Schur Algebra S( 4 ,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 4. . The dimension of M is 8143 .

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

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, 5, 5, 5, 5, 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

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

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, 5, 5, 5, 5, 5, 5, 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

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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 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

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

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

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

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

2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6

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

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

3, 3, 6, 6, 6

2, 2, 2



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

3, 3, 6, 6, 6

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

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

2, 2, 2, 2, 2, 2, 6, 6, 6, 6, 6, 6, 6, 6

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

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

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

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

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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 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

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, 5, 5, 5, 5, 5, 5, 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

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

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, 5, 5, 5, 5, 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

1, 1, 1, 1, 1, 1, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 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



The module M has simple direct summands:

30 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). 6 direct summands of the form:


radical layers
6
5
6



socle layers
6
5
6


2). 2 direct summands of the form:


radical layers
5, 6
3, 6
5



socle layers
5
3, 6
5, 6


3). 8 direct summands of the form:


radical layers
3
5
4
5
3



socle layers
3
5
4
5
3


4). 5 direct summands of the form:


radical layers
5
3, 6
5, 6
3
5



socle layers
5
3
5, 6
3, 6
5


5). 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


6). 2 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


7). 1 direct summand 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


8). 7 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


9). 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


10). 3 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


11). 2 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


12). 1 direct summand 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


13). 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 64, 384, 536, 321, 494, 832 .

The cartan matrix of A is



The determinant of the Cartan matrix is 610.

The blocks of A consist of the following irreducible modules:

Projective module number 1 is simple.

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


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



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



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



socle layers
5
3, 4
5, 5, 5
3, 3, 4, 4, 5, 6
3, 3, 4, 5, 5, 5, 6, 6, 6
2, 3, 4, 5, 5, 5, 6, 6
2, 2, 3, 3, 4, 5, 5, 6, 6
3, 4, 4, 5, 5, 6, 6, 6, 6
2, 3, 3, 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, 5, 5, 5, 5, 6, 6
2, 3, 3, 4, 4, 5, 6, 6, 6
2, 3, 4, 5, 6, 6, 6
2, 3, 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, 5, 5, 5, 6, 6, 6
3, 3, 3, 5, 5, 5, 6, 6, 6
2, 3, 3, 4, 4, 6, 6, 6, 6
2, 4, 4, 5, 5, 6, 6, 6
2, 2, 3, 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 726 .

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.


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 1, 24, 55, 18, 30, 29, 86, 39, 31, 56, 8, 46, 136, 53, 114 .

The cartan matrix of H is



The determinant of the Cartan matrix is 1.

The blocks of H consist of the following irreducible modules:

Projective module number 1 is simple.

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


Projective module number 2


radical layers
2
7, 15
12, 13, 14
7, 9, 15
3, 10, 12, 13
5, 7, 13
2, 3
7, 15
13, 14
15
10



socle layers
2
7
12, 13
7, 9, 15
12, 13, 14
3, 7, 15
2, 5, 10
3, 13, 15
7, 14
13, 15
10



Projective module number 3


radical layers
3
5, 7, 13, 15
3, 12, 13, 14
7, 7, 8, 9, 10, 15
2, 3, 4, 12, 13, 13, 13, 15
5, 6, 7, 7, 8, 10, 13, 14, 15
2, 3, 12, 13, 14, 15
7, 7, 9, 15, 15
3, 10, 12, 13, 13, 14
5, 7, 13, 15
3, 10



socle layers
3
5, 7
3, 12, 13, 13
7, 7, 9, 15
2, 3, 12, 13, 14
5, 7, 7, 8, 10, 13, 15
2, 3, 4, 10, 12, 13, 13, 15
7, 7, 8, 9, 14, 15, 15
3, 12, 13, 13, 14, 14, 15
5, 6, 7, 10, 13, 15, 15
3, 10, 13



