z_42 ,
z_45*z_27*z_50*z_13*z_50 ,
z_45*z_27*z_50*z_13*z_52 ,
z_46*z_34*z_52*z_26*z_45 + z_45*z_27*z_52 ,
z_46*z_34*z_52*z_27*z_50 + z_45*z_24*z_4*z_38 + z_45*z_27*z_50 ,
z_47*z_44*z_46*z_34*z_51 + z_45*z_27*z_51 ,
z_48*z_6*z_48*z_3*z_27 + z_50*z_13*z_52*z_27 + z_51*z_23*z_52*z_27 + z_52*z_27*z_53*z_34 + z_52*z_27*z_54*z_56 + z_53*z_34*z_51*z_23 + z_53*z_34*z_52*z_27 ,
z_48*z_6*z_51*z_22*z_38 + z_53*z_34*z_52*z_27*z_50 + z_48*z_4*z_38 + z_50*z_12*z_42 + z_54*z_55*z_42 ,
z_48*z_6*z_53*z_31*z_15 + z_52*z_27*z_48*z_4*z_40 ,
z_49*z_8*z_51*z_22*z_38 ,
z_49*z_8*z_54*z_56*z_48 + z_48*z_4*z_35 ,
z_49*z_8*z_54*z_56*z_49 + z_52*z_27*z_49 ,
z_49*z_8*z_54*z_56*z_52 ,
z_49*z_8*z_54*z_56*z_54 + z_54*z_56*z_54*z_56*z_54 + z_52*z_24*z_6*z_54 + z_49*z_8*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 + z_52*z_27*z_54 + z_54*z_55*z_43 + z_54*z_56*z_54 ,
z_50*z_12*z_42*z_11*z_40 + z_52*z_27*z_48*z_4*z_40 + z_48*z_2*z_15 + z_48*z_4*z_40 ,
z_50*z_13*z_52*z_27*z_50 + z_48*z_4*z_38 + z_50*z_12*z_42 + z_50*z_13*z_50 + z_51*z_22*z_38 + z_54*z_56*z_50 ,
z_51*z_22*z_35*z_3*z_27 + z_50*z_13*z_52*z_27 + z_51*z_23*z_52*z_27 + z_52*z_26*z_45*z_27 + z_52*z_27*z_53*z_34 + z_53*z_34*z_51*z_23 + z_53*z_34*z_52*z_27 + z_54*z_56*z_52*z_27 ,
z_51*z_23*z_49*z_7*z_36 + z_48*z_6*z_49 + z_50*z_13*z_49 + z_51*z_23*z_49 + z_54*z_56*z_49 ,
z_51*z_23*z_49*z_8*z_51 + z_54*z_56*z_52*z_27*z_51 ,
z_51*z_23*z_49*z_8*z_54 + z_54*z_56*z_54*z_56*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 + z_52*z_27*z_54 ,
z_51*z_23*z_52*z_27*z_49 + z_54*z_56*z_50*z_13*z_49 + z_48*z_6*z_49 ,
z_51*z_23*z_52*z_27*z_50 + z_50*z_13*z_50 + z_51*z_22*z_38 + z_54*z_55*z_42 + z_54*z_56*z_50 ,
z_51*z_23*z_52*z_27*z_51 + z_50*z_11*z_39 ,
z_52*z_24*z_5*z_42*z_12 + z_50*z_12*z_42*z_12 + z_51*z_22*z_35*z_5 + z_54*z_56*z_54*z_55 ,
z_52*z_24*z_6*z_54*z_56 + z_49*z_8*z_54*z_56 + z_54*z_56*z_49*z_8 + z_54*z_56*z_52*z_27 ,
z_52*z_25*z_10*z_35*z_4 + z_48*z_5*z_42*z_11 + z_50*z_12*z_42*z_11 + z_54*z_55*z_42*z_11 ,
z_52*z_25*z_10*z_35*z_5 + z_50*z_12*z_42*z_12 + z_51*z_22*z_35*z_5 + z_52*z_27*z_50*z_12 + z_53*z_34*z_48*z_5 + z_54*z_56*z_48*z_5 + z_54*z_56*z_50*z_12 + z_48*z_5 + z_50*z_12 + z_54*z_55 ,
z_52*z_25*z_10*z_38*z_12 + z_50*z_12*z_42*z_12 + z_51*z_22*z_35*z_5 + z_54*z_56*z_54*z_55 ,
z_52*z_25*z_10*z_38*z_13 + z_49*z_8*z_54*z_56 + z_50*z_13*z_52*z_27 + z_51*z_23*z_52*z_27 + z_52*z_27*z_48*z_6 + z_52*z_27*z_50*z_13 + z_52*z_27*z_51*z_23 + z_52*z_27*z_53*z_34 + z_52*z_27*z_54*z_56 + z_53*z_34*z_51*z_23 + z_53*z_34*z_52*z_27 + z_54*z_56*z_49*z_8 + z_54*z_56*z_52*z_27 ,
z_52*z_25*z_10*z_40*z_28 + z_48*z_6*z_53*z_31 + z_53*z_32*z_19*z_31 ,
z_52*z_25*z_10*z_40*z_30 + z_48*z_6*z_51*z_22 + z_49*z_8*z_51*z_22 + z_50*z_12*z_42*z_11 + z_51*z_22*z_35*z_4 + z_52*z_27*z_48*z_4 + z_52*z_27*z_50*z_11 + z_52*z_27*z_51*z_22 + z_53*z_32*z_18*z_30 + z_53*z_34*z_51*z_22 + z_54*z_56*z_49*z_7 + z_52*z_24*z_4 ,
z_52*z_26*z_45*z_25*z_10 + z_48*z_5*z_42*z_11 + z_48*z_6*z_51*z_22 + z_51*z_22*z_35*z_4 + z_54*z_56*z_49*z_7 ,
z_52*z_27*z_50*z_11*z_40 + z_48*z_4*z_40 + z_51*z_22*z_40 + z_53*z_31*z_15 + z_53*z_32*z_18 ,
z_52*z_27*z_50*z_12*z_42 + z_53*z_34*z_52*z_27*z_50 + z_48*z_4*z_38 + z_48*z_5*z_42 ,
z_52*z_27*z_50*z_13*z_50 + z_53*z_34*z_52*z_27*z_50 + z_48*z_4*z_38 + z_50*z_12*z_42 + z_54*z_55*z_42 ,
z_52*z_27*z_50*z_13*z_52 + z_48*z_6*z_48*z_3 + z_52*z_27*z_48*z_3 + z_53*z_31*z_14*z_3 + z_54*z_56*z_48*z_3 + z_50*z_13*z_52 + z_51*z_23*z_52 + z_52*z_24*z_3 + z_52*z_25*z_9 + z_52*z_26*z_45 + z_54*z_56*z_52 ,
z_52*z_27*z_51*z_23*z_49 + z_48*z_6*z_49 + z_49*z_7*z_36 + z_52*z_27*z_49 ,
z_52*z_27*z_51*z_23*z_52 + z_48*z_6*z_48*z_3 + z_51*z_22*z_35*z_3 + z_52*z_27*z_48*z_3 + z_52*z_24*z_3 + z_52*z_25*z_9 + z_54*z_56*z_52 ,
z_52*z_27*z_52*z_26*z_45 + z_48*z_6*z_48*z_3 + z_51*z_22*z_35*z_3 + z_53*z_31*z_14*z_3 + z_54*z_56*z_48*z_3 + z_50*z_13*z_52 + z_51*z_23*z_52 + z_52*z_26*z_45 ,
z_52*z_27*z_52*z_27*z_50 + z_48*z_5*z_42 + z_50*z_12*z_42 + z_54*z_55*z_42 ,
z_52*z_27*z_52*z_27*z_52 + z_48*z_6*z_48*z_3 ,
z_52*z_27*z_53*z_34*z_48 ,
z_52*z_27*z_53*z_34*z_51 + z_53*z_32*z_17 + z_53*z_34*z_51 ,
z_52*z_27*z_53*z_34*z_52 + z_52*z_27*z_48*z_3 + z_52*z_27*z_52 ,
z_52*z_27*z_54*z_56*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 ,
z_53*z_31*z_14*z_3*z_27 + z_52*z_27*z_53*z_34 + z_53*z_34*z_51*z_23 + z_53*z_34*z_52*z_27 ,
z_53*z_33*z_47*z_44*z_46 + z_52*z_27*z_53 + z_53*z_32*z_19 ,
z_53*z_34*z_52*z_25*z_10 + z_48*z_6*z_51*z_22 + z_50*z_11*z_40*z_30 + z_52*z_27*z_50*z_11 + z_53*z_32*z_18*z_30 + z_48*z_4 + z_49*z_7 ,
z_53*z_34*z_52*z_26*z_45 + z_52*z_27*z_48*z_3 + z_52*z_27*z_52 ,
z_54*z_56*z_48*z_3*z_26 + z_54*z_56*z_52*z_26 ,
z_54*z_56*z_49*z_8*z_54 + z_54*z_56*z_54*z_56*z_54 + z_52*z_24*z_6*z_54 + z_48*z_6*z_54 + z_49*z_8*z_54 + z_50*z_12*z_43 + z_52*z_27*z_54 + z_54*z_56*z_54 ,
z_54*z_56*z_50*z_11*z_40 ,
z_54*z_56*z_50*z_12*z_43 + z_54*z_56*z_54*z_56*z_54 + z_52*z_24*z_6*z_54 + z_49*z_8*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 + z_52*z_27*z_54 + z_54*z_55*z_43 + z_54*z_56*z_54 ,
z_54*z_56*z_50*z_13*z_54 + z_54*z_56*z_54*z_56*z_54 + z_52*z_24*z_6*z_54 + z_49*z_8*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 + z_52*z_27*z_54 + z_54*z_55*z_43 + z_54*z_56*z_54 ,
z_54*z_56*z_52*z_27*z_52 ,
z_54*z_56*z_52*z_27*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 ,
z_54*z_56*z_54*z_55*z_42 + z_54*z_55*z_42 + z_54*z_56*z_50 ,
z_54*z_56*z_54*z_55*z_43 + z_52*z_24*z_6*z_54 + z_48*z_6*z_54 + z_49*z_8*z_54 + z_50*z_12*z_43 + z_52*z_27*z_54 + z_54*z_56*z_54 ,
z_54*z_56*z_54*z_56*z_49 + z_48*z_6*z_49 ,
z_54*z_56*z_54*z_56*z_50 + z_54*z_55*z_42 + z_54*z_56*z_50 ,
z_54*z_56*z_54*z_56*z_52 ,
z_56*z_49*z_8*z_54*z_56 + z_56*z_52*z_24*z_6 + z_56*z_48*z_6 + z_56*z_49*z_8 + z_56*z_50*z_13 + z_56*z_54*z_56 ,
z_56*z_50*z_11*z_40*z_30 + z_56*z_52*z_24*z_4 + z_56*z_52*z_25*z_10 + z_56*z_48*z_4 + z_56*z_49*z_7 ,
z_56*z_52*z_24*z_6*z_54 + z_56*z_50*z_12*z_43 + z_56*z_50*z_13*z_54 + z_56*z_52*z_27*z_54 ,
