# 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 7. . The dimension of M is 11481 .

The dimensions of the irreducible submodules modules are 20, 14, 8, 6, 1 .

The simple module number 1 has dimension 20 and corresponds to the partition [ 4, 2, 1 ] .
The simple module number 2 has dimension 14 and corresponds to the partition [ 5, 2 ] .
The simple module number 3 has dimension 8 and corresponds to the partition [ 4, 3 ] .
The simple module number 4 has dimension 6 and corresponds to the partition [ 6, 1 ] .
The simple module number 5 has dimension 1 and corresponds to the partition [ 7 ] .

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

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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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

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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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, 2, 2, 2, 2, 2, 2, 2, 2, 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, 5

3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4

The module M has socle filtration (socle series)
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4

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, 2, 2, 2, 2, 2, 2, 2, 2, 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, 5

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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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

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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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

#### The module M has simple direct summands:

7 copies of simple module number 2
7 copies of simple module number 4
5 copies of simple module number 5

4
3
4

socle layers
4
3
4

2, 5
2, 5

socle layers
2, 5
2, 5

2
2, 5
1
5
2

socle layers
2
5
1
2, 5
2

4
3
4
4
3
4

socle layers
4
3
4
4
3
4

3
4
4
3
4
4
3

socle layers
3
4
4
3
4
4
3

1, 5
1, 5
2, 5
5
1

socle layers
1
5
2, 5
1, 5
1, 5

1
1, 5
2, 5
2, 5
1, 5
1

socle layers
1
1, 5
2, 5
2, 5
1, 5
1

2, 2, 5
1, 2, 5
1, 5
2, 5

socle layers
2, 5
1, 5
1, 2, 5
2, 2, 5

2
2, 2, 5
1, 2, 5
1, 5
2, 5
2

socle layers
2
2, 5
1, 5
1, 2, 5
2, 2, 5
2

4
3, 4
3, 4
4, 4
3, 4
3, 4
4

socle layers
4
3, 4
3, 4
4, 4
3, 4
3, 4
4

5
1, 2, 5
1, 2, 5, 5
1, 2, 5, 5
1, 2, 5
5

socle layers
5
1, 2, 5
1, 2, 5, 5
1, 2, 5, 5
1, 2, 5
5

2, 2, 5
1, 2, 2, 2, 5, 5
1, 1, 5, 5
1, 2, 5, 5
2, 2, 5

socle layers
2, 2, 5
1, 2, 5, 5
1, 1, 5, 5
1, 2, 2, 2, 5, 5
2, 2, 5

## 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 112, 128, 48, 80, 144 .

#### The cartan matrix of A is

4, 2, 0, 0, 4
2, 6, 0, 0, 4
0, 0, 3, 4, 0
0, 0, 4, 8, 0
4, 4, 0, 0, 8

The determinant of the Cartan matrix is 512.

(1). 1, 2, 5
(2). 3, 4

1
1, 5
2, 5
2, 5
1, 5
1

socle layers
1
1, 5
2, 5
2, 5
1, 5
1

2
2, 2, 5
1, 2, 5
1, 5
2, 5
2

socle layers
2
2, 5
1, 5
1, 2, 5
2, 2, 5
2

3
4
4
3
4
4
3

socle layers
3
4
4
3
4
4
3

4
3, 4
3, 4
4, 4
3, 4
3, 4
4

socle layers
4
3, 4
3, 4
4, 4
3, 4
3, 4
4

#### Projective module number 5

5
1, 2, 5
1, 2, 5, 5
1, 2, 5, 5
1, 2, 5
5

socle layers
5
1, 2, 5
1, 2, 5, 5
1, 2, 5, 5
1, 2, 5
5

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

## The Basic Algebra H of the Schur Algebra

The dimension of H is 327 .

The dimensions of the irreducible H-modules are 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.

Simple H-module 1 corresponds to the direct summand of M isomorphic to simple A-module 4.
Simple H-module 2 corresponds to the direct summand of M isomorphic to simple A-module 2.
Simple H-module 3 corresponds to the direct summand of M isomorphic to simple A-module 5.
Simple H-module 4 corresponds to the direct summand of M isomorphic to the nonsimple A-module 1.
Simple H-module 5 corresponds to the direct summand of M isomorphic to the nonsimple A-module 2.
Simple H-module 6 corresponds to the direct summand of M isomorphic to the nonsimple A-module 3.
Simple H-module 7 corresponds to the direct summand of M isomorphic to the nonsimple A-module 4.
Simple H-module 8 corresponds to the direct summand of M isomorphic to the nonsimple A-module 5.
Simple H-module 9 corresponds to the direct summand of M isomorphic to the nonsimple A-module 6.
Simple H-module 10 corresponds to the direct summand of M isomorphic to the nonsimple A-module 7.
Simple H-module 11 corresponds to the direct summand of M isomorphic to the nonsimple A-module 8.
Simple H-module 12 corresponds to the direct summand of M isomorphic to the nonsimple A-module 9.
Simple H-module 13 corresponds to the direct summand of M isomorphic to the nonsimple A-module 10.
Simple H-module 14 corresponds to the direct summand of M isomorphic to the nonsimple A-module 11.
Simple H-module 15 corresponds to the direct summand of M isomorphic to the nonsimple A-module 12.

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

The dimensions of the projective modules of H are 20, 23, 31, 10, 8, 12, 4, 8, 19, 6, 42, 21, 22, 64, 37 .

#### The cartan matrix of H is

4, 1, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 4, 4
1, 3, 3, 0, 0, 0, 0, 1, 0, 0, 4, 2, 1, 6, 2
2, 3, 6, 0, 0, 0, 0, 1, 0, 0, 4, 2, 1, 8, 4
0, 0, 0, 3, 1, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0
0, 0, 0, 1, 2, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0
0, 0, 0, 2, 2, 3, 1, 0, 4, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0
0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 0
0, 0, 0, 4, 2, 4, 1, 0, 8, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1
2, 4, 4, 0, 0, 0, 0, 2, 0, 1, 8, 4, 3, 10, 4
0, 2, 2, 0, 0, 0, 0, 1, 0, 1, 4, 3, 1, 5, 2
3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 3, 1, 4, 4, 4
4, 6, 8, 0, 0, 0, 0, 2, 0, 1, 10, 5, 4, 16, 8
4, 2, 4, 0, 0, 0, 0, 0, 0, 1, 4, 2, 4, 8, 8

The determinant of the Cartan matrix is 1.

#### The blocks of H consist of the following irreducible modules:

(1). 1, 2, 3, 8, 10, 11, 12, 13, 14, 15
(2). 4, 5, 6, 7, 9

1
13, 15
1, 14
3, 11, 15
13, 14
2, 15
1, 14
3, 11
13, 14
15
1

socle layers
1
15
13, 14
3, 11
1, 14
2, 15
13, 14
3, 11, 15
1, 14
13, 15
1

2
14
3, 11
12, 13, 14
11, 15
1, 8, 14
2, 15
14
3, 11
12
11
14
2
14
3

socle layers
2
14
11
12
11
14
2
8, 14
3, 11
12, 13, 14
11, 15
1, 14
2, 3, 15
14
3

3
14
2, 3, 15
1, 14
3, 11, 15
12, 13, 14, 14
3, 11, 15
1, 8, 14
2, 15
14
3, 11
12
11
14
2
14
3

socle layers
3
14
2
14
11
12
3, 11
14
2, 15
1, 8, 14
3, 11, 15
12, 13, 14, 14
3, 11, 15
1, 14
2, 3, 15
14
3

4
9
6
5, 9
4
9
6
9
4

socle layers
4
9
6
9
4
5, 9
6
9
4

5
6, 7
5, 9
4, 6
9

socle layers
5
6, 7
5, 9
4, 6
9

6
5, 9
4, 7
5, 9
6, 6
9
4
9

socle layers
6
9
4
5, 9
6, 7
5, 9
4, 6
9

7
5
6
9

socle layers
7
5
6
9

8
11
12
11
14
2
14
3

socle layers
8
11
12
11
14
2
14
3

9
4, 6
5, 9, 9
4, 6, 7
5, 9, 9
4, 6
9, 9
4, 6
9

socle layers
9
4, 6
9, 9
4, 6
5, 9, 9
4, 6, 7
5, 9, 9
4, 6
9

10
12, 13
11
14
15

socle layers
10
12, 13
11
14
15

#### Projective module number 11

11
8, 12, 13, 14
2, 10, 11, 11, 15
1, 8, 12, 13, 14, 14
2, 3, 11, 11, 15
12, 13, 14, 14
3, 11, 11, 15
1, 12, 14, 14
2, 11, 15
14, 14
2, 3
14
3

socle layers
11
12
11
14, 14
2, 2
8, 8, 14, 14
11, 11
12, 12, 13
3, 10, 11, 11, 11, 15
1, 12, 13, 14, 14, 14
2, 2, 3, 11, 13, 15, 15
1, 14, 14, 14
3, 3, 15

12
10, 11
8, 12, 13, 14
2, 11, 15
14
3, 11
12, 14
11, 15
14
2
14
3

socle layers
12
11
14
2
8, 14
11
12
10, 11
12, 13, 14
2, 3, 11, 15
14, 14
3, 15

#### Projective module number 13

13
1, 10, 11
12, 13, 13, 14, 15
2, 11, 15
1, 14, 14
3, 11, 15
13, 14
15
1

socle layers
13
11
1, 14
2, 15
10, 13, 14
3, 11, 12, 13, 15
1, 11, 14
13, 14, 15
1, 15

#### Projective module number 14

14
2, 3, 11, 15
1, 12, 13, 14, 14
2, 3, 10, 11, 11, 15, 15
1, 8, 12, 13, 13, 14, 14, 14, 14
2, 3, 3, 11, 11, 15, 15
1, 8, 12, 13, 14, 14, 14
2, 3, 11, 11, 15, 15
1, 12, 14, 14
3, 11, 11, 15
12, 14
2, 11
14, 14
2, 3
14
3

socle layers
14
2
14
11, 11
12, 12
3, 11, 11
14, 14
2, 2, 15
1, 8, 8, 14, 14, 14
2, 3, 11, 11, 15
12, 12, 13, 13, 14, 14, 14
3, 3, 10, 11, 11, 11, 15, 15
1, 1, 12, 13, 14, 14, 14
2, 2, 3, 3, 11, 13, 15, 15, 15
1, 14, 14, 14
3, 3, 15

#### Projective module number 15

15
1, 14
3, 11, 13, 15, 15
1, 12, 13, 14, 14
2, 3, 10, 11, 15, 15
1, 13, 14, 14
2, 3, 11, 15
12, 13, 14, 14
3, 11, 15
1, 14
15

socle layers
15
1, 14
3, 11, 15
12, 13, 14, 14
2, 3, 11, 15
1, 13, 14, 14
2, 3, 10, 11, 15, 15
1, 12, 13, 14, 14
3, 11, 13, 15, 15
1, 14
15

### A presentation for H is the quotient of a polynomial ring P in noncommuting variables b_1 , b_2 , b_3 , b_4 , b_5 , b_6 , b_7 , b_8 , b_9 , b_10 , b_11 , b_12 , b_13 , b_14 , b_15 , z_1 , z_2 , z_3 , z_4 , z_5 , z_6 , z_7 , z_8 , z_9 , z_10 , z_11 , z_12 , z_13 , z_14 , z_15 , z_16 , z_17 , z_18 , z_19 , z_20 , z_21 , z_22 , z_23 , z_24 , z_25 , z_26 , z_27 , z_28 , z_29 , z_30 , by an ideal of relations.