Projective module number 4


radical layers
4
8, 9, 14
5, 12, 13, 15
7, 11
3, 12
9
4, 13
8, 14
15



socle layers
4
9
12
8, 11
12, 13
7, 9, 14
4, 5, 13, 15
3, 8, 14
15



Projective module number 5


radical layers
5
3, 9, 14
4, 5, 7, 13, 15
9, 12, 13, 14
5, 7, 8, 10
2, 3, 15
7, 13, 15
12, 13, 14
7, 15
3, 10



socle layers
5
3
7, 9
12, 13, 14
5, 7, 13, 15
2, 3, 4, 10
7, 8, 9, 15
12, 13, 14, 14
5, 7, 13, 15, 15
3, 10



Projective module number 6


radical layers
6
13, 15
6, 8, 10
13, 13, 15, 15
6, 6, 7
3, 13
8, 10, 13
13, 15, 15
6, 7
13
8, 10
13, 15
6



socle layers
6
13, 15
8, 10
13
6, 7
13, 15, 15
8, 10, 13
3, 13
6, 6, 7
13, 13, 15, 15
6, 8, 10
13, 15
6



Projective module number 7


radical layers
7
2, 3, 12, 13
5, 7, 7, 8, 9, 10, 13, 15
2, 3, 3, 4, 12, 12, 13, 13, 13, 14, 15, 15
5, 6, 7, 7, 7, 7, 7, 8, 9, 13, 14, 14, 15, 15
2, 3, 3, 10, 12, 12, 13, 13, 13, 13, 14, 15, 15
5, 7, 7, 7, 8, 9, 10, 10, 13, 15, 15
2, 3, 3, 10, 12, 13, 13, 13, 14, 15
5, 6, 7, 7, 13, 15, 15
3, 10, 13, 14
15
10



socle layers
7
2, 3
5, 7, 13
3, 8, 10, 12, 12, 13
7, 7, 9, 9, 13, 13, 15, 15
2, 3, 7, 7, 12, 12, 13, 13, 14, 14
3, 5, 7, 7, 7, 13, 13, 15, 15
2, 2, 3, 4, 5, 8, 10, 10, 12, 13, 13, 15
3, 7, 7, 8, 9, 13, 14, 15, 15, 15
3, 6, 7, 10, 12, 13, 14, 14, 14, 15
5, 7, 10, 13, 13, 13, 15, 15, 15, 15
3, 6, 10, 10, 13



Projective module number 8


radical layers
8
4, 13, 15
6, 7, 8, 9, 14
3, 12, 13, 13, 15
5, 7, 8, 10, 11, 13
3, 12, 13, 15, 15
6, 7, 9
4, 13, 13
8, 8, 10, 14
13, 15, 15
6



socle layers
8
13
4, 7
9, 13, 15
8, 10, 12
3, 8, 11, 13
6, 7, 12, 13
7, 9, 13, 13, 14, 15, 15
4, 5, 6, 8, 10, 13, 15
3, 8, 13, 14, 15
6, 15



Projective module number 9


radical layers
9
4, 5, 12, 13
7, 8, 9, 11, 14
2, 3, 5, 12, 15
7, 9, 13, 15
4, 12, 13, 13, 14
7, 8, 14, 15
3, 10, 15



socle layers
9
12, 13
5, 7, 11
2, 3, 4, 12
7, 8, 9, 9, 15
4, 12, 13, 13, 14, 14
5, 7, 8, 13, 14, 15, 15
3, 10, 15



Projective module number 10


radical layers
10
13, 15
6, 7, 14
3, 13, 15
2, 5, 8, 10, 10, 13
3, 7, 13, 13, 15, 15, 15
6, 7, 7, 12, 13, 14, 14
7, 9, 13, 13, 15, 15
3, 8, 10, 10, 10, 12, 13
5, 7, 13, 13, 15
2, 3, 6
7, 15
13, 14
15
10



socle layers
10
15
13, 14
7, 15
2, 3
5, 7, 13
3, 8, 10, 10, 12, 13
7, 9, 13, 13, 15, 15
7, 7, 12, 13, 14, 14
3, 7, 13, 13, 15, 15
2, 5, 6, 8, 10, 10
3, 13, 13, 15, 15
6, 7, 10, 14
13, 13, 15, 15
6, 10