z_56*z_52*z_25*z_10*z_35 + z_55*z_41 + z_56*z_48 ,
z_56*z_52*z_25*z_10*z_38 + z_56*z_54*z_55*z_42 + z_56*z_54*z_56*z_50 ,
z_56*z_52*z_25*z_10*z_40 + z_56*z_48*z_4*z_40 ,
z_56*z_52*z_27*z_51*z_22 + z_56*z_52*z_24*z_4 + z_56*z_52*z_25*z_10 + z_55*z_42*z_11 + z_56*z_50*z_11 ,
z_56*z_52*z_27*z_51*z_23 + z_56*z_52*z_24*z_6 + z_55*z_41*z_6 + z_55*z_42*z_13 + z_56*z_48*z_6 + z_56*z_50*z_13 ,
z_56*z_52*z_27*z_52*z_26 + z_56*z_48*z_3*z_26 + z_56*z_52*z_26 ,
z_56*z_52*z_27*z_52*z_27 + z_55*z_41*z_6 + z_55*z_42*z_13 + z_55*z_43*z_56 + z_56*z_52*z_27 ,
z_56*z_52*z_27*z_54*z_56 + z_55*z_41*z_6 + z_56*z_48*z_6 ,
z_56*z_54*z_55*z_42*z_11 + z_56*z_52*z_24*z_4 + z_56*z_52*z_25*z_10 + z_55*z_42*z_11 + z_56*z_50*z_11 ,
z_56*z_54*z_55*z_43*z_56 + z_56*z_52*z_24*z_6 + z_55*z_41*z_6 + z_55*z_43*z_56 + z_56*z_48*z_6 + z_56*z_49*z_8 + z_56*z_52*z_27 + z_56*z_54*z_56 ,
z_56*z_54*z_56*z_49*z_7 + z_56*z_52*z_24*z_4 ,
z_56*z_54*z_56*z_49*z_8 + z_56*z_52*z_24*z_6 + z_55*z_42*z_13 + z_55*z_43*z_56 + z_56*z_49*z_8 + z_56*z_50*z_13 + z_56*z_52*z_27 + z_56*z_54*z_56 ,
z_56*z_54*z_56*z_50*z_11 + z_56*z_52*z_24*z_4 + z_56*z_52*z_25*z_10 + z_55*z_42*z_11 + z_56*z_50*z_11 ,
z_56*z_54*z_56*z_50*z_12 + z_56*z_54*z_56*z_54*z_55 + z_55*z_41*z_5 + z_56*z_50*z_12 + z_56*z_54*z_55 ,
z_56*z_54*z_56*z_50*z_13 + z_55*z_41*z_6 + z_55*z_42*z_13 + z_56*z_49*z_8 + z_56*z_54*z_56 ,
z_56*z_54*z_56*z_52*z_26 + z_56*z_48*z_3*z_26 + z_56*z_52*z_26 ,
z_56*z_54*z_56*z_52*z_27 + z_55*z_41*z_6 + z_55*z_42*z_13 + z_55*z_43*z_56 + z_56*z_52*z_27 ,
z_56*z_54*z_56*z_54*z_56 + z_55*z_41*z_6 + z_55*z_43*z_56 + z_56*z_50*z_13 + z_56*z_52*z_27 ,
z_2*z_14*z_5*z_42 + z_3*z_27*z_50 + z_5*z_42 ,
z_3*z_26*z_45*z_24 + z_6*z_52*z_24 ,
z_3*z_26*z_45*z_25 + z_4*z_37 ,
z_3*z_26*z_45*z_26 + z_6*z_52*z_26 + z_6*z_53*z_33 ,
z_3*z_26*z_45*z_27 + z_4*z_37*z_9*z_27 + z_6*z_49*z_8 ,
z_3*z_27*z_50*z_11 + z_4*z_38*z_11 ,
z_3*z_27*z_50*z_13 + z_6*z_49*z_8 + z_6*z_54*z_56 ,
z_3*z_27*z_51*z_22 + z_2*z_14*z_4 + z_4*z_37*z_10 + z_4*z_40*z_30 + z_5*z_42*z_11 ,
z_3*z_27*z_51*z_23 + z_6*z_48*z_6 + z_6*z_49*z_8 + z_6*z_51*z_23 ,
z_3*z_27*z_52*z_24 + z_4*z_35 + z_6*z_48 ,
z_3*z_27*z_52*z_25 + z_4*z_40*z_30*z_37 ,
z_3*z_27*z_52*z_26 + z_6*z_52*z_26 ,
z_3*z_27*z_52*z_27 + z_4*z_37*z_9*z_27 + z_6*z_48*z_3*z_27 ,
z_3*z_27*z_54*z_56 + z_6*z_49*z_8 ,
z_4*z_35*z_5*z_42 ,
z_4*z_35*z_5*z_43 + z_3*z_27*z_54 + z_5*z_43 + z_6*z_54 ,
z_4*z_37*z_9*z_26 + z_2*z_16*z_33 + z_6*z_52*z_26 + z_6*z_53*z_33 ,
z_4*z_37*z_10*z_35 + z_4*z_35 ,
z_4*z_37*z_10*z_40 + z_6*z_53*z_31*z_15 + z_2*z_15 + z_4*z_40 ,
z_4*z_38*z_11*z_35 ,
z_4*z_38*z_11*z_38 ,
z_4*z_38*z_11*z_39 ,
z_4*z_38*z_11*z_40 + z_6*z_53*z_31*z_15 + z_6*z_53*z_32*z_18 + z_2*z_15 + z_4*z_40 ,
z_4*z_40*z_30*z_35 + z_6*z_53*z_34*z_48 ,
z_4*z_40*z_30*z_38 + z_4*z_38 + z_5*z_42 ,
z_4*z_40*z_30*z_39 + z_3*z_27*z_51 + z_6*z_51 ,
z_5*z_42*z_11*z_35 ,
z_5*z_42*z_11*z_38 ,
z_5*z_42*z_11*z_39 ,
z_5*z_42*z_11*z_40 + z_6*z_53*z_32*z_18 + z_2*z_15 + z_4*z_40 ,
z_5*z_42*z_12*z_41 ,
z_5*z_42*z_12*z_42 + z_6*z_51*z_22*z_38 + z_3*z_27*z_50 + z_4*z_38 ,
z_5*z_42*z_12*z_43 + z_3*z_27*z_54 ,
z_6*z_48*z_2*z_15 ,
z_6*z_48*z_3*z_26 + z_2*z_16*z_33 + z_6*z_53*z_33 ,
z_6*z_48*z_4*z_35 ,
z_6*z_48*z_4*z_37 ,
z_6*z_48*z_4*z_38 + z_6*z_51*z_22*z_38 ,
z_6*z_48*z_4*z_40 ,
z_6*z_48*z_5*z_42 + z_6*z_51*z_22*z_38 ,
z_6*z_48*z_6*z_48 ,
z_6*z_48*z_6*z_49 ,
z_6*z_48*z_6*z_51 ,
z_6*z_48*z_6*z_52 + z_6*z_53*z_34*z_52 + z_3*z_27*z_52 + z_4*z_37*z_9 ,
z_6*z_48*z_6*z_53 ,
z_6*z_48*z_6*z_54 + z_3*z_27*z_54 + z_5*z_43 + z_6*z_54 ,
z_6*z_49*z_8*z_51 ,
z_6*z_49*z_8*z_54 + z_3*z_27*z_54 + z_5*z_43 + z_6*z_54 ,
z_6*z_51*z_22*z_35 + z_6*z_53*z_34*z_48 + z_4*z_35 ,
z_6*z_51*z_22*z_40 + z_6*z_53*z_32*z_18 ,
z_6*z_51*z_23*z_49 + z_6*z_49 ,
z_6*z_51*z_23*z_52 + z_6*z_52*z_26*z_45 + z_6*z_53*z_34*z_52 + z_3*z_27*z_52 + z_4*z_37*z_9 + z_6*z_48*z_3 ,
z_6*z_52*z_24*z_3 + z_6*z_53*z_34*z_52 + z_3*z_27*z_52 + z_6*z_48*z_3 ,
z_6*z_52*z_24*z_4 + z_2*z_14*z_4 + z_4*z_40*z_30 ,
z_6*z_52*z_24*z_5 + z_4*z_35*z_5 + z_5*z_42*z_12 + z_6*z_48*z_5 ,
z_6*z_52*z_24*z_6 + z_6*z_48*z_6 + z_6*z_49*z_8 + z_6*z_51*z_23 + z_6*z_54*z_56 ,
z_6*z_52*z_27*z_48 + z_6*z_53*z_34*z_48 + z_6*z_48 ,
z_6*z_52*z_27*z_49 ,
z_6*z_52*z_27*z_50 + z_4*z_38 + z_5*z_42 ,
z_6*z_52*z_27*z_51 + z_3*z_27*z_51 + z_6*z_51 ,
z_6*z_52*z_27*z_52 + z_6*z_53*z_34*z_52 + z_3*z_27*z_52 + z_4*z_37*z_9 + z_6*z_48*z_3 ,
z_6*z_52*z_27*z_53 + z_2*z_16 + z_6*z_53 ,
z_6*z_52*z_27*z_54 ,
z_6*z_53*z_31*z_14 + z_4*z_35 + z_6*z_48 ,
z_6*z_53*z_32*z_17 + z_3*z_27*z_51 + z_6*z_51 ,
z_6*z_53*z_32*z_19 + z_2*z_16 + z_6*z_53 ,
z_6*z_53*z_33*z_47 ,
z_6*z_53*z_34*z_51 + z_3*z_27*z_51 + z_6*z_51 ,
z_6*z_54*z_56*z_48 ,
z_6*z_54*z_56*z_49 + z_6*z_49 ,
z_6*z_54*z_56*z_50 ,
z_6*z_54*z_56*z_52 ,
z_6*z_54*z_56*z_54 + z_5*z_43 + z_6*z_54 ,
z_7*z_36*z_7*z_36 + z_8*z_54*z_56*z_49 + z_8*z_49 ,
z_7*z_36*z_8*z_50 + z_8*z_51*z_22*z_38 ,
z_7*z_36*z_8*z_54 ,
z_7*z_38*z_11*z_35 + z_8*z_54*z_56*z_48 ,
z_7*z_38*z_11*z_38 ,
z_7*z_38*z_11*z_39 + z_8*z_50*z_11*z_39 ,
z_7*z_38*z_11*z_40 ,
z_7*z_38*z_13*z_48 + z_8*z_54*z_56*z_48 ,
z_7*z_38*z_13*z_49 + z_8*z_50*z_13*z_49 + z_8*z_49 ,
z_7*z_38*z_13*z_52 + z_8*z_51*z_23*z_52 ,
z_7*z_38*z_13*z_54 + z_8*z_54*z_55*z_43 ,
z_8*z_50*z_11*z_40 ,
z_8*z_50*z_13*z_50 ,
z_8*z_50*z_13*z_52 + z_8*z_51*z_23*z_52 ,
z_8*z_50*z_13*z_54 + z_8*z_54*z_55*z_43 ,
z_8*z_51*z_22*z_35 + z_8*z_54*z_56*z_48 ,
z_8*z_51*z_22*z_40 ,
z_8*z_54*z_55*z_42 ,
z_8*z_54*z_56*z_50 + z_7*z_38 + z_8*z_50 ,
z_9*z_26*z_45*z_24 + z_9*z_27*z_48 ,
z_9*z_26*z_45*z_25 ,
z_9*z_26*z_45*z_26 + z_9*z_27*z_53*z_33 ,
z_9*z_26*z_45*z_27 ,
z_9*z_27*z_48*z_3 + z_10*z_38*z_13*z_52 ,
z_9*z_27*z_48*z_5 + z_10*z_38*z_12 ,
z_9*z_27*z_48*z_6 + z_10*z_38*z_13 ,
z_9*z_27*z_50*z_11 ,
z_9*z_27*z_50*z_12 + z_10*z_38*z_12 ,
z_9*z_27*z_50*z_13 + z_10*z_38*z_13 ,
z_9*z_27*z_52*z_24 + z_9*z_27*z_48 + z_10*z_35 ,
z_9*z_27*z_52*z_26 ,
z_9*z_27*z_53*z_31 + z_10*z_40*z_28 ,
z_9*z_27*z_53*z_32 ,
z_9*z_27*z_54*z_56 ,