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:
z_25*z_3*z_27*z_17*z_21*z_16*z_11 + z_27*z_19*z_25*z_3*z_27 + z_28*z_29*z_1*z_24 + z_27*z_19*z_27 + z_28*z_30*z_27 ,
z_4*z_28*z_29*z_2*z_30*z_26 + z_4*z_26*z_4*z_26 + z_4*z_28*z_30*z_26 ,
z_4*z_28*z_30*z_27*z_19*z_26 + z_4*z_28*z_30*z_26 ,
z_4*z_28*z_30*z_27*z_19*z_28 ,
z_4*z_28*z_30*z_28*z_29*z_2 + z_4*z_25*z_3*z_28 ,
z_5*z_13*z_9*z_12*z_5*z_13 + z_5*z_13*z_8*z_6 ,
z_9*z_12*z_5*z_13*z_9*z_12 + z_8*z_6*z_9*z_12 ,
z_17*z_21*z_19*z_25*z_3*z_26 + z_19*z_26*z_4*z_26 + z_19*z_26 ,
z_19*z_27*z_19*z_25*z_3*z_27 ,
z_21*z_19*z_27*z_19*z_25*z_3 + z_21*z_18*z_24*z_19 + z_21*z_19*z_28*z_30 ,
z_25*z_3*z_27*z_17*z_21*z_19 + z_26*z_4*z_26*z_4 + z_27*z_19*z_27*z_19 + z_28*z_29*z_2*z_30 + z_28*z_30*z_26*z_4 + z_28*z_30*z_27*z_19 + z_26*z_4 + z_27*z_19 ,
z_30*z_28*z_30*z_27*z_19*z_26 ,
z_1*z_22*z_2*z_30*z_26 + z_2*z_30*z_28*z_30*z_26 ,
z_1*z_24*z_18*z_22*z_2 ,
z_1*z_24*z_18*z_24*z_18 + z_2*z_30*z_28*z_29*z_1 ,
z_2*z_30*z_28*z_29*z_2 ,
z_2*z_30*z_28*z_30*z_27 + z_1*z_24*z_18*z_24 ,
z_3*z_27*z_18*z_22*z_2 + z_3*z_28 ,
z_3*z_27*z_18*z_24*z_17 ,
z_3*z_27*z_19*z_26*z_4 + z_3*z_28*z_30 ,
z_3*z_28*z_30*z_26*z_4 ,
z_4*z_28*z_29*z_1*z_22 + z_4*z_28*z_30*z_28*z_29 ,
z_4*z_28*z_30*z_26*z_4 ,
z_4*z_28*z_30*z_27*z_18 ,
z_11*z_19*z_25*z_3*z_26 + z_11*z_19*z_26 ,
z_11*z_19*z_25*z_3*z_27 ,
z_15*z_24*z_19*z_28*z_29 ,
z_15*z_24*z_19*z_28*z_30 ,
z_18*z_24*z_19*z_25*z_3 + z_19*z_27*z_19*z_25*z_3 + z_16*z_11*z_19 + z_19*z_26*z_4 + z_19*z_27*z_19 ,
z_19*z_25*z_3*z_27*z_17 + z_16*z_11*z_17 + z_18*z_24*z_17 ,
z_19*z_26*z_4*z_26*z_4 ,
z_19*z_28*z_29*z_2*z_30 + z_19*z_26*z_4 ,
z_19*z_28*z_30*z_26*z_4 ,
z_19*z_28*z_30*z_28*z_29 + z_19*z_28*z_29 + z_18*z_22 ,
z_21*z_18*z_24*z_19*z_25 ,
z_21*z_19*z_25*z_3*z_27 + z_21*z_16*z_11 + z_21*z_18*z_24 + z_21*z_19*z_27 ,
z_22*z_2*z_30*z_28*z_29 + z_24*z_19*z_28*z_29 + z_24*z_18*z_22 ,
z_22*z_2*z_30*z_28*z_30 ,
z_24*z_19*z_25*z_3*z_26 + z_22*z_2*z_30*z_26 ,
z_24*z_19*z_25*z_3*z_27 + z_24*z_18*z_24 ,
z_24*z_19*z_28*z_29*z_2 + z_24*z_18*z_22*z_2 ,
z_24*z_19*z_28*z_30*z_26 ,
z_24*z_19*z_28*z_30*z_28 + z_22*z_2*z_30*z_28 + z_24*z_18*z_22*z_2 ,
z_26*z_4*z_25*z_3*z_27 + z_28*z_30*z_27 ,
z_26*z_4*z_25*z_3*z_28 + z_28*z_30*z_28*z_29*z_2 + z_25*z_3*z_28 ,
z_26*z_4*z_26*z_4*z_25 + z_28*z_29*z_2*z_30*z_25 ,
z_26*z_4*z_26*z_4*z_26 + z_28*z_29*z_2*z_30*z_26 + z_28*z_30*z_27*z_19*z_26 + z_26*z_4*z_26 + z_27*z_19*z_26 ,
z_27*z_18*z_24*z_17*z_21 + z_27*z_19*z_27 ,
z_27*z_19*z_25*z_3*z_26 + z_28*z_29*z_2*z_30*z_26 + z_26*z_4*z_26 + z_27*z_19*z_26 + z_28*z_30*z_26 ,
z_27*z_19*z_26*z_4*z_26 + z_28*z_29*z_2*z_30*z_26 + z_28*z_30*z_27*z_19*z_26 + z_26*z_4*z_26 + z_27*z_19*z_26 ,
z_27*z_19*z_27*z_19*z_25 ,
z_28*z_29*z_1*z_22*z_2 + z_25*z_3*z_28 ,
z_28*z_29*z_1*z_24*z_18 ,
z_28*z_29*z_1*z_24*z_19 + z_26*z_4*z_26*z_4 + z_27*z_19*z_26*z_4 ,
z_28*z_30*z_27*z_18*z_22 + z_28*z_29*z_1*z_22 + z_28*z_30*z_28*z_29 ,
z_28*z_30*z_27*z_18*z_23 ,
z_28*z_30*z_27*z_19*z_27 ,
z_28*z_30*z_28*z_29*z_1 ,
z_29*z_1*z_22*z_2*z_30 + z_30*z_25*z_3 + z_30*z_26*z_4 + z_30*z_27*z_19 + z_30*z_28*z_30 ,
z_29*z_1*z_24*z_18*z_22 ,
z_29*z_1*z_24*z_18*z_24 + z_30*z_27*z_19*z_27 ,
z_30*z_27*z_18*z_22*z_2 + z_29*z_1*z_22*z_2 + z_30*z_25*z_3*z_28 + z_30*z_28*z_29*z_2 ,
z_30*z_27*z_18*z_23*z_15 + z_29*z_1*z_24*z_18 ,
z_30*z_27*z_19*z_26*z_4 + z_30*z_25*z_3 + z_30*z_28*z_30 ,
z_30*z_27*z_19*z_27*z_19 + z_30*z_25*z_3 + z_30*z_28*z_30 ,
z_30*z_28*z_29*z_1*z_22 + z_30*z_27*z_18*z_22 + z_29*z_1*z_22 + z_30*z_28*z_29 ,
z_30*z_28*z_29*z_1*z_24 + z_30*z_27*z_19*z_27 ,
z_30*z_28*z_29*z_2*z_30 + z_30*z_26*z_4 + z_30*z_27*z_19 ,
z_30*z_28*z_30*z_26*z_4 + z_30*z_28*z_30*z_27*z_19 ,
z_30*z_28*z_30*z_27*z_18 + z_29*z_1*z_24*z_18 + z_30*z_28*z_29*z_1 ,
z_1*z_24*z_19*z_25 + z_2*z_30*z_25 ,
z_1*z_24*z_19*z_28 + z_1*z_22*z_2 + z_2*z_30*z_28 ,
z_2*z_30*z_25*z_3 + z_2*z_30*z_28*z_30 ,
z_2*z_30*z_26*z_4 + z_1*z_24*z_19 ,
z_3*z_27*z_18*z_23 ,
z_3*z_27*z_19*z_25 ,
z_3*z_27*z_19*z_27 ,
z_3*z_28*z_30*z_27 ,
z_3*z_28*z_30*z_28 ,
z_5*z_13*z_8*z_7 ,
z_6*z_9*z_12*z_5 + z_7*z_10*z_6*z_9 ,
z_8*z_7*z_10*z_6 + z_9*z_12*z_5*z_13 + z_8*z_6 ,
z_10*z_6*z_9*z_12 ,
z_11*z_17*z_21*z_16 ,
z_11*z_17*z_21*z_19 + z_11*z_19*z_25*z_3 + z_11*z_19 ,
z_11*z_19*z_26*z_4 ,
z_12*z_5*z_13*z_8 + z_13*z_8*z_7*z_10 ,
z_15*z_24*z_19*z_25 ,
z_16*z_11*z_17*z_21 + z_18*z_24*z_17*z_21 + z_19*z_27 ,
z_16*z_11*z_19*z_25 + z_19*z_27*z_19*z_25 ,
z_16*z_11*z_19*z_26 + z_19*z_28*z_30*z_26 ,
z_17*z_21*z_19*z_27 + z_19*z_25*z_3*z_27 + z_16*z_11 + z_18*z_24 + z_19*z_27 ,
z_17*z_21*z_19*z_28 + z_18*z_22*z_2 ,
z_18*z_22*z_2*z_30 + z_19*z_26*z_4 ,
z_18*z_24*z_18*z_22 + z_19*z_28*z_29 + z_18*z_22 ,
z_18*z_24*z_18*z_24 ,
z_18*z_24*z_19*z_28 + z_19*z_28*z_29*z_2 + z_19*z_28*z_30*z_28 + z_18*z_22*z_2 ,
z_19*z_25*z_3*z_28 + z_19*z_28*z_29*z_2 + z_18*z_22*z_2 ,
z_19*z_26*z_4*z_25 ,
z_19*z_27*z_19*z_26 ,
z_19*z_27*z_19*z_27 ,
z_19*z_27*z_19*z_28 + z_19*z_28*z_29*z_2 + z_18*z_22*z_2 ,
z_19*z_28*z_29*z_1 + z_18*z_24*z_18 ,
z_19*z_28*z_30*z_27 ,
z_21*z_16*z_11*z_19 + z_21*z_18*z_24*z_19 + z_21*z_19*z_27*z_19 + z_21*z_19*z_28*z_30 ,
z_21*z_18*z_24*z_17 ,
z_21*z_18*z_24*z_18 ,
z_21*z_19*z_28*z_29 ,
z_22*z_2*z_30*z_25 ,
z_24*z_17*z_21*z_16 ,
z_24*z_17*z_21*z_19 + z_24*z_19*z_25*z_3 + z_24*z_19*z_28*z_30 + z_22*z_2*z_30 ,
z_24*z_18*z_24*z_17 ,
z_24*z_18*z_24*z_19 + z_24*z_19*z_28*z_30 ,
z_25*z_3*z_27*z_18 + z_27*z_18*z_23*z_15 + z_28*z_29*z_1 ,
z_25*z_3*z_27*z_19 + z_26*z_4*z_25*z_3 + z_27*z_19*z_26*z_4 + z_28*z_30*z_26*z_4 + z_28*z_30 ,
z_25*z_3*z_28*z_30 + z_28*z_30*z_26*z_4 + z_28*z_30*z_27*z_19 ,
z_27*z_18*z_24*z_18 + z_28*z_30*z_27*z_18 ,
z_27*z_19*z_28*z_29 + z_28*z_29*z_1*z_22 + z_28*z_30*z_28*z_29 + z_27*z_18*z_22 ,