Projective module number 11


radical layers
11
12
9
4, 13
8, 14
15



socle layers
11
12
9
4, 13
8, 14
15



Projective module number 12


radical layers
12
7, 9, 11
2, 3, 4, 12, 12, 13
5, 7, 7, 8, 9, 13, 14, 15
2, 3, 4, 12, 13, 13, 14, 15
7, 7, 8, 9, 14, 15, 15
3, 10, 12, 13, 13, 14, 15
5, 7, 13, 15
3, 10



socle layers
12
7, 9
2, 3, 12, 13
5, 7, 7, 11
2, 3, 4, 12, 12, 13, 13, 15
7, 7, 8, 9, 9, 14, 15
3, 4, 12, 13, 13, 14, 14, 15
5, 7, 8, 10, 13, 14, 15, 15
3, 10, 13, 15



Projective module number 13


radical layers
13
3, 6, 7, 8, 9, 10
2, 3, 4, 5, 7, 12, 13, 13, 13, 13, 13, 13, 15, 15, 15
5, 6, 6, 7, 7, 7, 8, 8, 10, 11, 12, 13, 13, 14, 14, 15
2, 3, 3, 3, 7, 8, 9, 10, 12, 12, 13, 13, 13, 14, 15, 15, 15, 15
2, 3, 6, 7, 7, 7, 7, 8, 9, 9, 10, 10, 13, 13, 13, 14, 15, 15, 15
3, 4, 5, 6, 7, 10, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15
5, 6, 7, 7, 7, 8, 8, 10, 10, 12, 13, 13, 14, 14, 15
2, 3, 3, 7, 10, 13, 13, 15, 15, 15
3, 6, 7, 8, 10, 10, 15
13, 13, 13, 14, 15
6, 15
10



socle layers
13
7
2, 3, 8, 10
3, 5, 7, 13, 13
3, 7, 7, 8, 10, 12, 13, 15
7, 9, 9, 12, 13, 13, 13, 13, 14, 15, 15, 15
6, 7, 7, 7, 8, 10, 12, 12, 13, 13, 13, 13, 14, 14, 15
2, 3, 3, 3, 5, 7, 7, 10, 11, 13, 13, 13, 13, 15, 15, 15
2, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 10, 10, 10, 12, 15
3, 7, 8, 9, 9, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15
4, 6, 6, 7, 7, 8, 10, 10, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15
3, 5, 6, 7, 8, 10, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15
3, 6, 6, 10, 10, 13, 15



Projective module number 14


radical layers
14
4, 5, 15
2, 3, 8, 9, 10, 14, 14
5, 7, 12, 13, 13, 15, 15, 15
7, 7, 11, 12, 13, 14
3, 7, 9, 12, 13, 15
3, 9, 10, 10, 12, 13
4, 5, 7, 13, 13
2, 3, 8, 14
7, 15, 15
13, 14
15
10



socle layers
14
15
2
5, 7
3, 4, 10, 12, 13
7, 9, 9, 13, 15
7, 12, 12, 13, 14, 14
3, 7, 8, 11, 13, 15, 15
2, 5, 10, 10, 12, 13
3, 7, 9, 13, 14, 15
4, 5, 7, 13, 14, 15
3, 8, 13, 14, 15
10, 15



Projective module number 15


radical layers
15
2, 3, 6, 8, 10, 14
4, 5, 7, 13, 13, 13, 15, 15, 15, 15, 15
2, 3, 6, 6, 7, 7, 8, 9, 10, 12, 13, 14, 14, 14
3, 7, 7, 9, 12, 13, 13, 13, 13, 15, 15, 15, 15
3, 5, 7, 7, 8, 8, 10, 10, 10, 11, 12, 12, 13, 13, 13, 14
3, 5, 7, 7, 9, 12, 13, 13, 13, 13, 15, 15, 15, 15
2, 3, 3, 6, 6, 7, 9, 10, 10, 12, 13
4, 5, 7, 7, 13, 13, 13, 15
2, 3, 8, 8, 10, 13, 14, 14
7, 13, 15, 15, 15, 15
6, 10, 13, 14
15
10