z_10*z_35*z_4*z_37 ,
z_10*z_35*z_4*z_38 ,
z_10*z_35*z_5*z_42 + z_9*z_27*z_50 + z_10*z_38 ,
z_10*z_35*z_5*z_43 + z_9*z_27*z_54 ,
z_10*z_38*z_12*z_42 ,
z_10*z_38*z_13*z_48 ,
z_10*z_38*z_13*z_49 ,
z_10*z_38*z_13*z_54 + z_9*z_27*z_54 ,
z_10*z_40*z_28*z_16 ,
z_10*z_40*z_30*z_35 + z_9*z_27*z_48 + z_10*z_35 ,
z_10*z_40*z_30*z_37 ,
z_10*z_40*z_30*z_38 + z_10*z_38 ,
z_10*z_40*z_30*z_39 ,
z_11*z_35*z_3*z_26 + z_13*z_48*z_3*z_26 + z_13*z_52*z_26 ,
z_11*z_35*z_4*z_37 + z_11*z_37 ,
z_11*z_35*z_4*z_38 + z_13*z_48*z_4*z_38 + z_11*z_38 ,
z_11*z_35*z_6*z_49 + z_13*z_54*z_56*z_49 ,
z_11*z_35*z_6*z_51 + z_13*z_48*z_6*z_51 ,
z_11*z_35*z_6*z_52 + z_13*z_48*z_6*z_52 + z_13*z_52*z_26*z_45 ,
z_11*z_35*z_6*z_54 + z_13*z_54*z_55*z_43 ,
z_11*z_38*z_11*z_35 ,
z_11*z_38*z_11*z_38 ,
z_11*z_38*z_11*z_39 ,
z_11*z_38*z_11*z_40 + z_13*z_48*z_2*z_15 + z_13*z_48*z_4*z_40 ,
z_11*z_39*z_22*z_35 + z_12*z_41 + z_13*z_48 ,
z_11*z_39*z_22*z_38 + z_13*z_54*z_56*z_50 + z_13*z_50 ,
z_11*z_39*z_23*z_48 ,
z_11*z_39*z_23*z_49 + z_13*z_49*z_7*z_36 ,
z_11*z_39*z_23*z_52 + z_13*z_52*z_25*z_9 + z_13*z_48*z_3 ,
z_11*z_39*z_23*z_53 ,
z_11*z_40*z_30*z_35 + z_11*z_35 + z_13*z_48 ,
z_11*z_40*z_30*z_37 + z_13*z_52*z_25 + z_11*z_37 ,
z_11*z_40*z_30*z_38 + z_12*z_42 ,
z_11*z_40*z_30*z_39 ,
z_12*z_41*z_3*z_26 + z_13*z_48*z_3*z_26 ,
z_12*z_41*z_3*z_27 + z_11*z_35*z_6 + z_12*z_42*z_13 + z_13*z_54*z_56 ,
z_12*z_41*z_4*z_37 ,
z_12*z_41*z_4*z_40 + z_13*z_48*z_4*z_40 ,
z_12*z_41*z_5*z_42 + z_13*z_48*z_4*z_38 + z_11*z_38 ,
z_12*z_42*z_11*z_35 + z_12*z_42*z_13*z_48 + z_12*z_41 + z_13*z_48 ,
z_12*z_42*z_11*z_38 + z_13*z_48*z_4*z_38 + z_13*z_54*z_56*z_50 ,
z_12*z_42*z_11*z_39 ,
z_12*z_42*z_12*z_41 + z_12*z_42*z_13*z_48 ,
z_12*z_42*z_12*z_42 + z_13*z_48*z_4*z_38 + z_13*z_54*z_56*z_50 + z_13*z_50 ,
z_12*z_42*z_12*z_43 + z_13*z_54*z_55*z_43 + z_13*z_54*z_56*z_54 + z_12*z_43 + z_13*z_54 ,
z_12*z_42*z_13*z_49 ,
z_12*z_42*z_13*z_50 ,
z_12*z_42*z_13*z_52 + z_13*z_48*z_6*z_52 ,
z_12*z_42*z_13*z_54 + z_13*z_54*z_55*z_43 + z_13*z_54*z_56*z_54 + z_12*z_43 + z_13*z_54 ,
z_13*z_48*z_4*z_35 ,
z_13*z_48*z_4*z_37 ,
z_13*z_48*z_5*z_42 + z_13*z_54*z_56*z_50 + z_11*z_38 ,
z_13*z_48*z_6*z_48 + z_12*z_41 + z_13*z_48 ,
z_13*z_48*z_6*z_49 + z_13*z_54*z_56*z_49 ,
z_13*z_48*z_6*z_54 + z_13*z_54*z_55*z_43 ,
z_13*z_49*z_8*z_51 ,
z_13*z_49*z_8*z_54 + z_13*z_54*z_56*z_54 + z_12*z_43 + z_13*z_54 ,
z_13*z_50*z_12*z_42 ,
z_13*z_50*z_12*z_43 + z_12*z_43 + z_13*z_54 ,
z_13*z_50*z_13*z_49 ,
z_13*z_50*z_13*z_50 ,
z_13*z_50*z_13*z_52 + z_12*z_41*z_3 + z_13*z_48*z_3 ,
z_13*z_50*z_13*z_54 + z_12*z_43 + z_13*z_54 ,
z_13*z_52*z_25*z_10 + z_11*z_39*z_22 + z_12*z_42*z_11 + z_13*z_49*z_7 ,
z_13*z_52*z_27*z_48 + z_11*z_35 + z_12*z_41 ,
z_13*z_52*z_27*z_49 + z_13*z_54*z_56*z_49 ,
z_13*z_52*z_27*z_51 + z_11*z_39 ,
z_13*z_52*z_27*z_52 + z_11*z_35*z_3 + z_12*z_41*z_3 ,
z_13*z_52*z_27*z_53 ,
z_13*z_52*z_27*z_54 + z_12*z_43 + z_13*z_54 ,
z_13*z_54*z_55*z_42 + z_13*z_54*z_56*z_50 ,
z_13*z_54*z_56*z_48 ,
z_13*z_54*z_56*z_52 ,
z_14*z_3*z_26*z_45 + z_14*z_6*z_52 ,
z_14*z_3*z_27*z_50 + z_14*z_5*z_42 ,
z_14*z_3*z_27*z_51 + z_16*z_34*z_51 ,
z_14*z_3*z_27*z_52 + z_16*z_31*z_14*z_3 ,
z_14*z_3*z_27*z_54 ,
z_14*z_5*z_42*z_11 + z_16*z_34*z_51*z_22 + z_14*z_4 + z_15*z_30 ,
z_14*z_5*z_42*z_12 + z_16*z_31*z_14*z_5 ,
z_14*z_6*z_52*z_24 + z_16*z_31*z_14 ,
z_14*z_6*z_52*z_26 + z_14*z_3*z_26 + z_16*z_33 ,
z_14*z_6*z_52*z_27 + z_16*z_34*z_52*z_27 ,
z_15*z_30*z_37*z_9 + z_16*z_31*z_14*z_3 ,
z_15*z_30*z_37*z_10 + z_16*z_31*z_15*z_30 + z_14*z_4 + z_15*z_30 ,
z_15*z_30*z_38*z_11 + z_16*z_34*z_51*z_22 + z_14*z_4 + z_15*z_30 ,
z_15*z_30*z_38*z_12 + z_16*z_31*z_14*z_5 + z_16*z_34*z_48*z_5 ,
z_15*z_30*z_38*z_13 ,
z_16*z_32*z_18*z_30 + z_16*z_34*z_51*z_22 ,
z_16*z_34*z_51*z_23 + z_14*z_6 + z_16*z_34 ,
z_16*z_34*z_52*z_25 + z_15*z_30*z_37 ,
z_16*z_34*z_52*z_26 + z_14*z_3*z_26 + z_16*z_33 ,
z_19*z_31*z_14*z_3 ,
z_19*z_31*z_15*z_30 + z_19*z_34*z_51*z_22 ,
z_19*z_34*z_51*z_23 ,
z_19*z_34*z_52*z_25 ,
z_19*z_34*z_52*z_26 ,
z_19*z_34*z_52*z_27 + z_17*z_23 + z_19*z_34 ,
z_21*z_19*z_34*z_51 + z_23*z_53*z_32*z_17 ,
z_21*z_19*z_34*z_52 + z_23*z_53*z_34*z_52 ,
z_22*z_35*z_3*z_26 ,
z_22*z_35*z_4*z_37 ,
z_22*z_35*z_4*z_38 + z_23*z_52*z_27*z_50 + z_22*z_38 ,
z_22*z_35*z_5*z_42 + z_23*z_52*z_27*z_50 + z_22*z_38 ,
z_22*z_35*z_5*z_43 + z_23*z_49*z_8*z_54 ,
z_22*z_35*z_6*z_49 + z_23*z_52*z_27*z_49 ,
z_22*z_35*z_6*z_51 + z_23*z_49*z_8*z_51 ,
z_22*z_35*z_6*z_52 ,
z_22*z_35*z_6*z_54 + z_23*z_49*z_8*z_54 ,
z_22*z_38*z_11*z_35 ,
z_22*z_38*z_11*z_38 ,
z_22*z_38*z_11*z_39 + z_23*z_49*z_8*z_51 ,
z_22*z_38*z_11*z_40 ,
z_22*z_38*z_13*z_48 ,
z_22*z_38*z_13*z_49 + z_23*z_49*z_7*z_36 + z_23*z_52*z_27*z_49 ,
z_22*z_38*z_13*z_52 + z_22*z_35*z_3 ,
z_22*z_38*z_13*z_54 ,
z_22*z_40*z_30*z_35 + z_23*z_48 ,
z_22*z_40*z_30*z_37 ,
z_22*z_40*z_30*z_38 ,
z_22*z_40*z_30*z_39 ,
z_23*z_48*z_4*z_35 ,
z_23*z_48*z_4*z_37 ,
z_23*z_48*z_4*z_38 ,
z_23*z_48*z_4*z_40 ,
z_23*z_48*z_5*z_42 ,
z_23*z_52*z_26*z_45 ,
z_23*z_52*z_27*z_48 + z_23*z_48 ,
z_23*z_52*z_27*z_52 ,
z_23*z_52*z_27*z_53 + z_21*z_19 + z_23*z_53 ,
z_23*z_52*z_27*z_54 ,
z_23*z_53*z_31*z_14 + z_23*z_48 ,
z_23*z_53*z_31*z_15 + z_21*z_18 + z_22*z_40 ,
z_23*z_53*z_32*z_18 + z_21*z_18 + z_22*z_40 ,
z_23*z_53*z_32*z_19 ,
z_23*z_53*z_34*z_48 ,
z_23*z_53*z_34*z_51 ,
z_24*z_2*z_14*z_4 + z_26*z_45*z_24*z_4 + z_27*z_48*z_4 ,
z_24*z_2*z_14*z_5 + z_24*z_5*z_42*z_12 + z_25*z_10*z_35*z_5 + z_26*z_45*z_24*z_5 + z_27*z_50*z_12 ,
z_24*z_3*z_26*z_45 + z_26*z_45*z_26*z_45 + z_27*z_51*z_23*z_52 + z_27*z_53*z_34*z_52 + z_24*z_6*z_52 + z_24*z_3 + z_25*z_9 ,
z_24*z_3*z_27*z_50 + z_27*z_50*z_13*z_50 + z_24*z_4*z_38 ,
z_24*z_3*z_27*z_51 + z_24*z_6*z_51 ,
z_24*z_3*z_27*z_52 + z_26*z_45*z_26*z_45 + z_27*z_50*z_13*z_52 + z_27*z_51*z_23*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_24*z_3*z_27*z_54 + z_24*z_5*z_43 + z_24*z_6*z_54 ,
z_24*z_4*z_37*z_9 + z_27*z_50*z_13*z_52 + z_27*z_51*z_23*z_52 + z_27*z_52*z_26*z_45 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_24*z_4*z_37*z_10 + z_24*z_6*z_48*z_4 + z_25*z_10*z_35*z_4 ,