z_27*z_19*z_28*z_30 + z_28*z_30*z_26*z_4 ,
z_28*z_30*z_28*z_30 ,
z_29*z_2*z_30*z_28 + z_30*z_28*z_29*z_2 ,
z_30*z_25*z_3*z_26 + z_30*z_28*z_30*z_26 ,
z_30*z_25*z_3*z_27 + z_30*z_28*z_30*z_27 ,
z_30*z_26*z_4*z_25 + z_30*z_25 ,
z_30*z_26*z_4*z_26 ,
z_30*z_27*z_17*z_21 + z_30*z_27*z_19*z_27 + z_29*z_1*z_24 ,
z_30*z_27*z_18*z_24 + z_30*z_27*z_19*z_27 + z_30*z_28*z_30*z_27 ,
z_30*z_27*z_19*z_25 + z_30*z_25 ,
z_30*z_28*z_30*z_28 ,
z_1*z_24*z_17 ,
z_2*z_30*z_27 + z_1*z_24 ,
z_3*z_26*z_4 + z_3*z_27*z_19 + z_3*z_28*z_30 ,
z_3*z_28*z_29 ,
z_11*z_19*z_27 ,
z_11*z_19*z_28 ,
z_15*z_24*z_17 ,
z_15*z_24*z_18 ,
z_17*z_21*z_18 + z_18*z_23*z_15 ,
z_19*z_27*z_17 ,
z_19*z_27*z_18 ,
z_21*z_18*z_22 ,
z_21*z_18*z_23 ,
z_21*z_19*z_26 ,
z_23*z_15*z_24 + z_24*z_17*z_21 ,
z_24*z_18*z_23 ,
z_24*z_19*z_26 ,
z_24*z_19*z_27 ,
z_26*z_4*z_28 + z_27*z_19*z_28 ,
z_28*z_30*z_25 ,
b_2^2 + b_2 ,
b_2*b_3 ,
b_2*b_4 ,
b_2*b_5 ,
b_2*b_6 ,
b_2*b_7 ,
b_2*b_8 ,
b_2*b_9 ,
b_2*b_10 ,
b_2*b_11 ,
b_2*b_12 ,
b_2*b_13 ,
b_2*b_14 ,
b_2*b_15 ,
b_2*z_1 ,
b_2*z_2 ,
b_2*z_3 + z_3 ,
b_2*z_4 ,
b_2*z_5 ,
b_2*z_6 ,
b_2*z_7 ,
b_2*z_8 ,
b_2*z_9 ,
b_2*z_10 ,
b_2*z_11 ,
b_2*z_12 ,
b_2*z_13 ,
b_2*z_14 ,
b_2*z_15 ,
b_2*z_16 ,
b_2*z_17 ,
b_2*z_18 ,
b_2*z_19 ,
b_2*z_20 ,
b_2*z_21 ,
b_2*z_22 ,
b_2*z_23 ,
b_2*z_24 ,
b_2*z_25 ,
b_2*z_26 ,
b_2*z_27 ,
b_2*z_28 ,
b_2*z_29 ,
b_2*z_30 ,
b_3*b_2 ,
b_3^2 + b_3 ,
b_3*b_4 ,
b_3*b_5 ,
b_3*b_6 ,
b_3*b_7 ,
b_3*b_8 ,
b_3*b_9 ,
b_3*b_10 ,
b_3*b_11 ,
b_3*b_12 ,
b_3*b_13 ,
b_3*b_14 ,
b_3*b_15 ,
b_3*z_1 ,
b_3*z_2 ,
b_3*z_3 ,
b_3*z_4 + z_4 ,
b_3*z_5 ,
b_3*z_6 ,
b_3*z_7 ,
b_3*z_8 ,
b_3*z_9 ,
b_3*z_10 ,
b_3*z_11 ,
b_3*z_12 ,
b_3*z_13 ,
b_3*z_14 ,
b_3*z_15 ,
b_3*z_16 ,
b_3*z_17 ,
b_3*z_18 ,
b_3*z_19 ,
b_3*z_20 ,
b_3*z_21 ,
b_3*z_22 ,
b_3*z_23 ,
b_3*z_24 ,
b_3*z_25 ,
b_3*z_26 ,
b_3*z_27 ,
b_3*z_28 ,
b_3*z_29 ,
b_3*z_30 ,
b_4*b_2 ,
b_4*b_3 ,
b_4^2 + b_4 ,
b_4*b_5 ,
b_4*b_6 ,
b_4*b_7 ,
b_4*b_8 ,
b_4*b_9 ,
b_4*b_10 ,
b_4*b_11 ,
b_4*b_12 ,
b_4*b_13 ,
b_4*b_14 ,
b_4*b_15 ,
b_4*z_1 ,
b_4*z_2 ,
b_4*z_3 ,
b_4*z_4 ,
b_4*z_5 + z_5 ,
b_4*z_6 ,
b_4*z_7 ,
b_4*z_8 ,
b_4*z_9 ,
b_4*z_10 ,
b_4*z_11 ,
b_4*z_12 ,
b_4*z_13 ,
b_4*z_14 ,
b_4*z_15 ,
b_4*z_16 ,
b_4*z_17 ,
b_4*z_18 ,
b_4*z_19 ,
b_4*z_20 ,
b_4*z_21 ,
b_4*z_22 ,
b_4*z_23 ,
b_4*z_24 ,
b_4*z_25 ,
b_4*z_26 ,
b_4*z_27 ,
b_4*z_28 ,
b_4*z_29 ,
b_4*z_30 ,
b_5*b_2 ,
b_5*b_3 ,
b_5*b_4 ,
b_5^2 + b_5 ,
b_5*b_6 ,
b_5*b_7 ,
b_5*b_8 ,
b_5*b_9 ,
b_5*b_10 ,
b_5*b_11 ,
b_5*b_12 ,
b_5*b_13 ,
b_5*b_14 ,
b_5*b_15 ,
b_5*z_1 ,
b_5*z_2 ,
b_5*z_3 ,
b_5*z_4 ,
b_5*z_5 ,
b_5*z_6 + z_6 ,
b_5*z_7 + z_7 ,
b_5*z_8 ,
b_5*z_9 ,
b_5*z_10 ,
b_5*z_11 ,
b_5*z_12 ,
b_5*z_13 ,
b_5*z_14 ,
b_5*z_15 ,
b_5*z_16 ,
b_5*z_17 ,
b_5*z_18 ,
b_5*z_19 ,
b_5*z_20 ,
b_5*z_21 ,
b_5*z_22 ,
b_5*z_23 ,
b_5*z_24 ,
b_5*z_25 ,
b_5*z_26 ,
b_5*z_27 ,
b_5*z_28 ,
b_5*z_29 ,
b_5*z_30 ,
b_6*b_2 ,
b_6*b_3 ,
b_6*b_4 ,
b_6*b_5 ,
b_6^2 + b_6 ,
b_6*b_7 ,
b_6*b_8 ,
b_6*b_9 ,
b_6*b_10 ,
b_6*b_11 ,
b_6*b_12 ,
b_6*b_13 ,
b_6*b_14 ,
b_6*b_15 ,
b_6*z_1 ,
b_6*z_2 ,
b_6*z_3 ,
b_6*z_4 ,
b_6*z_5 ,
b_6*z_6 ,
b_6*z_7 ,
b_6*z_8 + z_8 ,
b_6*z_9 + z_9 ,
b_6*z_10 ,
b_6*z_11 ,
b_6*z_12 ,
b_6*z_13 ,
b_6*z_14 ,
b_6*z_15 ,
b_6*z_16 ,
b_6*z_17 ,
b_6*z_18 ,
b_6*z_19 ,
b_6*z_20 ,
b_6*z_21 ,
b_6*z_22 ,
b_6*z_23 ,
b_6*z_24 ,
b_6*z_25 ,
b_6*z_26 ,
b_6*z_27 ,
b_6*z_28 ,
b_6*z_29 ,
b_6*z_30 ,
b_7*b_2 ,
b_7*b_3 ,
b_7*b_4 ,
b_7*b_5 ,
b_7*b_6 ,
b_7^2 + b_7 ,
b_7*b_8 ,
b_7*b_9 ,
b_7*b_10 ,
b_7*b_11 ,
b_7*b_12 ,
b_7*b_13 ,
b_7*b_14 ,
b_7*b_15 ,
b_7*z_1 ,
b_7*z_2 ,
b_7*z_3 ,
b_7*z_4 ,
b_7*z_5 ,
b_7*z_6 ,
b_7*z_7 ,
b_7*z_8 ,
b_7*z_9 ,
b_7*z_10 + z_10 ,
b_7*z_11 ,
b_7*z_12 ,
b_7*z_13 ,
b_7*z_14 ,
b_7*z_15 ,
b_7*z_16 ,
b_7*z_17 ,
b_7*z_18 ,
b_7*z_19 ,
b_7*z_20 ,
b_7*z_21 ,
b_7*z_22 ,
b_7*z_23 ,
b_7*z_24 ,
b_7*z_25 ,
b_7*z_26 ,
b_7*z_27 ,
b_7*z_28 ,
b_7*z_29 ,
b_7*z_30 ,
b_8*b_2 ,
b_8*b_3 ,
b_8*b_4 ,
b_8*b_5 ,
b_8*b_6 ,
b_8*b_7 ,
b_8^2 + b_8 ,
b_8*b_9 ,
b_8*b_10 ,
b_8*b_11 ,
b_8*b_12 ,
b_8*b_13 ,
b_8*b_14 ,
b_8*b_15 ,
b_8*z_1 ,
b_8*z_2 ,
b_8*z_3 ,
b_8*z_4 ,
b_8*z_5 ,
b_8*z_6 ,
b_8*z_7 ,
b_8*z_8 ,
b_8*z_9 ,
b_8*z_10 ,
b_8*z_11 + z_11 ,
b_8*z_12 ,
b_8*z_13 ,
b_8*z_14 ,
b_8*z_15 ,
b_8*z_16 ,
b_8*z_17 ,
b_8*z_18 ,
b_8*z_19 ,
b_8*z_20 ,
b_8*z_21 ,
b_8*z_22 ,
b_8*z_23 ,
b_8*z_24 ,
b_8*z_25 ,
b_8*z_26 ,
b_8*z_27 ,
b_8*z_28 ,
b_8*z_29 ,
b_8*z_30 ,
b_9*b_2 ,
b_9*b_3 ,
b_9*b_4 ,
b_9*b_5 ,
b_9*b_6 ,
b_9*b_7 ,
b_9*b_8 ,
b_9^2 + b_9 ,
b_9*b_10 ,
b_9*b_11 ,
b_9*b_12 ,
b_9*b_13 ,
b_9*b_14 ,
b_9*b_15 ,
b_9*z_1 ,
b_9*z_2 ,
b_9*z_3 ,
b_9*z_4 ,
b_9*z_5 ,
b_9*z_6 ,
b_9*z_7 ,
b_9*z_8 ,
b_9*z_9 ,
b_9*z_10 ,
b_9*z_11 ,
b_9*z_12 + z_12 ,
b_9*z_13 + z_13 ,
b_9*z_14 ,
b_9*z_15 ,
b_9*z_16 ,
b_9*z_17 ,
b_9*z_18 ,
b_9*z_19 ,
b_9*z_20 ,
b_9*z_21 ,
b_9*z_22 ,
b_9*z_23 ,
b_9*z_24 ,
b_9*z_25 ,
b_9*z_26 ,
b_9*z_27 ,
b_9*z_28 ,
b_9*z_29 ,
b_9*z_30 ,
b_10*b_2 ,
b_10*b_3 ,
b_10*b_4 ,
b_10*b_5 ,
b_10*b_6 ,
b_10*b_7 ,
b_10*b_8 ,
b_10*b_9 ,
b_10^2 + b_10 ,
b_10*b_11 ,
b_10*b_12 ,
b_10*b_13 ,
b_10*b_14 ,
b_10*b_15 ,
b_10*z_1 ,
b_10*z_2 ,
b_10*z_3 ,
b_10*z_4 ,
b_10*z_5 ,
b_10*z_6 ,
b_10*z_7 ,
b_10*z_8 ,
b_10*z_9 ,
b_10*z_10 ,
b_10*z_11 ,
b_10*z_12 ,
b_10*z_13 ,
b_10*z_14 + z_14 ,
b_10*z_15 + z_15 ,
b_10*z_16 ,
b_10*z_17 ,
b_10*z_18 ,
b_10*z_19 ,
b_10*z_20 ,
b_10*z_21 ,
b_10*z_22 ,
b_10*z_23 ,
b_10*z_24 ,
b_10*z_25 ,
b_10*z_26 ,
b_10*z_27 ,
b_10*z_28 ,
b_10*z_29 ,
b_10*z_30 ,
b_11*b_2 ,
b_11*b_3 ,
b_11*b_4 ,
b_11*b_5 ,
b_11*b_6 ,
b_11*b_7 ,
b_11*b_8 ,
b_11*b_9 ,
b_11*b_10 ,
b_11^2 + b_11 ,
b_11*b_12 ,
b_11*b_13 ,
b_11*b_14 ,
b_11*b_15 ,
b_11*z_1 ,
b_11*z_2 ,
b_11*z_3 ,
b_11*z_4 ,
b_11*z_5 ,
b_11*z_6 ,
b_11*z_7 ,
b_11*z_8 ,
b_11*z_9 ,
b_11*z_10 ,
b_11*z_11 ,
b_11*z_12 ,
b_11*z_13 ,
b_11*z_14 ,
b_11*z_15 ,
b_11*z_16 + z_16 ,
b_11*z_17 + z_17 ,
b_11*z_18 + z_18 ,