socle layers
15
14
15
2, 2, 3, 8, 10
5, 7, 7, 13
3, 4, 6, 7, 10, 12, 12, 13, 13, 13
7, 7, 9, 9, 9, 13, 13, 15, 15, 15, 15, 15
7, 7, 8, 10, 12, 12, 12, 13, 13, 14, 14, 14
3, 3, 3, 7, 7, 8, 11, 13, 13, 13, 13, 15, 15, 15
2, 2, 5, 5, 6, 6, 7, 8, 10, 10, 10, 10, 12, 13
3, 3, 7, 9, 13, 13, 13, 13, 14, 15, 15, 15, 15
4, 5, 6, 7, 7, 8, 10, 13, 14, 14, 15, 15
3, 8, 13, 13, 13, 13, 14, 15, 15, 15
6, 6, 10, 10, 15


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_12*z_40*z_46*z_40*z_45*z_26 ,
z_25*z_34*z_18*z_35*z_21*z_45 ,
z_27*z_46*z_40*z_42*z_6*z_41 + z_27*z_46*z_40*z_41 + z_26*z_34*z_15 ,
z_27*z_46*z_40*z_45*z_26*z_34 + z_27*z_42*z_5*z_34 ,
z_40*z_46*z_40*z_42*z_6*z_41 ,
z_40*z_46*z_40*z_45*z_26*z_34 + z_39*z_10*z_5*z_34 + z_40*z_42*z_5*z_34 ,
z_46*z_38*z_8*z_24*z_31*z_28 + z_44*z_20*z_34*z_17 ,
z_1*z_18*z_32*z_6*z_41 ,
z_1*z_18*z_32*z_6*z_45 + z_2*z_45 ,
z_1*z_18*z_34*z_15*z_2 + z_2*z_42*z_6 ,
z_1*z_18*z_36*z_25*z_34 + z_2*z_42*z_5*z_34 + z_1*z_18*z_34 ,
z_1*z_18*z_36*z_25*z_35 ,
z_1*z_18*z_37*z_26*z_34 + z_2*z_42*z_5*z_34 ,
z_2*z_42*z_5*z_34*z_16 ,
z_6*z_41*z_1*z_18*z_34 + z_6*z_44*z_20*z_34 + z_3*z_10*z_4 + z_4*z_17*z_29 + z_4*z_18*z_34 + z_5*z_32*z_4 + z_5*z_34 ,
z_6*z_41*z_1*z_18*z_36 + z_5*z_36 ,
z_6*z_41*z_1*z_18*z_37 + z_6*z_46*z_40*z_45 + z_5*z_37 + z_6*z_45 ,
z_6*z_44*z_20*z_34*z_17 ,
z_6*z_44*z_20*z_34*z_18 + z_5*z_32*z_5 + z_5*z_36*z_25 ,
z_6*z_46*z_40*z_41*z_1 + z_5*z_32*z_4 ,
z_6*z_46*z_40*z_41*z_2 + z_5*z_35*z_21 + z_5*z_37*z_27 + z_6*z_45*z_27 ,
z_6*z_46*z_40*z_45*z_26 + z_6*z_42*z_5 ,
z_6*z_46*z_40*z_45*z_27 + z_5*z_37*z_27 + z_6*z_45*z_27 ,
z_6*z_46*z_40*z_46*z_39 ,
z_6*z_46*z_40*z_46*z_40 + z_5*z_35*z_21 + z_6*z_41*z_2 + z_6*z_44*z_21 + z_6*z_45*z_27 ,
z_8*z_24*z_30*z_22*z_9 + z_9*z_39*z_12 ,
z_11*z_25*z_34*z_18*z_35 ,
z_11*z_25*z_34*z_18*z_37 + z_12*z_40*z_46*z_40*z_45 ,
z_12*z_40*z_41*z_1*z_17 + z_10*z_4*z_17 + z_11*z_24 ,
z_12*z_40*z_41*z_1*z_18 + z_11*z_25*z_34*z_18 + z_12*z_40*z_44*z_20 ,
z_12*z_40*z_44*z_20*z_34 + z_12*z_40*z_41*z_1 + z_10*z_5*z_34 + z_11*z_25*z_34 ,