z_24*z_4*z_38*z_11 + z_24*z_6*z_48*z_4 + z_24*z_6*z_51*z_22 + z_25*z_10*z_35*z_4 ,
z_24*z_4*z_40*z_30 + z_25*z_10*z_35*z_4 + z_26*z_45*z_24*z_4 + z_27*z_48*z_4 ,
z_24*z_5*z_42*z_11 + z_24*z_6*z_48*z_4 + z_24*z_6*z_51*z_22 ,
z_24*z_6*z_48*z_2 ,
z_24*z_6*z_48*z_3 + z_27*z_50*z_13*z_52 + z_27*z_51*z_23*z_52 + z_27*z_52*z_26*z_45 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_24*z_6*z_48*z_5 + z_25*z_10*z_35*z_5 + z_25*z_10*z_38*z_12 ,
z_24*z_6*z_48*z_6 ,
z_24*z_6*z_51*z_23 + z_24*z_6*z_54*z_56 + z_25*z_10*z_38*z_13 ,
z_24*z_6*z_52*z_24 + z_27*z_53*z_34*z_48 + z_25*z_10*z_35 ,
z_24*z_6*z_52*z_26 ,
z_24*z_6*z_53*z_31 + z_25*z_10*z_40*z_28 ,
z_24*z_6*z_53*z_32 ,
z_24*z_6*z_53*z_33 + z_26*z_45*z_26 + z_27*z_52*z_26 + z_27*z_53*z_33 ,
z_24*z_6*z_53*z_34 + z_26*z_45*z_24*z_6 + z_27*z_48*z_6 + z_27*z_54*z_56 ,
z_25*z_9*z_26*z_45 + z_27*z_50*z_13*z_52 + z_27*z_52*z_27*z_52 + z_27*z_53*z_34*z_52 + z_24*z_6*z_52 + z_27*z_48*z_3 + z_24*z_3 + z_25*z_9 + z_27*z_52 ,
z_25*z_9*z_27*z_48 + z_24*z_6*z_48 + z_25*z_10*z_35 ,
z_25*z_9*z_27*z_50 + z_27*z_50*z_13*z_50 + z_25*z_10*z_38 ,
z_25*z_9*z_27*z_52 + z_26*z_45*z_26*z_45 + z_27*z_52*z_26*z_45 + z_27*z_53*z_34*z_52 ,
z_25*z_9*z_27*z_53 + z_24*z_6*z_53 ,
z_25*z_9*z_27*z_54 + z_24*z_5*z_43 + z_24*z_6*z_54 ,
z_26*z_45*z_24*z_3 + z_26*z_45*z_26*z_45 + z_27*z_51*z_23*z_52 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_24*z_3 + z_25*z_9 ,
z_26*z_45*z_25*z_9 + z_26*z_45*z_26*z_45 + z_27*z_50*z_13*z_52 + z_27*z_52*z_26*z_45 + z_27*z_52*z_27*z_52 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_24*z_3 + z_25*z_9 ,
z_26*z_45*z_27*z_48 + z_27*z_53*z_34*z_48 + z_24*z_2*z_14 + z_26*z_45*z_24 + z_27*z_48 ,
z_26*z_45*z_27*z_50 + z_27*z_50*z_12*z_42 + z_24*z_4*z_38 + z_24*z_5*z_42 ,
z_26*z_45*z_27*z_51 ,
z_26*z_45*z_27*z_52 + z_27*z_50*z_13*z_52 + z_27*z_51*z_23*z_52 + z_27*z_52*z_26*z_45 + z_27*z_52*z_27*z_52 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_27*z_48*z_3*z_26 + z_27*z_52*z_26 ,
z_27*z_48*z_3*z_27 + z_27*z_52*z_27 ,
z_27*z_48*z_4*z_35 ,
z_27*z_48*z_4*z_37 + z_24*z_4*z_37 ,
z_27*z_48*z_4*z_38 + z_27*z_50*z_13*z_50 + z_27*z_52*z_27*z_50 ,
z_27*z_48*z_5*z_42 + z_27*z_50*z_12*z_42 + z_27*z_50*z_13*z_50 ,
z_27*z_48*z_6*z_48 + z_27*z_53*z_34*z_48 ,
z_27*z_48*z_6*z_49 ,
z_27*z_48*z_6*z_51 ,
z_27*z_48*z_6*z_52 + z_27*z_52*z_26*z_45 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_27*z_48*z_6*z_53 + z_27*z_53*z_32*z_19 ,
z_27*z_48*z_6*z_54 + z_24*z_5*z_43 + z_24*z_6*z_54 + z_27*z_54 ,
z_27*z_50*z_11*z_39 + z_24*z_6*z_51 ,
z_27*z_50*z_12*z_43 + z_24*z_5*z_43 + z_24*z_6*z_54 + z_27*z_54 ,
z_27*z_50*z_13*z_49 + z_27*z_51*z_23*z_49 + z_27*z_49 ,
z_27*z_50*z_13*z_54 + z_24*z_5*z_43 + z_24*z_6*z_54 + z_27*z_54 ,
z_27*z_51*z_22*z_35 + z_24*z_2*z_14 + z_24*z_6*z_48 + z_26*z_45*z_24 + z_27*z_48 ,
z_27*z_51*z_22*z_38 + z_24*z_5*z_42 + z_25*z_10*z_38 ,
z_27*z_51*z_22*z_40 + z_27*z_53*z_32*z_18 ,
z_27*z_52*z_24*z_3 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_27*z_52*z_25*z_9 + z_27*z_53*z_34*z_52 + z_27*z_48*z_3 + z_27*z_52 ,
z_27*z_52*z_27*z_48 + z_24*z_2*z_14 + z_24*z_6*z_48 + z_26*z_45*z_24 + z_27*z_48 ,
z_27*z_52*z_27*z_49 ,
z_27*z_52*z_27*z_51 ,
z_27*z_52*z_27*z_53 + z_27*z_53*z_32*z_19 ,
z_27*z_52*z_27*z_54 + z_27*z_54*z_56*z_54 ,
z_27*z_53*z_31*z_14 + z_27*z_52*z_24 ,
z_27*z_53*z_32*z_17 + z_27*z_53*z_34*z_51 ,
z_27*z_53*z_33*z_47 ,
z_27*z_54*z_56*z_48 ,
z_27*z_54*z_56*z_49 ,
z_27*z_54*z_56*z_50 ,
z_27*z_54*z_56*z_52 ,
z_28*z_15*z_30*z_37 + z_30*z_35*z_4*z_37 ,
z_28*z_15*z_30*z_38 + z_30*z_35*z_5*z_42 + z_30*z_38*z_11*z_38 ,
z_28*z_16*z_31*z_14 + z_30*z_38*z_11*z_35 + z_30*z_38*z_13*z_48 ,
z_28*z_16*z_31*z_15 + z_30*z_37*z_10*z_40 + z_30*z_38*z_11*z_40 ,
z_28*z_16*z_32*z_18 + z_29*z_19*z_31*z_15 ,
z_28*z_16*z_32*z_19 ,
z_29*z_19*z_34*z_51 + z_30*z_35*z_6*z_51 ,
z_29*z_19*z_34*z_52 + z_30*z_39*z_23*z_52 ,
z_30*z_35*z_3*z_26 + z_28*z_16*z_33 ,
z_30*z_35*z_4*z_38 + z_30*z_35*z_5*z_42 + z_30*z_38*z_11*z_38 ,
z_30*z_35*z_5*z_43 ,
z_30*z_35*z_6*z_49 ,
z_30*z_35*z_6*z_54 ,
z_30*z_37*z_10*z_35 + z_30*z_38*z_13*z_48 + z_30*z_39*z_22*z_35 ,
z_30*z_38*z_11*z_39 ,
z_30*z_38*z_13*z_49 ,
z_30*z_39*z_22*z_38 ,
z_30*z_39*z_23*z_48 ,
z_30*z_39*z_23*z_53 ,
z_31*z_14*z_3*z_26 + z_34*z_52*z_26 ,
z_31*z_14*z_5*z_42 + z_34*z_52*z_27*z_50 ,
z_31*z_15*z_30*z_37 ,
z_31*z_15*z_30*z_38 + z_34*z_52*z_27*z_50 ,
z_32*z_19*z_31*z_14 + z_34*z_48 ,
z_32*z_19*z_31*z_15 ,
z_34*z_48*z_5*z_42 ,
z_34*z_51*z_22*z_35 + z_34*z_48 ,
z_34*z_51*z_22*z_38 ,
z_34*z_51*z_22*z_40 ,
z_34*z_51*z_23*z_49 ,
z_34*z_51*z_23*z_52 + z_34*z_52*z_26*z_45 ,
z_34*z_52*z_25*z_9 + z_31*z_14*z_3 ,
z_34*z_52*z_27*z_48 + z_34*z_48 ,
z_34*z_52*z_27*z_49 ,
z_34*z_52*z_27*z_51 + z_32*z_17 + z_34*z_51 ,
z_34*z_52*z_27*z_52 ,
z_34*z_52*z_27*z_53 ,
z_34*z_52*z_27*z_54 ,
z_35*z_3*z_26*z_45 + z_40*z_30*z_35*z_3 + z_35*z_6*z_52 ,
z_35*z_3*z_27*z_51 + z_35*z_6*z_51 + z_39*z_21*z_17 + z_40*z_30*z_39 ,
z_35*z_3*z_27*z_54 + z_35*z_5*z_43 + z_35*z_6*z_54 ,
z_35*z_4*z_37*z_9 + z_38*z_11*z_35*z_3 + z_39*z_22*z_35*z_3 ,
z_35*z_4*z_37*z_10 + z_38*z_11*z_35*z_4 + z_39*z_22*z_35*z_4 + z_40*z_28*z_15*z_30 + z_40*z_30*z_35*z_4 ,
z_35*z_4*z_38*z_11 + z_38*z_13*z_48*z_4 + z_38*z_13*z_49*z_7 + z_39*z_22*z_38*z_11 + z_39*z_23*z_48*z_4 + z_40*z_28*z_15*z_30 + z_40*z_30*z_35*z_4 ,
z_35*z_5*z_42*z_11 + z_38*z_13*z_48*z_4 + z_38*z_13*z_49*z_7 + z_39*z_22*z_38*z_11 ,
z_35*z_5*z_42*z_12 + z_36*z_8*z_54*z_55 + z_38*z_13*z_48*z_5 + z_38*z_13*z_54*z_55 ,
z_35*z_6*z_49*z_8 ,
z_35*z_6*z_51*z_22 + z_38*z_13*z_49*z_7 + z_39*z_22*z_35*z_4 + z_39*z_22*z_38*z_11 ,
z_35*z_6*z_51*z_23 + z_38*z_11*z_39*z_23 + z_39*z_22*z_38*z_13 ,
z_35*z_6*z_52*z_26 ,
z_35*z_6*z_54*z_56 + z_36*z_8*z_54*z_56 ,
z_36*z_7*z_36*z_7 + z_38*z_13*z_49*z_7 + z_39*z_22*z_38*z_11 ,
z_36*z_7*z_36*z_8 + z_38*z_13*z_54*z_56 + z_39*z_22*z_35*z_6 ,
z_36*z_8*z_50*z_11 + z_39*z_22*z_38*z_11 ,