b_11*z_19 + z_19 ,
b_11*z_20 ,
b_11*z_21 ,
b_11*z_22 ,
b_11*z_23 ,
b_11*z_24 ,
b_11*z_25 ,
b_11*z_26 ,
b_11*z_27 ,
b_11*z_28 ,
b_11*z_29 ,
b_11*z_30 ,
b_12*b_2 ,
b_12*b_3 ,
b_12*b_4 ,
b_12*b_5 ,
b_12*b_6 ,
b_12*b_7 ,
b_12*b_8 ,
b_12*b_9 ,
b_12*b_10 ,
b_12*b_11 ,
b_12^2 + b_12 ,
b_12*b_13 ,
b_12*b_14 ,
b_12*b_15 ,
b_12*z_1 ,
b_12*z_2 ,
b_12*z_3 ,
b_12*z_4 ,
b_12*z_5 ,
b_12*z_6 ,
b_12*z_7 ,
b_12*z_8 ,
b_12*z_9 ,
b_12*z_10 ,
b_12*z_11 ,
b_12*z_12 ,
b_12*z_13 ,
b_12*z_14 ,
b_12*z_15 ,
b_12*z_16 ,
b_12*z_17 ,
b_12*z_18 ,
b_12*z_19 ,
b_12*z_20 + z_20 ,
b_12*z_21 + z_21 ,
b_12*z_22 ,
b_12*z_23 ,
b_12*z_24 ,
b_12*z_25 ,
b_12*z_26 ,
b_12*z_27 ,
b_12*z_28 ,
b_12*z_29 ,
b_12*z_30 ,
b_13*b_2 ,
b_13*b_3 ,
b_13*b_4 ,
b_13*b_5 ,
b_13*b_6 ,
b_13*b_7 ,
b_13*b_8 ,
b_13*b_9 ,
b_13*b_10 ,
b_13*b_11 ,
b_13*b_12 ,
b_13^2 + b_13 ,
b_13*b_14 ,
b_13*b_15 ,
b_13*z_1 ,
b_13*z_2 ,
b_13*z_3 ,
b_13*z_4 ,
b_13*z_5 ,
b_13*z_6 ,
b_13*z_7 ,
b_13*z_8 ,
b_13*z_9 ,
b_13*z_10 ,
b_13*z_11 ,
b_13*z_12 ,
b_13*z_13 ,
b_13*z_14 ,
b_13*z_15 ,
b_13*z_16 ,
b_13*z_17 ,
b_13*z_18 ,
b_13*z_19 ,
b_13*z_20 ,
b_13*z_21 ,
b_13*z_22 + z_22 ,
b_13*z_23 + z_23 ,
b_13*z_24 + z_24 ,
b_13*z_25 ,
b_13*z_26 ,
b_13*z_27 ,
b_13*z_28 ,
b_13*z_29 ,
b_13*z_30 ,
b_14*b_2 ,
b_14*b_3 ,
b_14*b_4 ,
b_14*b_5 ,
b_14*b_6 ,
b_14*b_7 ,
b_14*b_8 ,
b_14*b_9 ,
b_14*b_10 ,
b_14*b_11 ,
b_14*b_12 ,
b_14*b_13 ,
b_14^2 + b_14 ,
b_14*b_15 ,
b_14*z_1 ,
b_14*z_2 ,
b_14*z_3 ,
b_14*z_4 ,
b_14*z_5 ,
b_14*z_6 ,
b_14*z_7 ,
b_14*z_8 ,
b_14*z_9 ,
b_14*z_10 ,
b_14*z_11 ,
b_14*z_12 ,
b_14*z_13 ,
b_14*z_14 ,
b_14*z_15 ,
b_14*z_16 ,
b_14*z_17 ,
b_14*z_18 ,
b_14*z_19 ,
b_14*z_20 ,
b_14*z_21 ,
b_14*z_22 ,
b_14*z_23 ,
b_14*z_24 ,
b_14*z_25 + z_25 ,
b_14*z_26 + z_26 ,
b_14*z_27 + z_27 ,
b_14*z_28 + z_28 ,
b_14*z_29 ,
b_14*z_30 ,
b_15*b_2 ,
b_15*b_3 ,
b_15*b_4 ,
b_15*b_5 ,
b_15*b_6 ,
b_15*b_7 ,
b_15*b_8 ,
b_15*b_9 ,
b_15*b_10 ,
b_15*b_11 ,
b_15*b_12 ,
b_15*b_13 ,
b_15*b_14 ,
b_15^2 + b_15 ,
b_15*z_1 ,
b_15*z_2 ,
b_15*z_3 ,
b_15*z_4 ,
b_15*z_5 ,
b_15*z_6 ,
b_15*z_7 ,
b_15*z_8 ,
b_15*z_9 ,
b_15*z_10 ,
b_15*z_11 ,
b_15*z_12 ,
b_15*z_13 ,
b_15*z_14 ,
b_15*z_15 ,
b_15*z_16 ,
b_15*z_17 ,
b_15*z_18 ,
b_15*z_19 ,
b_15*z_20 ,
b_15*z_21 ,
b_15*z_22 ,
b_15*z_23 ,
b_15*z_24 ,
b_15*z_25 ,
b_15*z_26 ,
b_15*z_27 ,
b_15*z_28 ,
b_15*z_29 + z_29 ,
b_15*z_30 + z_30 ,
z_1*b_2 ,
z_1*b_3 ,
z_1*b_4 ,
z_1*b_5 ,
z_1*b_6 ,
z_1*b_7 ,
z_1*b_8 ,
z_1*b_9 ,
z_1*b_10 ,
z_1*b_11 ,
z_1*b_12 ,
z_1*b_13 + z_1 ,
z_1*b_14 ,
z_1*b_15 ,
z_1^2 ,
z_1*z_2 ,
z_1*z_3 ,
z_1*z_4 ,
z_1*z_5 ,
z_1*z_6 ,
z_1*z_7 ,
z_1*z_8 ,
z_1*z_9 ,
z_1*z_10 ,
z_1*z_11 ,
z_1*z_12 ,
z_1*z_13 ,
z_1*z_14 ,
z_1*z_15 ,
z_1*z_16 ,
z_1*z_17 ,
z_1*z_18 ,
z_1*z_19 ,
z_1*z_20 ,
z_1*z_21 ,
z_1*z_23 ,
z_1*z_25 ,
z_1*z_26 ,
z_1*z_27 ,
z_1*z_28 ,
z_1*z_29 ,
z_1*z_30 ,
z_2*b_2 ,
z_2*b_3 ,
z_2*b_4 ,
z_2*b_5 ,
z_2*b_6 ,
z_2*b_7 ,
z_2*b_8 ,
z_2*b_9 ,
z_2*b_10 ,
z_2*b_11 ,
z_2*b_12 ,
z_2*b_13 ,
z_2*b_14 ,
z_2*b_15 + z_2 ,
z_2*z_1 ,
z_2^2 ,
z_2*z_3 ,
z_2*z_4 ,
z_2*z_5 ,
z_2*z_6 ,
z_2*z_7 ,
z_2*z_8 ,
z_2*z_9 ,
z_2*z_10 ,
z_2*z_11 ,
z_2*z_12 ,
z_2*z_13 ,
z_2*z_14 ,
z_2*z_15 ,
z_2*z_16 ,
z_2*z_17 ,
z_2*z_18 ,
z_2*z_19 ,
z_2*z_20 ,
z_2*z_21 ,
z_2*z_22 ,
z_2*z_23 ,
z_2*z_24 ,
z_2*z_25 ,
z_2*z_26 ,
z_2*z_27 ,
z_2*z_28 ,
z_2*z_29 ,
z_3*b_2 ,
z_3*b_3 ,
z_3*b_4 ,
z_3*b_5 ,
z_3*b_6 ,
z_3*b_7 ,
z_3*b_8 ,
z_3*b_9 ,
z_3*b_10 ,
z_3*b_11 ,
z_3*b_12 ,
z_3*b_13 ,
z_3*b_14 + z_3 ,
z_3*b_15 ,
z_3*z_1 ,
z_3*z_2 ,
z_3^2 ,
z_3*z_4 ,
z_3*z_5 ,
z_3*z_6 ,
z_3*z_7 ,
z_3*z_8 ,
z_3*z_9 ,
z_3*z_10 ,
z_3*z_11 ,
z_3*z_12 ,
z_3*z_13 ,
z_3*z_14 ,
z_3*z_15 ,
z_3*z_16 ,
z_3*z_17 ,
z_3*z_18 ,
z_3*z_19 ,
z_3*z_20 ,
z_3*z_21 ,
z_3*z_22 ,
z_3*z_23 ,
z_3*z_24 ,
z_3*z_25 ,
z_3*z_29 ,
z_3*z_30 ,
z_4*b_2 ,
z_4*b_3 ,
z_4*b_4 ,
z_4*b_5 ,
z_4*b_6 ,
z_4*b_7 ,
z_4*b_8 ,
z_4*b_9 ,
z_4*b_10 ,
z_4*b_11 ,
z_4*b_12 ,
z_4*b_13 ,
z_4*b_14 + z_4 ,
z_4*b_15 ,
z_4*z_1 ,
z_4*z_2 ,
z_4*z_3 ,
z_4^2 ,
z_4*z_5 ,
z_4*z_6 ,
z_4*z_7 ,
z_4*z_8 ,
z_4*z_9 ,
z_4*z_10 ,
z_4*z_11 ,
z_4*z_12 ,
z_4*z_13 ,
z_4*z_14 ,
z_4*z_15 ,
z_4*z_16 ,
z_4*z_17 ,
z_4*z_18 ,
z_4*z_19 ,
z_4*z_20 ,
z_4*z_21 ,
z_4*z_22 ,
z_4*z_23 ,
z_4*z_24 ,
z_4*z_27 ,
z_4*z_29 ,
z_4*z_30 ,
z_5*b_2 ,
z_5*b_3 ,
z_5*b_4 ,
z_5*b_5 ,
z_5*b_6 ,
z_5*b_7 ,
z_5*b_8 ,
z_5*b_9 + z_5 ,
z_5*b_10 ,
z_5*b_11 ,
z_5*b_12 ,
z_5*b_13 ,
z_5*b_14 ,
z_5*b_15 ,
z_5*z_1 ,
z_5*z_2 ,
z_5*z_3 ,
z_5*z_4 ,
z_5^2 ,
z_5*z_6 ,
z_5*z_7 ,
z_5*z_8 ,
z_5*z_9 ,
z_5*z_10 ,
z_5*z_11 ,
z_5*z_12 ,
z_5*z_14 ,
z_5*z_15 ,
z_5*z_16 ,
z_5*z_17 ,
z_5*z_18 ,
z_5*z_19 ,
z_5*z_20 ,
z_5*z_21 ,
z_5*z_22 ,
z_5*z_23 ,
z_5*z_24 ,
z_5*z_25 ,
z_5*z_26 ,
z_5*z_27 ,
z_5*z_28 ,
z_5*z_29 ,
z_5*z_30 ,
z_6*b_2 ,
z_6*b_3 ,
z_6*b_4 ,
z_6*b_5 ,
z_6*b_6 + z_6 ,
z_6*b_7 ,
z_6*b_8 ,
z_6*b_9 ,
z_6*b_10 ,
z_6*b_11 ,
z_6*b_12 ,
z_6*b_13 ,
z_6*b_14 ,
z_6*b_15 ,
z_6*z_1 ,
z_6*z_2 ,
z_6*z_3 ,
z_6*z_4 ,
z_6*z_5 ,
z_6^2 ,
z_6*z_7 ,
z_6*z_8 ,
z_6*z_10 ,
z_6*z_11 ,
z_6*z_12 ,
z_6*z_13 ,
z_6*z_14 ,
z_6*z_15 ,
z_6*z_16 ,
z_6*z_17 ,
z_6*z_18 ,
z_6*z_19 ,
z_6*z_20 ,
z_6*z_21 ,
z_6*z_22 ,
z_6*z_23 ,
z_6*z_24 ,
z_6*z_25 ,
z_6*z_26 ,
z_6*z_27 ,
z_6*z_28 ,
z_6*z_29 ,
z_6*z_30 ,
z_7*b_2 ,
z_7*b_3 ,
z_7*b_4 ,
z_7*b_5 ,
z_7*b_6 ,
z_7*b_7 + z_7 ,
z_7*b_8 ,
z_7*b_9 ,
z_7*b_10 ,
z_7*b_11 ,
z_7*b_12 ,
z_7*b_13 ,
z_7*b_14 ,
z_7*b_15 ,
z_7*z_1 ,
z_7*z_2 ,
z_7*z_3 ,
z_7*z_4 ,
z_7*z_5 ,
z_7*z_6 ,
z_7^2 ,
z_7*z_8 ,
z_7*z_9 ,
z_7*z_11 ,
z_7*z_12 ,
z_7*z_13 ,
z_7*z_14 ,
z_7*z_15 ,
z_7*z_16 ,
z_7*z_17 ,
z_7*z_18 ,
z_7*z_19 ,
z_7*z_20 ,
z_7*z_21 ,
z_7*z_22 ,
z_7*z_23 ,
z_7*z_24 ,
z_7*z_25 ,
z_7*z_26 ,
z_7*z_27 ,
z_7*z_28 ,
z_7*z_29 ,
z_7*z_30 ,
z_8*b_2 ,
z_8*b_3 ,
z_8*b_4 ,
z_8*b_5 + z_8 ,
z_8*b_6 ,
z_8*b_7 ,
z_8*b_8 ,
z_8*b_9 ,
z_8*b_10 ,
z_8*b_11 ,
z_8*b_12 ,
z_8*b_13 ,
z_8*b_14 ,
z_8*b_15 ,
z_8*z_1 ,
z_8*z_2 ,