z_36*z_8*z_50*z_13 + z_36*z_8*z_54*z_56 + z_38*z_11*z_39*z_23 ,
z_36*z_8*z_51*z_22 + z_38*z_13*z_49*z_7 + z_39*z_22*z_38*z_11 + z_39*z_23*z_49*z_7 ,
z_36*z_8*z_51*z_23 + z_38*z_11*z_39*z_23 + z_39*z_22*z_35*z_6 + z_39*z_23*z_49*z_8 ,
z_37*z_9*z_26*z_45 + z_38*z_13*z_48*z_3 + z_39*z_22*z_35*z_3 + z_40*z_30*z_35*z_3 + z_40*z_30*z_37*z_9 + z_38*z_13*z_52 + z_39*z_23*z_52 + z_35*z_3 ,
z_37*z_9*z_27*z_48 + z_37*z_10*z_35 + z_38*z_11*z_35 + z_38*z_13*z_48 + z_39*z_23*z_48 ,
z_37*z_9*z_27*z_50 + z_38*z_12*z_42 ,
z_37*z_10*z_35*z_4 + z_38*z_11*z_40*z_30 + z_38*z_13*z_49*z_7 + z_39*z_22*z_35*z_4 + z_39*z_22*z_38*z_11 + z_39*z_23*z_48*z_4 + z_39*z_23*z_49*z_7 + z_40*z_28*z_15*z_30 + z_40*z_30*z_35*z_4 + z_40*z_30*z_37*z_10 + z_40*z_30*z_38*z_11 + z_36*z_7 + z_37*z_10 + z_38*z_11 + z_39*z_22 ,
z_37*z_10*z_35*z_5 + z_38*z_12*z_42*z_12 + z_38*z_13*z_48*z_5 + z_38*z_13*z_54*z_55 + z_39*z_23*z_48*z_5 ,
z_37*z_10*z_40*z_28 + z_38*z_13*z_48*z_2 + z_40*z_29*z_19*z_31 ,
z_37*z_10*z_40*z_30 + z_38*z_11*z_35*z_4 + z_38*z_11*z_40*z_30 + z_38*z_13*z_48*z_4 + z_40*z_30*z_39*z_22 ,
z_38*z_11*z_35*z_6 + z_38*z_13*z_48*z_6 ,
z_38*z_11*z_38*z_11 ,
z_38*z_11*z_39*z_22 + z_38*z_13*z_49*z_7 ,
z_38*z_12*z_42*z_11 ,
z_38*z_12*z_42*z_13 + z_38*z_13*z_48*z_6 + z_39*z_22*z_35*z_6 ,
z_38*z_13*z_49*z_8 + z_38*z_13*z_54*z_56 + z_39*z_22*z_35*z_6 + z_39*z_23*z_49*z_8 ,
z_38*z_13*z_52*z_25 ,
z_38*z_13*z_52*z_26 ,
z_39*z_23*z_53*z_31 + z_40*z_29*z_19*z_31 ,
z_39*z_23*z_53*z_32 + z_39*z_21 + z_40*z_29 ,
z_39*z_23*z_53*z_33 + z_40*z_29*z_19*z_33 ,
z_39*z_23*z_53*z_34 + z_40*z_30*z_39*z_23 ,
z_40*z_28*z_16*z_32 + z_39*z_21 + z_40*z_29 ,
z_41*z_2*z_14*z_4 + z_41*z_4*z_40*z_30 + z_42*z_11*z_35*z_4 ,
z_41*z_2*z_14*z_5 + z_42*z_12*z_41*z_5 + z_42*z_13*z_48*z_5 + z_43*z_56*z_54*z_55 + z_41*z_5 + z_43*z_55 ,
z_41*z_2*z_16*z_33 + z_41*z_6*z_53*z_33 + z_42*z_13*z_52*z_26 ,
z_41*z_3*z_27*z_50 + z_42*z_13*z_50 + z_43*z_56*z_50 ,
z_41*z_3*z_27*z_51 + z_41*z_6*z_51 + z_42*z_11*z_39 ,
z_41*z_3*z_27*z_54 + z_42*z_12*z_43 + z_43*z_55*z_43 + z_43*z_56*z_54 ,
z_41*z_4*z_37*z_9 + z_41*z_6*z_52 + z_42*z_13*z_52 ,
z_41*z_4*z_37*z_10 + z_42*z_11*z_39*z_22 + z_42*z_12*z_42*z_11 + z_43*z_56*z_49*z_7 ,
z_41*z_5*z_42*z_11 + z_42*z_13*z_48*z_4 + z_43*z_56*z_49*z_7 + z_43*z_56*z_50*z_11 ,
z_41*z_5*z_42*z_12 + z_42*z_12*z_41*z_5 ,
z_41*z_6*z_48*z_2 + z_41*z_6*z_53*z_31 + z_42*z_13*z_48*z_2 ,
z_41*z_6*z_48*z_3 + z_42*z_11*z_35*z_3 + z_42*z_13*z_48*z_3 ,
z_41*z_6*z_48*z_4 + z_42*z_11*z_35*z_4 + z_42*z_13*z_48*z_4 ,
z_41*z_6*z_48*z_5 + z_42*z_12*z_41*z_5 + z_43*z_56*z_54*z_55 ,
z_41*z_6*z_48*z_6 + z_42*z_11*z_39*z_23 + z_43*z_56*z_49*z_8 + z_43*z_56*z_50*z_13 + z_43*z_56*z_54*z_56 ,
z_41*z_6*z_51*z_22 + z_42*z_11*z_35*z_4 + z_42*z_12*z_42*z_11 + z_42*z_13*z_48*z_4 + z_43*z_56*z_50*z_11 ,
z_41*z_6*z_51*z_23 + z_42*z_13*z_48*z_6 + z_43*z_56*z_50*z_13 ,
z_41*z_6*z_52*z_24 + z_42*z_11*z_35 ,
z_41*z_6*z_52*z_27 + z_42*z_11*z_39*z_23 + z_42*z_12*z_42*z_13 + z_42*z_13*z_48*z_6 + z_42*z_13*z_52*z_27 + z_43*z_56*z_49*z_8 ,
z_41*z_6*z_53*z_34 + z_42*z_11*z_39*z_23 + z_43*z_56*z_49*z_8 + z_43*z_56*z_50*z_13 + z_43*z_56*z_54*z_56 + z_41*z_3*z_27 + z_41*z_6 + z_42*z_13 + z_43*z_56 ,
z_42*z_11*z_35*z_6 + z_42*z_11*z_39*z_23 + z_42*z_13*z_48*z_6 ,
z_42*z_11*z_38*z_11 ,
z_42*z_12*z_41*z_3 + z_42*z_13*z_48*z_3 ,
z_42*z_12*z_41*z_4 + z_42*z_13*z_48*z_4 ,
z_42*z_13*z_49*z_7 + z_43*z_56*z_49*z_7 ,
z_42*z_13*z_49*z_8 + z_43*z_56*z_50*z_13 + z_43*z_56*z_54*z_56 ,
z_42*z_13*z_50*z_13 + z_43*z_56*z_49*z_8 + z_43*z_56*z_50*z_13 + z_43*z_56*z_54*z_56 ,
z_42*z_13*z_52*z_25 + z_41*z_4*z_37 ,
z_42*z_13*z_54*z_55 + z_43*z_56*z_54*z_55 ,
z_42*z_13*z_54*z_56 + z_43*z_56*z_49*z_8 ,
z_43*z_55*z_43*z_56 + z_43*z_56*z_50*z_13 ,
z_43*z_56*z_50*z_12 + z_43*z_56*z_54*z_55 ,
z_44*z_46*z_32*z_19 ,
z_44*z_46*z_34*z_48 ,
z_44*z_46*z_34*z_52 ,
z_45*z_24*z_2*z_14 + z_46*z_31*z_14 + z_46*z_34*z_48 ,
z_45*z_24*z_3*z_26 + z_45*z_26 + z_46*z_33 ,
z_45*z_24*z_3*z_27 + z_45*z_27*z_50*z_13 + z_46*z_34*z_52*z_27 + z_47*z_44*z_46*z_34 + z_45*z_27 ,
z_45*z_24*z_4*z_37 ,
z_45*z_24*z_4*z_40 + z_46*z_31*z_15 ,
z_45*z_24*z_5*z_42 + z_45*z_27*z_50 ,
z_45*z_24*z_6*z_48 + z_46*z_34*z_48 ,
z_45*z_24*z_6*z_51 ,
z_45*z_24*z_6*z_52 + z_45*z_24*z_3 + z_45*z_25*z_9 + z_45*z_26*z_45 + z_45*z_27*z_52 + z_46*z_34*z_52 ,
z_45*z_24*z_6*z_53 + z_46*z_32*z_19 ,
z_45*z_25*z_9*z_26 + z_46*z_34*z_52*z_26 + z_45*z_26 + z_46*z_33 ,
z_45*z_25*z_9*z_27 + z_45*z_27*z_50*z_13 + z_47*z_44*z_46*z_34 + z_45*z_27 ,
z_45*z_25*z_10*z_35 + z_45*z_27*z_48 + z_46*z_34*z_48 ,
z_45*z_25*z_10*z_38 + z_45*z_27*z_50 ,
z_45*z_26*z_45*z_24 + z_45*z_27*z_48 + z_46*z_31*z_14 ,
z_45*z_26*z_45*z_25 + z_46*z_34*z_52*z_25 ,
z_45*z_26*z_45*z_26 ,
z_45*z_26*z_45*z_27 + z_46*z_34*z_52*z_27 ,
z_45*z_27*z_48*z_3 ,
z_45*z_27*z_48*z_4 ,
z_45*z_27*z_48*z_5 + z_45*z_27*z_50*z_12 ,
z_45*z_27*z_48*z_6 + z_45*z_27*z_50*z_13 ,
z_45*z_27*z_50*z_11 ,
z_45*z_27*z_51*z_23 ,
z_45*z_27*z_52*z_24 + z_46*z_34*z_48 ,
z_45*z_27*z_52*z_25 ,
z_45*z_27*z_52*z_26 ,
z_45*z_27*z_52*z_27 ,
z_46*z_31*z_14*z_3 + z_45*z_24*z_3 + z_45*z_25*z_9 + z_45*z_27*z_52 ,
z_46*z_32*z_18*z_30 + z_46*z_34*z_51*z_22 ,
z_46*z_32*z_19*z_31 + z_45*z_24*z_2 + z_46*z_31 ,
z_48*z_3*z_26*z_45 + z_48*z_6*z_48*z_3 + z_51*z_22*z_35*z_3 + z_52*z_27*z_48*z_3 + z_53*z_31*z_14*z_3 + z_54*z_56*z_48*z_3 + z_48*z_6*z_52 ,
z_48*z_3*z_27*z_50 + z_48*z_4*z_38 + z_50*z_13*z_50 ,
z_48*z_3*z_27*z_51 + z_48*z_6*z_51 ,
z_48*z_3*z_27*z_52 + z_48*z_6*z_48*z_3 + z_52*z_27*z_48*z_3 + z_53*z_31*z_14*z_3 + z_54*z_56*z_48*z_3 + z_50*z_13*z_52 + z_51*z_23*z_52 + z_52*z_26*z_45 + z_52*z_27*z_52 + z_54*z_56*z_52 ,
z_48*z_3*z_27*z_54 + z_52*z_27*z_54 ,
z_48*z_4*z_35*z_5 + z_54*z_56*z_48*z_5 + z_54*z_56*z_50*z_12 + z_54*z_56*z_54*z_55 ,
z_48*z_4*z_37*z_9 + z_51*z_22*z_35*z_3 + z_54*z_56*z_48*z_3 ,
z_48*z_4*z_37*z_10 + z_50*z_12*z_42*z_11 + z_51*z_22*z_35*z_4 + z_54*z_56*z_49*z_7 ,
z_48*z_4*z_38*z_11 + z_50*z_12*z_42*z_11 + z_54*z_55*z_42*z_11 ,
z_48*z_4*z_40*z_30 + z_48*z_5*z_42*z_11 + z_50*z_12*z_42*z_11 + z_52*z_27*z_48*z_4 + z_53*z_31*z_15*z_30 + z_54*z_55*z_42*z_11 ,
z_48*z_5*z_42*z_12 + z_50*z_12*z_42*z_12 + z_52*z_27*z_50*z_12 + z_53*z_34*z_48*z_5 + z_54*z_56*z_48*z_5 + z_54*z_56*z_54*z_55 + z_48*z_5 + z_50*z_12 + z_54*z_55 ,
z_48*z_6*z_48*z_2 ,
z_48*z_6*z_48*z_4 + z_48*z_6*z_51*z_22 + z_54*z_55*z_42*z_11 ,
z_48*z_6*z_48*z_5 + z_52*z_27*z_50*z_12 + z_48*z_5 + z_50*z_12 + z_54*z_55 ,
z_48*z_6*z_48*z_6 + z_52*z_27*z_54*z_56 ,
z_48*z_6*z_49*z_8 + z_52*z_27*z_54*z_56 ,
z_48*z_6*z_51*z_23 + z_49*z_8*z_54*z_56 + z_50*z_13*z_52*z_27 + z_51*z_23*z_52*z_27 + z_52*z_27*z_48*z_6 + z_52*z_27*z_50*z_13 + z_52*z_27*z_51*z_23 + z_52*z_27*z_53*z_34 + z_53*z_34*z_51*z_23 + z_53*z_34*z_52*z_27 + z_54*z_55*z_43*z_56 + z_54*z_56*z_49*z_8 + z_54*z_56*z_50*z_13 + z_54*z_56*z_52*z_27 + z_54*z_56*z_54*z_56 ,
z_48*z_6*z_52*z_24 + z_52*z_25*z_10*z_35 + z_48*z_6*z_48 + z_51*z_22*z_35 + z_54*z_56*z_48 ,
z_48*z_6*z_52*z_26 + z_54*z_56*z_52*z_26 ,
z_48*z_6*z_52*z_27 + z_50*z_13*z_52*z_27 + z_51*z_23*z_52*z_27 + z_52*z_27*z_52*z_27 ,
z_48*z_6*z_53*z_32 ,
z_48*z_6*z_53*z_33 + z_52*z_27*z_52*z_26 + z_53*z_34*z_52*z_26 + z_54*z_56*z_52*z_26 ,
z_48*z_6*z_53*z_34 + z_51*z_23*z_49*z_8 + z_52*z_27*z_48*z_6 + z_52*z_27*z_54*z_56 + z_53*z_34*z_51*z_23 + z_54*z_55*z_43*z_56 + z_54*z_56*z_50*z_13 + z_54*z_56*z_52*z_27 ,
z_48*z_6*z_54*z_56 + z_51*z_23*z_49*z_8 + z_52*z_27*z_54*z_56 + z_54*z_56*z_52*z_27 + z_54*z_56*z_54*z_56 ,
z_49*z_7*z_36*z_7 + z_49*z_8*z_51*z_22 + z_54*z_55*z_42*z_11 ,
z_49*z_7*z_36*z_8 ,
z_49*z_8*z_51*z_23 + z_49*z_8*z_54*z_56 + z_52*z_27*z_54*z_56 + z_54*z_55*z_43*z_56 + z_54*z_56*z_49*z_8 + z_54*z_56*z_50*z_13 + z_54*z_56*z_52*z_27 + z_54*z_56*z_54*z_56 ,
z_49*z_8*z_54*z_55 + z_54*z_56*z_48*z_5 + z_54*z_56*z_54*z_55 ,
z_50*z_11*z_39*z_22 + z_51*z_22*z_35*z_4 + z_51*z_23*z_49*z_7 + z_54*z_55*z_42*z_11 + z_54*z_56*z_50*z_11 ,
z_50*z_11*z_39*z_23 + z_52*z_26*z_45*z_27 + z_52*z_27*z_50*z_13 + z_52*z_27*z_51*z_23 + z_53*z_34*z_51*z_23 + z_54*z_56*z_50*z_13 + z_54*z_56*z_54*z_56 + z_52*z_24*z_6 + z_48*z_6 + z_49*z_8 + z_50*z_13 + z_51*z_23 + z_54*z_56 ,
z_50*z_12*z_42*z_13 + z_51*z_23*z_49*z_8 + z_52*z_27*z_54*z_56 + z_54*z_55*z_43*z_56 + z_54*z_56*z_49*z_8 + z_54*z_56*z_50*z_13 ,
z_50*z_13*z_49*z_7 + z_51*z_23*z_49*z_7 + z_54*z_55*z_42*z_11 + z_54*z_56*z_49*z_7 + z_54*z_56*z_50*z_11 ,
z_50*z_13*z_49*z_8 + z_51*z_23*z_49*z_8 + z_52*z_27*z_54*z_56 + z_54*z_56*z_49*z_8 ,
z_50*z_13*z_50*z_12 + z_54*z_56*z_48*z_5 + z_54*z_56*z_50*z_12 + z_54*z_56*z_54*z_55 ,
z_50*z_13*z_50*z_13 + z_52*z_27*z_54*z_56 ,
z_50*z_13*z_52*z_25 + z_48*z_4*z_37 ,
z_50*z_13*z_52*z_26 ,
z_50*z_13*z_54*z_55 + z_54*z_56*z_50*z_12 + z_54*z_56*z_54*z_55 ,
z_50*z_13*z_54*z_56 + z_51*z_23*z_49*z_8 + z_52*z_27*z_54*z_56 + z_54*z_55*z_43*z_56 + z_54*z_56*z_52*z_27 + z_54*z_56*z_54*z_56 ,
z_51*z_22*z_35*z_6 + z_51*z_23*z_49*z_8 + z_52*z_27*z_54*z_56 + z_54*z_55*z_43*z_56 + z_54*z_56*z_49*z_8 + z_54*z_56*z_52*z_27 + z_54*z_56*z_54*z_56 ,
z_51*z_22*z_38*z_11 + z_51*z_23*z_49*z_7 + z_54*z_55*z_42*z_11 + z_54*z_56*z_50*z_11 ,
z_51*z_22*z_38*z_13 + z_52*z_26*z_45*z_27 + z_52*z_27*z_50*z_13 + z_52*z_27*z_51*z_23 + z_53*z_34*z_51*z_23 + z_54*z_56*z_50*z_13 + z_54*z_56*z_54*z_56 + z_52*z_24*z_6 + z_48*z_6 + z_49*z_8 + z_50*z_13 + z_51*z_23 + z_54*z_56 ,
z_51*z_22*z_40*z_30 + z_53*z_34*z_51*z_22 ,
z_51*z_23*z_52*z_26 ,
z_52*z_24*z_3*z_26 + z_53*z_33*z_47*z_44 + z_53*z_34*z_52*z_26 + z_48*z_3*z_26 + z_52*z_26 ,
z_52*z_24*z_4*z_37 + z_52*z_26*z_45*z_25 + z_48*z_4*z_37 ,
z_52*z_24*z_4*z_38 + z_52*z_24*z_5*z_42 + z_48*z_5*z_42 + z_50*z_12*z_42 + z_50*z_13*z_50 + z_54*z_55*z_42 ,
z_52*z_24*z_4*z_40 + z_48*z_2*z_15 + z_53*z_31*z_15 ,
z_52*z_24*z_5*z_43 + z_52*z_24*z_6*z_54 + z_48*z_6*z_54 + z_50*z_12*z_43 + z_54*z_55*z_43 ,
z_52*z_24*z_6*z_48 + z_48*z_4*z_35 + z_48*z_6*z_48 + z_53*z_34*z_48 ,
z_52*z_24*z_6*z_51 + z_48*z_6*z_51 + z_49*z_8*z_51 ,
z_52*z_24*z_6*z_52 + z_52*z_27*z_48*z_3 + z_53*z_31*z_14*z_3 + z_48*z_6*z_52 + z_52*z_26*z_45 + z_52*z_27*z_52 ,
z_52*z_24*z_6*z_53 + z_48*z_6*z_53 + z_53*z_32*z_19 ,
z_52*z_25*z_9*z_26 + z_52*z_27*z_52*z_26 + z_53*z_33*z_47*z_44 + z_53*z_34*z_52*z_26 + z_54*z_56*z_52*z_26 + z_48*z_3*z_26 + z_52*z_26 ,
z_52*z_26*z_45*z_24 + z_48*z_6*z_48 + z_51*z_22*z_35 + z_53*z_34*z_48 + z_54*z_56*z_48 ,
z_52*z_26*z_45*z_26 + z_53*z_34*z_52*z_26 + z_54*z_56*z_52*z_26 ,
z_52*z_27*z_48*z_5 + z_53*z_34*z_48*z_5 + z_48*z_5 + z_50*z_12 + z_54*z_55 ,
z_52*z_27*z_52*z_24 + z_53*z_34*z_48 ,
z_52*z_27*z_52*z_25 ,
z_52*z_27*z_53*z_31 + z_53*z_32*z_19*z_31 ,
z_52*z_27*z_53*z_32 + z_51*z_21 + z_53*z_32 ,
z_52*z_27*z_53*z_33 + z_53*z_34*z_52*z_26 ,
z_54*z_55*z_42*z_13 + z_54*z_55*z_43*z_56 + z_54*z_56*z_49*z_8 + z_54*z_56*z_50*z_13 + z_54*z_56*z_52*z_27 + z_54*z_56*z_54*z_56 ,
z_54*z_56*z_48*z_4 + z_54*z_56*z_49*z_7 ,
z_54*z_56*z_48*z_6 + z_54*z_56*z_49*z_8 + z_54*z_56*z_50*z_13 + z_54*z_56*z_54*z_56 ,
z_54*z_56*z_52*z_24 + z_48*z_4*z_35 ,
z_54*z_56*z_52*z_25 ,
z_55*z_41*z_5*z_42 + z_55*z_42 + z_56*z_50 ,
z_55*z_41*z_6*z_48 + z_55*z_41 + z_56*z_48 ,
z_55*z_41*z_6*z_51 + z_56*z_52*z_27*z_51 ,
z_55*z_41*z_6*z_52 + z_56*z_48*z_3 + z_56*z_52 ,
z_55*z_41*z_6*z_53 ,
z_55*z_42*z_11*z_35 + z_56*z_52*z_24 ,
z_55*z_42*z_11*z_38 ,
z_55*z_42*z_11*z_39 ,
z_55*z_42*z_11*z_40 + z_56*z_48*z_4*z_40 + z_56*z_50*z_11*z_40 ,
z_55*z_42*z_13*z_48 + z_56*z_52*z_24 ,
z_55*z_42*z_13*z_49 + z_56*z_54*z_56*z_49 ,
z_55*z_42*z_13*z_50 + z_56*z_54*z_55*z_42 + z_56*z_54*z_56*z_50 ,
z_55*z_42*z_13*z_52 + z_56*z_52*z_27*z_52 + z_56*z_48*z_3 + z_56*z_52 ,
z_55*z_42*z_13*z_54 + z_56*z_50*z_13*z_54 + z_56*z_52*z_27*z_54 ,
z_55*z_43*z_56*z_49 + z_56*z_50*z_13*z_49 ,
z_55*z_43*z_56*z_50 + z_56*z_54*z_55*z_42 + z_56*z_54*z_56*z_50 + z_55*z_42 + z_56*z_50 ,
z_55*z_43*z_56*z_54 + z_56*z_54*z_55*z_43 ,
z_56*z_48*z_3*z_27 + z_55*z_42*z_13 + z_55*z_43*z_56 + z_56*z_48*z_6 ,
z_56*z_48*z_4*z_35 + z_55*z_41 + z_56*z_48 ,
z_56*z_48*z_4*z_37 + z_56*z_52*z_25 ,