z_8*z_3 ,
z_8*z_4 ,
z_8*z_5 ,
z_8^2 ,
z_8*z_9 ,
z_8*z_10 ,
z_8*z_11 ,
z_8*z_12 ,
z_8*z_13 ,
z_8*z_14 ,
z_8*z_15 ,
z_8*z_16 ,
z_8*z_17 ,
z_8*z_18 ,
z_8*z_19 ,
z_8*z_20 ,
z_8*z_21 ,
z_8*z_22 ,
z_8*z_23 ,
z_8*z_24 ,
z_8*z_25 ,
z_8*z_26 ,
z_8*z_27 ,
z_8*z_28 ,
z_8*z_29 ,
z_8*z_30 ,
z_9*b_2 ,
z_9*b_3 ,
z_9*b_4 ,
z_9*b_5 ,
z_9*b_6 ,
z_9*b_7 ,
z_9*b_8 ,
z_9*b_9 + z_9 ,
z_9*b_10 ,
z_9*b_11 ,
z_9*b_12 ,
z_9*b_13 ,
z_9*b_14 ,
z_9*b_15 ,
z_9*z_1 ,
z_9*z_2 ,
z_9*z_3 ,
z_9*z_4 ,
z_9*z_5 ,
z_9*z_6 ,
z_9*z_7 ,
z_9*z_8 ,
z_9^2 ,
z_9*z_10 ,
z_9*z_11 ,
z_9*z_13 ,
z_9*z_14 ,
z_9*z_15 ,
z_9*z_16 ,
z_9*z_17 ,
z_9*z_18 ,
z_9*z_19 ,
z_9*z_20 ,
z_9*z_21 ,
z_9*z_22 ,
z_9*z_23 ,
z_9*z_24 ,
z_9*z_25 ,
z_9*z_26 ,
z_9*z_27 ,
z_9*z_28 ,
z_9*z_29 ,
z_9*z_30 ,
z_10*b_2 ,
z_10*b_3 ,
z_10*b_4 ,
z_10*b_5 + z_10 ,
z_10*b_6 ,
z_10*b_7 ,
z_10*b_8 ,
z_10*b_9 ,
z_10*b_10 ,
z_10*b_11 ,
z_10*b_12 ,
z_10*b_13 ,
z_10*b_14 ,
z_10*b_15 ,
z_10*z_1 ,
z_10*z_2 ,
z_10*z_3 ,
z_10*z_4 ,
z_10*z_5 ,
z_10*z_7 ,
z_10*z_8 ,
z_10*z_9 ,
z_10^2 ,
z_10*z_11 ,
z_10*z_12 ,
z_10*z_13 ,
z_10*z_14 ,
z_10*z_15 ,
z_10*z_16 ,
z_10*z_17 ,
z_10*z_18 ,
z_10*z_19 ,
z_10*z_20 ,
z_10*z_21 ,
z_10*z_22 ,
z_10*z_23 ,
z_10*z_24 ,
z_10*z_25 ,
z_10*z_26 ,
z_10*z_27 ,
z_10*z_28 ,
z_10*z_29 ,
z_10*z_30 ,
z_11*b_2 ,
z_11*b_3 ,
z_11*b_4 ,
z_11*b_5 ,
z_11*b_6 ,
z_11*b_7 ,
z_11*b_8 ,
z_11*b_9 ,
z_11*b_10 ,
z_11*b_11 + z_11 ,
z_11*b_12 ,
z_11*b_13 ,
z_11*b_14 ,
z_11*b_15 ,
z_11*z_1 ,
z_11*z_2 ,
z_11*z_3 ,
z_11*z_4 ,
z_11*z_5 ,
z_11*z_6 ,
z_11*z_7 ,
z_11*z_8 ,
z_11*z_9 ,
z_11*z_10 ,
z_11^2 ,
z_11*z_12 ,
z_11*z_13 ,
z_11*z_14 ,
z_11*z_15 ,
z_11*z_16 ,
z_11*z_18 ,
z_11*z_20 ,
z_11*z_21 ,
z_11*z_22 ,
z_11*z_23 ,
z_11*z_24 ,
z_11*z_25 ,
z_11*z_26 ,
z_11*z_27 ,
z_11*z_28 ,
z_11*z_29 ,
z_11*z_30 ,
z_12*b_2 ,
z_12*b_3 ,
z_12*b_4 + z_12 ,
z_12*b_5 ,
z_12*b_6 ,
z_12*b_7 ,
z_12*b_8 ,
z_12*b_9 ,
z_12*b_10 ,
z_12*b_11 ,
z_12*b_12 ,
z_12*b_13 ,
z_12*b_14 ,
z_12*b_15 ,
z_12*z_1 ,
z_12*z_2 ,
z_12*z_3 ,
z_12*z_4 ,
z_12*z_6 ,
z_12*z_7 ,
z_12*z_8 ,
z_12*z_9 ,
z_12*z_10 ,
z_12*z_11 ,
z_12^2 ,
z_12*z_13 ,
z_12*z_14 ,
z_12*z_15 ,
z_12*z_16 ,
z_12*z_17 ,
z_12*z_18 ,
z_12*z_19 ,
z_12*z_20 ,
z_12*z_21 ,
z_12*z_22 ,
z_12*z_23 ,
z_12*z_24 ,
z_12*z_25 ,
z_12*z_26 ,
z_12*z_27 ,
z_12*z_28 ,
z_12*z_29 ,
z_12*z_30 ,
z_13*b_2 ,
z_13*b_3 ,
z_13*b_4 ,
z_13*b_5 ,
z_13*b_6 + z_13 ,
z_13*b_7 ,
z_13*b_8 ,
z_13*b_9 ,
z_13*b_10 ,
z_13*b_11 ,
z_13*b_12 ,
z_13*b_13 ,
z_13*b_14 ,
z_13*b_15 ,
z_13*z_1 ,
z_13*z_2 ,
z_13*z_3 ,
z_13*z_4 ,
z_13*z_5 ,
z_13*z_6 ,
z_13*z_7 ,
z_13*z_10 ,
z_13*z_11 ,
z_13*z_12 ,
z_13^2 ,
z_13*z_14 ,
z_13*z_15 ,
z_13*z_16 ,
z_13*z_17 ,
z_13*z_18 ,
z_13*z_19 ,
z_13*z_20 ,
z_13*z_21 ,
z_13*z_22 ,
z_13*z_23 ,
z_13*z_24 ,
z_13*z_25 ,
z_13*z_26 ,
z_13*z_27 ,
z_13*z_28 ,
z_13*z_29 ,
z_13*z_30 ,
z_14*b_2 ,
z_14*b_3 ,
z_14*b_4 ,
z_14*b_5 ,
z_14*b_6 ,
z_14*b_7 ,
z_14*b_8 ,
z_14*b_9 ,
z_14*b_10 ,
z_14*b_11 ,
z_14*b_12 + z_14 ,
z_14*b_13 ,
z_14*b_14 ,
z_14*b_15 ,
z_14*z_1 ,
z_14*z_2 ,
z_14*z_3 ,
z_14*z_4 ,
z_14*z_5 ,
z_14*z_6 ,
z_14*z_7 ,
z_14*z_8 ,
z_14*z_9 ,
z_14*z_10 ,
z_14*z_11 ,
z_14*z_12 ,
z_14*z_13 ,
z_14^2 ,
z_14*z_15 ,
z_14*z_16 ,
z_14*z_17 ,
z_14*z_18 ,
z_14*z_19 ,
z_14*z_20 ,
z_14*z_21 + z_15*z_24 ,
z_14*z_22 ,
z_14*z_23 ,
z_14*z_24 ,
z_14*z_25 ,
z_14*z_26 ,
z_14*z_27 ,
z_14*z_28 ,
z_14*z_29 ,
z_14*z_30 ,
z_15*b_2 ,
z_15*b_3 ,
z_15*b_4 ,
z_15*b_5 ,
z_15*b_6 ,
z_15*b_7 ,
z_15*b_8 ,
z_15*b_9 ,
z_15*b_10 ,
z_15*b_11 ,
z_15*b_12 ,
z_15*b_13 + z_15 ,
z_15*b_14 ,
z_15*b_15 ,
z_15*z_1 ,
z_15*z_2 ,
z_15*z_3 ,
z_15*z_4 ,
z_15*z_5 ,
z_15*z_6 ,
z_15*z_7 ,
z_15*z_8 ,
z_15*z_9 ,
z_15*z_10 ,
z_15*z_11 ,
z_15*z_12 ,
z_15*z_13 ,
z_15*z_14 ,
z_15^2 ,
z_15*z_16 ,
z_15*z_17 ,
z_15*z_18 ,
z_15*z_19 ,
z_15*z_20 ,
z_15*z_21 ,
z_15*z_22 ,
z_15*z_23 ,
z_15*z_25 ,
z_15*z_26 ,
z_15*z_27 ,
z_15*z_28 ,
z_15*z_29 ,
z_15*z_30 ,
z_16*b_2 ,
z_16*b_3 ,
z_16*b_4 ,
z_16*b_5 ,
z_16*b_6 ,
z_16*b_7 ,
z_16*b_8 + z_16 ,
z_16*b_9 ,
z_16*b_10 ,
z_16*b_11 ,
z_16*b_12 ,
z_16*b_13 ,
z_16*b_14 ,
z_16*b_15 ,
z_16*z_1 ,
z_16*z_2 ,
z_16*z_3 ,
z_16*z_4 ,
z_16*z_5 ,
z_16*z_6 ,
z_16*z_7 ,
z_16*z_8 ,
z_16*z_9 ,
z_16*z_10 ,
z_16*z_12 ,
z_16*z_13 ,
z_16*z_14 ,
z_16*z_15 ,
z_16^2 ,
z_16*z_17 ,
z_16*z_18 ,
z_16*z_19 ,
z_16*z_20 ,
z_16*z_21 ,
z_16*z_22 ,
z_16*z_23 ,
z_16*z_24 ,
z_16*z_25 ,
z_16*z_26 ,
z_16*z_27 ,
z_16*z_28 ,
z_16*z_29 ,
z_16*z_30 ,
z_17*b_2 ,
z_17*b_3 ,
z_17*b_4 ,
z_17*b_5 ,
z_17*b_6 ,
z_17*b_7 ,
z_17*b_8 ,
z_17*b_9 ,
z_17*b_10 ,
z_17*b_11 ,
z_17*b_12 + z_17 ,
z_17*b_13 ,
z_17*b_14 ,
z_17*b_15 ,
z_17*z_1 ,
z_17*z_2 ,
z_17*z_3 ,
z_17*z_4 ,
z_17*z_5 ,
z_17*z_6 ,
z_17*z_7 ,
z_17*z_8 ,
z_17*z_9 ,
z_17*z_10 ,
z_17*z_11 ,
z_17*z_12 ,
z_17*z_13 ,
z_17*z_14 ,
z_17*z_15 ,
z_17*z_16 ,
z_17^2 ,
z_17*z_18 ,
z_17*z_19 ,
z_17*z_20 + z_18*z_23 ,
z_17*z_22 ,
z_17*z_23 ,
z_17*z_24 ,
z_17*z_25 ,
z_17*z_26 ,
z_17*z_27 ,
z_17*z_28 ,
z_17*z_29 ,
z_17*z_30 ,
z_18*b_2 ,
z_18*b_3 ,
z_18*b_4 ,
z_18*b_5 ,
z_18*b_6 ,
z_18*b_7 ,
z_18*b_8 ,
z_18*b_9 ,
z_18*b_10 ,
z_18*b_11 ,
z_18*b_12 ,
z_18*b_13 + z_18 ,
z_18*b_14 ,
z_18*b_15 ,
z_18*z_1 ,
z_18*z_2 ,
z_18*z_3 ,
z_18*z_4 ,
z_18*z_5 ,
z_18*z_6 ,
z_18*z_7 ,
z_18*z_8 ,
z_18*z_9 ,
z_18*z_10 ,
z_18*z_11 ,
z_18*z_12 ,
z_18*z_13 ,
z_18*z_14 ,
z_18*z_15 ,
z_18*z_16 ,
z_18*z_17 ,
z_18^2 ,
z_18*z_19 ,
z_18*z_20 ,
z_18*z_21 ,
z_18*z_25 ,
z_18*z_26 ,
z_18*z_27 ,
z_18*z_28 ,
z_18*z_29 ,
z_18*z_30 ,
z_19*b_2 ,
z_19*b_3 ,
z_19*b_4 ,
z_19*b_5 ,
z_19*b_6 ,
z_19*b_7 ,
z_19*b_8 ,
z_19*b_9 ,
z_19*b_10 ,
z_19*b_11 ,
z_19*b_12 ,
z_19*b_13 ,
z_19*b_14 + z_19 ,
z_19*b_15 ,
z_19*z_1 ,
z_19*z_2 ,
z_19*z_3 ,
z_19*z_4 ,
z_19*z_5 ,
z_19*z_6 ,
z_19*z_7 ,
z_19*z_8 ,
z_19*z_9 ,
z_19*z_10 ,
z_19*z_11 ,
z_19*z_12 ,
z_19*z_13 ,
z_19*z_14 ,
z_19*z_15 ,
z_19*z_16 ,
z_19*z_17 ,
z_19*z_18 ,
z_19^2 ,
z_19*z_20 ,
z_19*z_21 ,
z_19*z_22 ,
z_19*z_23 ,
z_19*z_24 ,
z_19*z_29 ,
z_19*z_30 ,
z_20*b_2 ,
z_20*b_3 ,
z_20*b_4 ,
z_20*b_5 ,
z_20*b_6 ,
z_20*b_7 ,
z_20*b_8 ,
z_20*b_9 ,
z_20*b_10 + z_20 ,
z_20*b_11 ,
z_20*b_12 ,
z_20*b_13 ,
z_20*b_14 ,
z_20*b_15 ,
z_20*z_1 ,
z_20*z_2 ,
z_20*z_3 ,
z_20*z_4 ,
z_20*z_5 ,
z_20*z_6 ,
z_20*z_7 ,
z_20*z_8 ,
z_20*z_9 ,
z_20*z_10 ,
z_20*z_11 ,
z_20*z_12 ,
z_20*z_13 ,
z_20*z_15 + z_21*z_18 ,
z_20*z_16 ,
z_20*z_17 ,
z_20*z_18 ,
z_20*z_19 ,
z_20^2 ,
z_20*z_21 ,
z_20*z_22 ,
z_20*z_23 ,
z_20*z_24 ,
z_20*z_25 ,
z_20*z_26 ,
z_20*z_27 ,
z_20*z_28 ,
z_20*z_29 ,
z_20*z_30 ,
z_21*b_2 ,
z_21*b_3 ,
z_21*b_4 ,
z_21*b_5 ,
z_21*b_6 ,
z_21*b_7 ,
z_21*b_8 ,
z_21*b_9 ,
z_21*b_10 ,
z_21*b_11 + z_21 ,
z_21*b_12 ,
z_21*b_13 ,
z_21*b_14 ,
z_21*b_15 ,
z_21*z_1 ,
z_21*z_2 ,
z_21*z_3 ,
z_21*z_4 ,
z_21*z_5 ,
z_21*z_6 ,
z_21*z_7 ,
z_21*z_8 ,
z_21*z_9 ,
z_21*z_10 ,
z_21*z_11 ,
z_21*z_12 ,
z_21*z_13 ,
z_21*z_14 ,
z_21*z_15 ,
z_21*z_17 ,
z_21*z_20 ,
z_21^2 ,
z_21*z_22 ,
z_21*z_23 ,
z_21*z_24 ,
z_21*z_25 ,
z_21*z_26 ,
z_21*z_27 ,
z_21*z_28 ,
z_21*z_29 ,
z_21*z_30 ,
z_22*b_2 ,
z_22*b_3 ,
z_22*b_4 ,
z_22*b_5 ,
z_22*b_6 ,
z_22*b_7 ,
z_22*b_8 ,
z_22*b_9 ,
z_22*b_10 ,
z_22*b_11 ,
z_22*b_12 ,
z_22*b_13 ,
z_22*b_14 ,
z_22*b_15 ,
z_22*z_1 + z_24*z_18 ,
z_22*z_3 ,
z_22*z_4 ,
z_22*z_5 ,
z_22*z_6 ,
z_22*z_7 ,
z_22*z_8 ,
z_22*z_9 ,
z_22*z_10 ,
z_22*z_11 ,
z_22*z_12 ,
z_22*z_13 ,
z_22*z_14 ,
z_22*z_15 ,
z_22*z_16 ,
z_22*z_17 ,
z_22*z_18 ,
z_22*z_19 ,
z_22*z_20 ,
z_22*z_21 ,
z_22^2 ,
z_22*z_23 ,
z_22*z_24 ,
z_22*z_25 ,
z_22*z_26 ,
z_22*z_27 ,
z_22*z_28 ,
z_22*z_29 ,
z_22*z_30 ,
z_23*b_2 ,
z_23*b_3 ,
z_23*b_4 ,
z_23*b_5 ,
z_23*b_6 ,
z_23*b_7 ,
z_23*b_8 ,
z_23*b_9 ,
z_23*b_10 + z_23 ,
z_23*b_11 ,
z_23*b_12 ,
z_23*b_13 ,
z_23*b_14 ,
z_23*b_15 ,
z_23*z_1 ,
z_23*z_2 ,
z_23*z_3 ,
z_23*z_4 ,
z_23*z_5 ,
z_23*z_6 ,
z_23*z_7 ,
z_23*z_8 ,
z_23*z_9 ,
z_23*z_10 ,
z_23*z_11 ,
z_23*z_12 ,
z_23*z_13 ,
z_23*z_14 + z_24*z_17 ,
z_23*z_16 ,
z_23*z_17 ,
z_23*z_18 ,
z_23*z_19 ,
z_23*z_20 ,
z_23*z_21 ,
z_23*z_22 ,
z_23^2 ,
z_23*z_24 ,
z_23*z_25 ,
z_23*z_26 ,
z_23*z_27 ,
z_23*z_28 ,
z_23*z_29 ,
z_23*z_30 ,
z_24*b_2 ,
z_24*b_3 ,
z_24*b_4 ,
z_24*b_5 ,
z_24*b_6 ,
z_24*b_7 ,
z_24*b_8 ,
z_24*b_9 ,
z_24*b_10 ,
z_24*b_11 + z_24 ,
z_24*b_12 ,
z_24*b_13 ,
z_24*b_14 ,
z_24*b_15 ,
z_24*z_1 ,
z_24*z_2 ,
z_24*z_3 ,
z_24*z_4 ,
z_24*z_5 ,
z_24*z_6 ,
z_24*z_7 ,
z_24*z_8 ,
z_24*z_9 ,
z_24*z_10 ,
z_24*z_11 ,
z_24*z_12 ,
z_24*z_13 ,
z_24*z_14 ,
z_24*z_15 ,
z_24*z_16 ,
z_24*z_20 ,
z_24*z_21 ,
z_24*z_22 ,
z_24*z_23 ,
z_24^2 ,
z_24*z_25 ,
z_24*z_26 ,
z_24*z_27 ,
z_24*z_28 ,
z_24*z_29 ,
z_24*z_30 ,
z_25*b_2 + z_25 ,
z_25*b_3 ,
z_25*b_4 ,
z_25*b_5 ,
z_25*b_6 ,
z_25*b_7 ,
z_25*b_8 ,
z_25*b_9 ,
z_25*b_10 ,
z_25*b_11 ,
z_25*b_12 ,
z_25*b_13 ,
z_25*b_14 ,
z_25*b_15 ,
z_25*z_1 ,
z_25*z_2 ,
z_25*z_4 ,
z_25*z_5 ,
z_25*z_6 ,
z_25*z_7 ,
z_25*z_8 ,
z_25*z_9 ,
z_25*z_10 ,
z_25*z_11 ,
z_25*z_12 ,
z_25*z_13 ,
z_25*z_14 ,
z_25*z_15 ,
z_25*z_16 ,
z_25*z_17 ,
z_25*z_18 ,
z_25*z_19 ,
z_25*z_20 ,
z_25*z_21 ,
z_25*z_22 ,
z_25*z_23 ,
z_25*z_24 ,
z_25^2 ,
z_25*z_26 ,
z_25*z_27 ,
z_25*z_28 ,
z_25*z_29 ,
z_25*z_30 ,
z_26*b_2 ,
z_26*b_3 + z_26 ,
z_26*b_4 ,
z_26*b_5 ,
z_26*b_6 ,
z_26*b_7 ,
z_26*b_8 ,
z_26*b_9 ,
z_26*b_10 ,
z_26*b_11 ,
z_26*b_12 ,
z_26*b_13 ,
z_26*b_14 ,
z_26*b_15 ,
z_26*z_1 ,
z_26*z_2 ,
z_26*z_3 ,
z_26*z_5 ,
z_26*z_6 ,
z_26*z_7 ,
z_26*z_8 ,
z_26*z_9 ,
z_26*z_10 ,
z_26*z_11 ,
z_26*z_12 ,
z_26*z_13 ,
z_26*z_14 ,
z_26*z_15 ,
z_26*z_16 ,
z_26*z_17 ,
z_26*z_18 ,
z_26*z_19 ,
z_26*z_20 ,
z_26*z_21 ,
z_26*z_22 ,
z_26*z_23 ,
z_26*z_24 ,
z_26*z_25 ,
z_26^2 ,
z_26*z_27 ,
z_26*z_28 ,
z_26*z_29 ,
z_26*z_30 ,
z_27*b_2 ,
z_27*b_3 ,
z_27*b_4 ,
z_27*b_5 ,
z_27*b_6 ,
z_27*b_7 ,
z_27*b_8 ,
z_27*b_9 ,
z_27*b_10 ,
z_27*b_11 + z_27 ,
z_27*b_12 ,
z_27*b_13 ,
z_27*b_14 ,
z_27*b_15 ,
z_27*z_1 ,
z_27*z_2 ,
z_27*z_3 ,
z_27*z_4 ,
z_27*z_5 ,
z_27*z_6 ,
z_27*z_7 ,
z_27*z_8 ,
z_27*z_9 ,
z_27*z_10 ,
z_27*z_11 ,
z_27*z_12 ,
z_27*z_13 ,
z_27*z_14 ,
z_27*z_15 ,
z_27*z_16 ,
z_27*z_20 ,
z_27*z_21 ,
z_27*z_22 ,
z_27*z_23 ,
z_27*z_24 ,
z_27*z_25 ,
z_27*z_26 ,
z_27^2 ,
z_27*z_28 ,
z_27*z_29 ,
z_27*z_30 ,
z_28*b_2 ,
z_28*b_3 ,
z_28*b_4 ,
z_28*b_5 ,
z_28*b_6 ,
z_28*b_7 ,
z_28*b_8 ,
z_28*b_9 ,
z_28*b_10 ,
z_28*b_11 ,
z_28*b_12 ,
z_28*b_13 ,
z_28*b_14 ,
z_28*b_15 + z_28 ,
z_28*z_1 ,
z_28*z_2 ,
z_28*z_3 ,
z_28*z_4 ,
z_28*z_5 ,
z_28*z_6 ,
z_28*z_7 ,
z_28*z_8 ,
z_28*z_9 ,
z_28*z_10 ,
z_28*z_11 ,
z_28*z_12 ,
z_28*z_13 ,
z_28*z_14 ,
z_28*z_15 ,
z_28*z_16 ,
z_28*z_17 ,
z_28*z_18 ,
z_28*z_19 ,
z_28*z_20 ,
z_28*z_21 ,
z_28*z_22 ,
z_28*z_23 ,
z_28*z_24 ,
z_28*z_25 ,
z_28*z_26 ,
z_28*z_27 ,
z_28^2 ,
z_29*b_2 ,
z_29*b_3 ,
z_29*b_4 ,
z_29*b_5 ,
z_29*b_6 ,
z_29*b_7 ,
z_29*b_8 ,
z_29*b_9 ,
z_29*b_10 ,
z_29*b_11 ,
z_29*b_12 ,
z_29*b_13 ,
z_29*b_14 ,
z_29*b_15 ,
z_29*z_3 ,
z_29*z_4 ,
z_29*z_5 ,
z_29*z_6 ,
z_29*z_7 ,
z_29*z_8 ,
z_29*z_9 ,
z_29*z_10 ,
z_29*z_11 ,
z_29*z_12 ,
z_29*z_13 ,
z_29*z_14 ,
z_29*z_15 ,
z_29*z_16 ,
z_29*z_17 ,
z_29*z_18 ,
z_29*z_19 ,
z_29*z_20 ,
z_29*z_21 ,
z_29*z_22 ,
z_29*z_23 ,
z_29*z_24 ,
z_29*z_25 ,
z_29*z_26 ,
z_29*z_27 ,
z_29*z_28 ,
z_29^2 ,
z_29*z_30 ,
z_30*b_2 ,
z_30*b_3 ,
z_30*b_4 ,
z_30*b_5 ,
z_30*b_6 ,
z_30*b_7 ,
z_30*b_8 ,
z_30*b_9 ,
z_30*b_10 ,
z_30*b_11 ,
z_30*b_12 ,
z_30*b_13 ,
z_30*b_14 + z_30 ,
z_30*b_15 ,
z_30*z_1 ,
z_30*z_2 ,
z_30*z_3 ,
z_30*z_4 ,
z_30*z_5 ,
z_30*z_6 ,
z_30*z_7 ,
z_30*z_8 ,
z_30*z_9 ,
z_30*z_10 ,
z_30*z_11 ,
z_30*z_12 ,
z_30*z_13 ,
z_30*z_14 ,
z_30*z_15 ,
z_30*z_16 ,
z_30*z_17 ,
z_30*z_18 ,
z_30*z_19 ,
z_30*z_20 ,
z_30*z_21 ,
z_30*z_22 ,
z_30*z_23 ,
z_30*z_24 ,
z_30*z_29 ,
z_30^2 ,
b_1 + b_2 + b_3 + b_4 + b_5 + b_6 + b_7 + b_8 + b_9 + b_10 + b_11 + b_12 + b_13 + b_14 + b_15 + 1 .