z_56*z_48*z_4*z_38 + z_56*z_54*z_55*z_42 + z_56*z_54*z_56*z_50 + z_55*z_42 + z_56*z_50 ,
z_56*z_48*z_5*z_42 + z_55*z_42 + z_56*z_50 ,
z_56*z_48*z_6*z_48 + z_55*z_41 + z_56*z_48 ,
z_56*z_48*z_6*z_49 + z_56*z_50*z_13*z_49 + z_56*z_54*z_56*z_49 ,
z_56*z_48*z_6*z_51 + z_56*z_52*z_27*z_51 ,
z_56*z_48*z_6*z_52 + z_56*z_48*z_3 + z_56*z_52 ,
z_56*z_48*z_6*z_53 ,
z_56*z_48*z_6*z_54 + z_56*z_50*z_13*z_54 + z_56*z_54*z_55*z_43 ,
z_56*z_49*z_7*z_36 ,
z_56*z_49*z_8*z_51 + z_56*z_52*z_27*z_51 ,
z_56*z_50*z_11*z_39 ,
z_56*z_50*z_12*z_42 + z_56*z_54*z_56*z_50 + z_55*z_42 + z_56*z_50 ,
z_56*z_50*z_13*z_50 + z_56*z_54*z_55*z_42 + z_56*z_54*z_56*z_50 ,
z_56*z_50*z_13*z_52 + z_56*z_52*z_27*z_52 + z_56*z_48*z_3 + z_56*z_52 ,
z_56*z_52*z_24*z_3 + z_56*z_52*z_27*z_52 ,
z_56*z_52*z_24*z_5 + z_56*z_48*z_5 + z_56*z_50*z_12 + z_56*z_54*z_55 ,
z_56*z_52*z_25*z_9 + z_56*z_52*z_27*z_52 ,
z_56*z_52*z_26*z_45 + z_56*z_52*z_27*z_52 + z_56*z_54*z_56*z_52 + z_56*z_48*z_3 + z_56*z_52 ,
z_56*z_52*z_27*z_48 + z_56*z_52*z_24 ,
z_56*z_52*z_27*z_49 ,
z_56*z_52*z_27*z_50 + z_56*z_54*z_55*z_42 + z_56*z_54*z_56*z_50 + z_55*z_42 + z_56*z_50 ,
z_56*z_52*z_27*z_53 ,
z_56*z_54*z_56*z_48 + z_56*z_52*z_24 ,
z_2*z_14*z_3 + z_3*z_26*z_45 + z_6*z_52 ,
z_2*z_14*z_6 + z_6*z_53*z_34 ,
z_2*z_15*z_30 + z_4*z_37*z_10 + z_4*z_38*z_11 + z_4*z_40*z_30 + z_6*z_51*z_22 ,
z_2*z_16*z_31 + z_6*z_48*z_2 + z_6*z_53*z_31 ,
z_2*z_16*z_32 + z_6*z_53*z_32 ,
z_2*z_16*z_34 + z_6*z_48*z_6 + z_6*z_49*z_8 + z_6*z_53*z_34 ,
z_3*z_27*z_48 + z_6*z_52*z_24 + z_4*z_35 ,
z_3*z_27*z_49 ,
z_3*z_27*z_53 + z_6*z_53 ,
z_4*z_35*z_3 ,
z_4*z_35*z_4 ,
z_4*z_35*z_6 + z_6*z_49*z_8 ,
z_4*z_38*z_12 + z_5*z_42*z_12 + z_6*z_48*z_5 ,
z_4*z_38*z_13 + z_6*z_54*z_56 ,
z_4*z_40*z_28 + z_6*z_48*z_2 ,
z_4*z_40*z_29 + z_6*z_53*z_32 ,
z_5*z_42*z_13 + z_6*z_49*z_8 + z_6*z_54*z_56 ,
z_5*z_43*z_55 ,
z_5*z_43*z_56 + z_6*z_49*z_8 + z_6*z_54*z_56 ,
z_6*z_49*z_7 ,
z_6*z_51*z_21 + z_6*z_53*z_32 ,
z_6*z_52*z_25 + z_4*z_37 ,
z_6*z_54*z_55 ,
z_7*z_38*z_12 + z_8*z_54*z_55 ,
z_8*z_49*z_7 ,
z_8*z_49*z_8 ,
z_8*z_50*z_12 + z_8*z_54*z_55 ,
z_8*z_51*z_21 ,
z_9*z_27*z_49 ,
z_9*z_27*z_51 ,
z_10*z_35*z_3 ,
z_10*z_35*z_6 + z_10*z_38*z_13 ,
z_10*z_38*z_11 ,
z_10*z_40*z_29 ,
z_11*z_35*z_5 + z_12*z_41*z_5 + z_13*z_48*z_5 + z_13*z_50*z_12 + z_13*z_54*z_55 ,
z_11*z_37*z_9 + z_12*z_41*z_3 + z_13*z_48*z_3 ,
z_11*z_37*z_10 + z_11*z_38*z_11 + z_12*z_41*z_4 + z_13*z_48*z_4 ,
z_11*z_38*z_12 + z_12*z_41*z_5 + z_13*z_48*z_5 ,
z_11*z_38*z_13 ,
z_11*z_39*z_21 ,
z_11*z_40*z_28 + z_13*z_48*z_2 ,
z_11*z_40*z_29 ,
z_12*z_41*z_2 + z_13*z_48*z_2 ,
z_12*z_41*z_6 + z_13*z_48*z_6 ,
z_12*z_43*z_55 + z_13*z_54*z_55 ,
z_12*z_43*z_56 + z_13*z_54*z_56 ,
z_13*z_50*z_11 ,
z_13*z_52*z_24 + z_11*z_35 ,
z_14*z_4*z_35 + z_16*z_34*z_48 ,
z_14*z_4*z_37 + z_15*z_30*z_37 ,
z_14*z_4*z_38 + z_15*z_30*z_38 ,
z_14*z_4*z_40 + z_16*z_31*z_15 ,
z_14*z_5*z_43 ,
z_14*z_6*z_48 + z_16*z_34*z_48 ,
z_14*z_6*z_49 ,
z_14*z_6*z_51 + z_16*z_34*z_51 ,
z_14*z_6*z_53 ,
z_14*z_6*z_54 ,
z_15*z_30*z_39 + z_16*z_34*z_51 ,
z_16*z_32*z_17 + z_16*z_34*z_51 ,
z_16*z_33*z_47 ,
z_17*z_23*z_48 ,
z_17*z_23*z_52 + z_19*z_34*z_52 ,
z_17*z_23*z_53 ,
z_18*z_30*z_38 ,
z_19*z_34*z_48 ,
z_21*z_17*z_23 + z_23*z_53*z_34 ,
z_21*z_18*z_30 + z_22*z_40*z_30 + z_23*z_48*z_4 ,
z_21*z_19*z_31 + z_23*z_53*z_31 ,
z_21*z_19*z_33 + z_23*z_53*z_33 ,
z_22*z_38*z_12 + z_23*z_48*z_5 ,
z_22*z_40*z_28 + z_23*z_53*z_31 ,
z_22*z_40*z_29 ,
z_23*z_48*z_2 ,
z_23*z_48*z_3 ,
z_23*z_48*z_6 ,
z_23*z_52*z_24 + z_22*z_35 ,
z_23*z_52*z_25 ,
z_24*z_2*z_15 + z_24*z_4*z_40 ,
z_24*z_2*z_16 + z_24*z_6*z_53 ,
z_24*z_4*z_35 ,
z_24*z_6*z_49 + z_27*z_49 ,
z_27*z_48*z_2 + z_27*z_53*z_31 ,
z_27*z_49*z_7 ,
z_27*z_49*z_8 ,
z_27*z_51*z_21 + z_27*z_53*z_32 ,
z_27*z_54*z_55 ,
z_28*z_16*z_34 + z_30*z_35*z_6 ,
z_31*z_14*z_4 + z_31*z_15*z_30 ,
z_31*z_14*z_6 + z_34*z_51*z_23 ,
z_32*z_17*z_23 + z_34*z_51*z_23 ,
z_32*z_19*z_33 + z_34*z_52*z_26 ,
z_32*z_19*z_34 + z_34*z_51*z_23 ,
z_34*z_48*z_2 ,
z_34*z_48*z_3 ,
z_34*z_48*z_4 ,
z_34*z_48*z_6 ,
z_34*z_51*z_21 ,
z_34*z_52*z_24 + z_31*z_14 + z_34*z_48 ,
z_35*z_4*z_35 ,
z_35*z_4*z_40 + z_37*z_10*z_40 + z_38*z_11*z_40 + z_39*z_21*z_18 + z_40*z_28*z_15 ,
z_35*z_6*z_48 + z_37*z_10*z_35 + z_38*z_13*z_48 + z_39*z_22*z_35 + z_39*z_23*z_48 ,
z_35*z_6*z_53 + z_40*z_28*z_16 ,
z_36*z_7*z_38 + z_36*z_8*z_50 ,
z_36*z_8*z_49 ,
z_37*z_10*z_38 + z_38*z_11*z_38 + z_38*z_12*z_42 ,
z_38*z_11*z_37 ,
z_38*z_12*z_41 + z_38*z_13*z_48 ,
z_38*z_12*z_43 + z_38*z_13*z_54 ,
z_38*z_13*z_50 ,
z_39*z_21*z_19 + z_40*z_29*z_19 ,
z_39*z_22*z_40 + z_40*z_29*z_18 ,
z_41*z_4*z_35 + z_41*z_6*z_48 + z_42*z_11*z_35 + z_42*z_12*z_41 ,
z_41*z_4*z_38 + z_43*z_56*z_50 ,
z_41*z_5*z_43 + z_42*z_13*z_54 + z_43*z_56*z_54 ,
z_41*z_6*z_49 + z_42*z_13*z_49 + z_43*z_56*z_49 ,
z_41*z_6*z_54 + z_43*z_55*z_43 ,
z_42*z_11*z_37 ,
z_43*z_55*z_41 ,
z_43*z_55*z_42 + z_43*z_56*z_50 ,
z_43*z_56*z_48 ,
z_43*z_56*z_52 ,
z_44*z_46*z_31 ,
z_44*z_46*z_33 ,
z_45*z_27*z_49 ,
z_45*z_27*z_53 + z_46*z_32*z_19 ,
z_45*z_27*z_54 ,
z_46*z_32*z_17 + z_46*z_34*z_51 ,
z_46*z_33*z_47 ,
z_48*z_2*z_14 + z_48*z_4*z_35 + z_48*z_6*z_48 + z_51*z_22*z_35 + z_52*z_27*z_48 + z_53*z_31*z_14 + z_53*z_34*z_48 + z_54*z_56*z_48 ,
z_48*z_2*z_16 + z_48*z_6*z_53 ,
z_48*z_5*z_43 + z_48*z_6*z_54 + z_50*z_12*z_43 + z_50*z_13*z_54 + z_52*z_27*z_54 ,
z_49*z_7*z_38 + z_54*z_55*z_42 ,
z_49*z_8*z_49 ,
z_49*z_8*z_50 + z_54*z_55*z_42 ,
z_50*z_11*z_35 + z_54*z_56*z_48 ,
z_50*z_11*z_37 ,
z_50*z_11*z_38 ,
z_50*z_12*z_41 + z_54*z_56*z_48 ,
z_50*z_13*z_48 + z_54*z_56*z_48 ,
z_51*z_21*z_17 + z_53*z_34*z_51 ,
z_51*z_21*z_18 + z_51*z_22*z_40 ,
z_51*z_21*z_19 + z_53*z_32*z_19 ,
z_51*z_23*z_48 + z_53*z_34*z_48 ,
z_51*z_23*z_53 + z_53*z_32*z_19 ,
z_52*z_24*z_2 + z_48*z_2 + z_53*z_31 ,
z_54*z_55*z_41 + z_54*z_56*z_48 ,
z_55*z_41*z_2 ,
z_55*z_41*z_3 + z_56*z_48*z_3 ,
z_55*z_41*z_4 + z_56*z_48*z_4 ,
z_55*z_42*z_12 + z_56*z_48*z_5 + z_56*z_54*z_55 ,
z_55*z_43*z_55 + z_56*z_50*z_12 + z_56*z_54*z_55 ,
z_56*z_48*z_2 ,

The projective resolutions of the simple modules.


Simple Module Number 1



The projective resolution of simple module no. 1 is graded.



Simple Module Number 2



The projective resolution of simple module no. 2 is not graded.



Simple Module Number 3



The projective resolution of simple module no. 3 is not graded.



Simple Module Number 4



The projective resolution of simple module no. 4 is not graded.



Simple Module Number 5



The projective resolution of simple module no. 5 is not graded.



Simple Module Number 6



The projective resolution of simple module no. 6 is not graded.



Simple Module Number 7



The projective resolution of simple module no. 7 is not graded.



Simple Module Number 8



The projective resolution of simple module no. 8 is graded.



Simple Module Number 9



The projective resolution of simple module no. 9 is not graded.



Simple Module Number 10



The projective resolution of simple module no. 10 is not graded.



Simple Module Number 11



The projective resolution of simple module no. 11 is not graded.



Simple Module Number 12



The projective resolution of simple module no. 12 is not graded.



Simple Module Number 13



The projective resolution of simple module no. 13 is not graded.



Simple Module Number 14



The projective resolution of simple module no. 14 is not graded.



Simple Module Number 15



The projective resolution of simple module no. 15 is not graded.



Simple Module Number 16



The projective resolution of simple module no. 16 is not graded.



Simple Module Number 17



The projective resolution of simple module no. 17 is not graded.



Simple Module Number 18



The projective resolution of simple module no. 18 is not graded.