# 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_25*z_3*z_27*z_17*z_21*z_16*z_11 + z_27*z_19*z_25*z_3*z_27 + z_28*z_29*z_1*z_24 + z_27*z_19*z_27 + z_28*z_30*z_27 ,
z_4*z_28*z_29*z_2*z_30*z_26 + z_4*z_26*z_4*z_26 + z_4*z_28*z_30*z_26 ,
z_4*z_28*z_30*z_27*z_19*z_26 + z_4*z_28*z_30*z_26 ,
z_4*z_28*z_30*z_27*z_19*z_28 ,
z_4*z_28*z_30*z_28*z_29*z_2 + z_4*z_25*z_3*z_28 ,
z_5*z_13*z_9*z_12*z_5*z_13 + z_5*z_13*z_8*z_6 ,
z_9*z_12*z_5*z_13*z_9*z_12 + z_8*z_6*z_9*z_12 ,
z_17*z_21*z_19*z_25*z_3*z_26 + z_19*z_26*z_4*z_26 + z_19*z_26 ,
z_19*z_27*z_19*z_25*z_3*z_27 ,
z_21*z_19*z_27*z_19*z_25*z_3 + z_21*z_18*z_24*z_19 + z_21*z_19*z_28*z_30 ,
z_25*z_3*z_27*z_17*z_21*z_19 + z_26*z_4*z_26*z_4 + z_27*z_19*z_27*z_19 + z_28*z_29*z_2*z_30 + z_28*z_30*z_26*z_4 + z_28*z_30*z_27*z_19 + z_26*z_4 + z_27*z_19 ,
z_30*z_28*z_30*z_27*z_19*z_26 ,
z_1*z_22*z_2*z_30*z_26 + z_2*z_30*z_28*z_30*z_26 ,
z_1*z_24*z_18*z_22*z_2 ,
z_1*z_24*z_18*z_24*z_18 + z_2*z_30*z_28*z_29*z_1 ,
z_2*z_30*z_28*z_29*z_2 ,
z_2*z_30*z_28*z_30*z_27 + z_1*z_24*z_18*z_24 ,
z_3*z_27*z_18*z_22*z_2 + z_3*z_28 ,
z_3*z_27*z_18*z_24*z_17 ,
z_3*z_27*z_19*z_26*z_4 + z_3*z_28*z_30 ,
z_3*z_28*z_30*z_26*z_4 ,
z_4*z_28*z_29*z_1*z_22 + z_4*z_28*z_30*z_28*z_29 ,
z_4*z_28*z_30*z_26*z_4 ,
z_4*z_28*z_30*z_27*z_18 ,
z_11*z_19*z_25*z_3*z_26 + z_11*z_19*z_26 ,
z_11*z_19*z_25*z_3*z_27 ,
z_15*z_24*z_19*z_28*z_29 ,
z_15*z_24*z_19*z_28*z_30 ,
z_18*z_24*z_19*z_25*z_3 + z_19*z_27*z_19*z_25*z_3 + z_16*z_11*z_19 + z_19*z_26*z_4 + z_19*z_27*z_19 ,
z_19*z_25*z_3*z_27*z_17 + z_16*z_11*z_17 + z_18*z_24*z_17 ,
z_19*z_26*z_4*z_26*z_4 ,
z_19*z_28*z_29*z_2*z_30 + z_19*z_26*z_4 ,
z_19*z_28*z_30*z_26*z_4 ,
z_19*z_28*z_30*z_28*z_29 + z_19*z_28*z_29 + z_18*z_22 ,
z_21*z_18*z_24*z_19*z_25 ,
z_21*z_19*z_25*z_3*z_27 + z_21*z_16*z_11 + z_21*z_18*z_24 + z_21*z_19*z_27 ,
z_22*z_2*z_30*z_28*z_29 + z_24*z_19*z_28*z_29 + z_24*z_18*z_22 ,
z_22*z_2*z_30*z_28*z_30 ,
z_24*z_19*z_25*z_3*z_26 + z_22*z_2*z_30*z_26 ,
z_24*z_19*z_25*z_3*z_27 + z_24*z_18*z_24 ,
z_24*z_19*z_28*z_29*z_2 + z_24*z_18*z_22*z_2 ,
z_24*z_19*z_28*z_30*z_26 ,
z_24*z_19*z_28*z_30*z_28 + z_22*z_2*z_30*z_28 + z_24*z_18*z_22*z_2 ,
z_26*z_4*z_25*z_3*z_27 + z_28*z_30*z_27 ,
z_26*z_4*z_25*z_3*z_28 + z_28*z_30*z_28*z_29*z_2 + z_25*z_3*z_28 ,
z_26*z_4*z_26*z_4*z_25 + z_28*z_29*z_2*z_30*z_25 ,
z_26*z_4*z_26*z_4*z_26 + z_28*z_29*z_2*z_30*z_26 + z_28*z_30*z_27*z_19*z_26 + z_26*z_4*z_26 + z_27*z_19*z_26 ,
z_27*z_18*z_24*z_17*z_21 + z_27*z_19*z_27 ,
z_27*z_19*z_25*z_3*z_26 + z_28*z_29*z_2*z_30*z_26 + z_26*z_4*z_26 + z_27*z_19*z_26 + z_28*z_30*z_26 ,
z_27*z_19*z_26*z_4*z_26 + z_28*z_29*z_2*z_30*z_26 + z_28*z_30*z_27*z_19*z_26 + z_26*z_4*z_26 + z_27*z_19*z_26 ,
z_27*z_19*z_27*z_19*z_25 ,
z_28*z_29*z_1*z_22*z_2 + z_25*z_3*z_28 ,
z_28*z_29*z_1*z_24*z_18 ,
z_28*z_29*z_1*z_24*z_19 + z_26*z_4*z_26*z_4 + z_27*z_19*z_26*z_4 ,
z_28*z_30*z_27*z_18*z_22 + z_28*z_29*z_1*z_22 + z_28*z_30*z_28*z_29 ,
z_28*z_30*z_27*z_18*z_23 ,
z_28*z_30*z_27*z_19*z_27 ,
z_28*z_30*z_28*z_29*z_1 ,
z_29*z_1*z_22*z_2*z_30 + z_30*z_25*z_3 + z_30*z_26*z_4 + z_30*z_27*z_19 + z_30*z_28*z_30 ,
z_29*z_1*z_24*z_18*z_22 ,
z_29*z_1*z_24*z_18*z_24 + z_30*z_27*z_19*z_27 ,
z_30*z_27*z_18*z_22*z_2 + z_29*z_1*z_22*z_2 + z_30*z_25*z_3*z_28 + z_30*z_28*z_29*z_2 ,
z_30*z_27*z_18*z_23*z_15 + z_29*z_1*z_24*z_18 ,
z_30*z_27*z_19*z_26*z_4 + z_30*z_25*z_3 + z_30*z_28*z_30 ,
z_30*z_27*z_19*z_27*z_19 + z_30*z_25*z_3 + z_30*z_28*z_30 ,
z_30*z_28*z_29*z_1*z_22 + z_30*z_27*z_18*z_22 + z_29*z_1*z_22 + z_30*z_28*z_29 ,
z_30*z_28*z_29*z_1*z_24 + z_30*z_27*z_19*z_27 ,
z_30*z_28*z_29*z_2*z_30 + z_30*z_26*z_4 + z_30*z_27*z_19 ,
z_30*z_28*z_30*z_26*z_4 + z_30*z_28*z_30*z_27*z_19 ,
z_30*z_28*z_30*z_27*z_18 + z_29*z_1*z_24*z_18 + z_30*z_28*z_29*z_1 ,
z_1*z_24*z_19*z_25 + z_2*z_30*z_25 ,
z_1*z_24*z_19*z_28 + z_1*z_22*z_2 + z_2*z_30*z_28 ,
z_2*z_30*z_25*z_3 + z_2*z_30*z_28*z_30 ,
z_2*z_30*z_26*z_4 + z_1*z_24*z_19 ,
z_3*z_27*z_18*z_23 ,
z_3*z_27*z_19*z_25 ,
z_3*z_27*z_19*z_27 ,
z_3*z_28*z_30*z_27 ,
z_3*z_28*z_30*z_28 ,
z_5*z_13*z_8*z_7 ,
z_6*z_9*z_12*z_5 + z_7*z_10*z_6*z_9 ,
z_8*z_7*z_10*z_6 + z_9*z_12*z_5*z_13 + z_8*z_6 ,
z_10*z_6*z_9*z_12 ,
z_11*z_17*z_21*z_16 ,
z_11*z_17*z_21*z_19 + z_11*z_19*z_25*z_3 + z_11*z_19 ,
z_11*z_19*z_26*z_4 ,
z_12*z_5*z_13*z_8 + z_13*z_8*z_7*z_10 ,
z_15*z_24*z_19*z_25 ,
z_16*z_11*z_17*z_21 + z_18*z_24*z_17*z_21 + z_19*z_27 ,
z_16*z_11*z_19*z_25 + z_19*z_27*z_19*z_25 ,
z_16*z_11*z_19*z_26 + z_19*z_28*z_30*z_26 ,
z_17*z_21*z_19*z_27 + z_19*z_25*z_3*z_27 + z_16*z_11 + z_18*z_24 + z_19*z_27 ,
z_17*z_21*z_19*z_28 + z_18*z_22*z_2 ,
z_18*z_22*z_2*z_30 + z_19*z_26*z_4 ,
z_18*z_24*z_18*z_22 + z_19*z_28*z_29 + z_18*z_22 ,
z_18*z_24*z_18*z_24 ,
z_18*z_24*z_19*z_28 + z_19*z_28*z_29*z_2 + z_19*z_28*z_30*z_28 + z_18*z_22*z_2 ,
z_19*z_25*z_3*z_28 + z_19*z_28*z_29*z_2 + z_18*z_22*z_2 ,
z_19*z_26*z_4*z_25 ,
z_19*z_27*z_19*z_26 ,
z_19*z_27*z_19*z_27 ,
z_19*z_27*z_19*z_28 + z_19*z_28*z_29*z_2 + z_18*z_22*z_2 ,
z_19*z_28*z_29*z_1 + z_18*z_24*z_18 ,
z_19*z_28*z_30*z_27 ,
z_21*z_16*z_11*z_19 + z_21*z_18*z_24*z_19 + z_21*z_19*z_27*z_19 + z_21*z_19*z_28*z_30 ,
z_21*z_19*z_28*z_29 ,
z_22*z_2*z_30*z_25 ,
z_24*z_17*z_21*z_19 + z_24*z_19*z_25*z_3 + z_24*z_19*z_28*z_30 + z_22*z_2*z_30 ,
z_24*z_18*z_24*z_19 + z_24*z_19*z_28*z_30 ,
z_25*z_3*z_27*z_18 + z_27*z_18*z_23*z_15 + z_28*z_29*z_1 ,
z_25*z_3*z_27*z_19 + z_26*z_4*z_25*z_3 + z_27*z_19*z_26*z_4 + z_28*z_30*z_26*z_4 + z_28*z_30 ,
z_25*z_3*z_28*z_30 + z_28*z_30*z_26*z_4 + z_28*z_30*z_27*z_19 ,
z_27*z_18*z_24*z_18 + z_28*z_30*z_27*z_18 ,
z_27*z_19*z_28*z_29 + z_28*z_29*z_1*z_22 + z_28*z_30*z_28*z_29 + z_27*z_18*z_22 ,
z_27*z_19*z_28*z_30 + z_28*z_30*z_26*z_4 ,
z_28*z_30*z_28*z_30 ,
z_29*z_2*z_30*z_28 + z_30*z_28*z_29*z_2 ,
z_30*z_25*z_3*z_26 + z_30*z_28*z_30*z_26 ,
z_30*z_25*z_3*z_27 + z_30*z_28*z_30*z_27 ,
z_30*z_26*z_4*z_25 + z_30*z_25 ,
z_30*z_26*z_4*z_26 ,
z_30*z_27*z_17*z_21 + z_30*z_27*z_19*z_27 + z_29*z_1*z_24 ,
z_30*z_27*z_18*z_24 + z_30*z_27*z_19*z_27 + z_30*z_28*z_30*z_27 ,
z_30*z_27*z_19*z_25 + z_30*z_25 ,
z_30*z_28*z_30*z_28 ,
z_2*z_30*z_27 + z_1*z_24 ,
z_3*z_26*z_4 + z_3*z_27*z_19 + z_3*z_28*z_30 ,
z_3*z_28*z_29 ,
z_11*z_19*z_27 ,
z_11*z_19*z_28 ,
z_19*z_27*z_17 ,
z_19*z_27*z_18 ,
z_21*z_19*z_26 ,
z_24*z_19*z_26 ,
z_24*z_19*z_27 ,
z_26*z_4*z_28 + z_27*z_19*z_28 ,
z_28*z_30*z_25 ,

## The projective resolutions of the simple modules.

Degree 0:
1

Degree 1:
13 15

Degree 2:
1 10 11 15

Degree 3:
1 8 11 14

Degree 4:
1 2 11 12

Degree 5:
12 13

Degree 6:
10

Degree 0:
2

Degree 1:
14

Degree 2:
2 2 10 15

Degree 3:
12 13 14

Degree 4:
1 2 10 10 11

Degree 5:
12 13

Degree 6:
10

Degree 0:
3

Degree 1:
14

Degree 2:
11

Degree 3:
8

Degree 0:
4

Degree 1:
9

Degree 2:
4 7

Degree 3:
5

Degree 4:
7

Degree 0:
5

Degree 1:
6 7

Degree 2:
5 9

Degree 3:
4 6

Degree 4:
5

Degree 5:
7

Degree 0:
6

Degree 1:
5 9

Degree 2:
6 6

Degree 3:
5

Degree 0:
7

Degree 1:
5

Degree 2:
4 7

Degree 3:
9

Degree 4:
4 7

Degree 5:
5

Degree 6:
7

Degree 0:
8

Degree 1:
11

Degree 2:
8 8 13 14

Degree 3:
1 3 11 11

Degree 4:
8 8 13 14

Degree 5:
11

Degree 6:
8

Degree 0:
9

Degree 1:
4 6

Degree 2:
5

Degree 3:
7

Degree 0:
10

Degree 1:
12 13

Degree 2:
1 2 10 10 11

Degree 3:
12 13 14

Degree 4:
2 2 10 10 15

Degree 5:
12 13 14

Degree 6:
1 2 10 10 11

Degree 7:
12 13

Degree 8:
10

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

#### Simple Module Number 11

Degree 0:
11

Degree 1:
8 12 13 14

Degree 2:
1 3 10 11 11 15

Degree 3:
1 8 8 13 14 14

Degree 4:
1 2 11 11

Degree 5:
8 12 13

Degree 6:
10

Degree 0:
12

Degree 1:
10 11

Degree 2:
12 13

Degree 3:
2 10 15

Degree 4:
1 12 14

Degree 5:
1 2 10 11

Degree 6:
12 13

Degree 7:
10

Degree 0:
13

Degree 1:
1 10 11

Degree 2:
8 12 13 14

Degree 3:
2 10 11 15

Degree 4:
8 13 14

Degree 5:
1 2 10 11

Degree 6:
12 13

Degree 7:
10

Degree 0:
14

Degree 1:
2 3 11 15

Degree 2:
8 13 14 14

Degree 3:
1 2 10 11 11

Degree 4:
8 12 13

Degree 5:
10

Degree 0:
15

Degree 1:
1 14

Degree 2:
1 2 11

Degree 3:
12 13

Degree 4:
10