z_12*z_40*z_44*z_20*z_35 ,
z_12*z_40*z_45*z_27*z_45 ,
z_12*z_40*z_46*z_40*z_42 ,
z_14*z_44*z_21*z_44*z_20 + z_13*z_37*z_26 + z_14*z_45*z_26 ,
z_14*z_44*z_21*z_44*z_21 + z_13*z_37*z_27 + z_14*z_45*z_27 ,
z_14*z_44*z_21*z_45*z_26 + z_13*z_34*z_18 + z_13*z_35*z_20 + z_14*z_43*z_13 + z_14*z_44*z_20 ,
z_14*z_44*z_21*z_45*z_27 + z_13*z_35*z_21 + z_14*z_42*z_6 + z_14*z_44*z_21 ,
z_14*z_45*z_27*z_43*z_13 + z_14*z_42*z_5 ,
z_16*z_6*z_44*z_20*z_34 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_18*z_35*z_20*z_34 + z_18*z_37*z_26*z_34 ,
z_16*z_6*z_46*z_40*z_41 + z_18*z_32*z_6*z_41 ,
z_16*z_6*z_46*z_40*z_45 + z_16*z_5*z_37 + z_16*z_6*z_45 ,
z_16*z_6*z_46*z_40*z_46 + z_16*z_3*z_12 + z_16*z_6*z_46 ,
z_17*z_29*z_15*z_2*z_46 + z_18*z_36*z_22*z_9 + z_18*z_37*z_27*z_46 + z_16*z_6*z_46 ,
z_17*z_29*z_16*z_5*z_37 + z_18*z_34*z_18*z_37 + z_18*z_35*z_21*z_45 + z_15*z_2*z_45 ,
z_17*z_30*z_25*z_34*z_15 + z_18*z_32*z_6*z_41 + z_18*z_34*z_15 ,
z_17*z_30*z_25*z_34*z_17 + z_17*z_29*z_17 + z_18*z_34*z_17 + z_18*z_36*z_24 ,
z_17*z_30*z_25*z_34*z_18 + z_17*z_29*z_16*z_5 + z_17*z_29*z_18 + z_18*z_33*z_13 ,
z_18*z_32*z_6*z_45*z_26 + z_18*z_33*z_13 ,
z_18*z_32*z_6*z_45*z_27 + z_16*z_6*z_44*z_21 + z_16*z_6*z_46*z_40 + z_17*z_29*z_16*z_6 + z_18*z_32*z_6 + z_18*z_33*z_14 ,
z_18*z_34*z_15*z_2*z_45 ,
z_18*z_34*z_15*z_2*z_46 + z_18*z_36*z_23*z_12 ,
z_18*z_34*z_16*z_4*z_17 + z_17*z_29*z_17 + z_18*z_34*z_17 + z_18*z_36*z_24 ,
z_18*z_34*z_16*z_4*z_18 + z_18*z_34*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_18*z_34*z_18 ,
z_18*z_34*z_16*z_5*z_32 ,
z_18*z_34*z_16*z_5*z_34 + z_17*z_30*z_25*z_34 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_18*z_37*z_26*z_34 + z_16*z_5*z_34 + z_18*z_32*z_4 + z_18*z_34 ,
z_18*z_34*z_16*z_5*z_37 + z_18*z_32*z_6*z_45 + z_18*z_34*z_18*z_37 + z_18*z_35*z_21*z_45 + z_16*z_5*z_37 + z_16*z_6*z_45 ,
z_18*z_34*z_16*z_6*z_44 ,
z_18*z_34*z_16*z_6*z_45 + z_18*z_32*z_6*z_45 + z_18*z_34*z_18*z_37 + z_18*z_35*z_21*z_45 + z_15*z_2*z_45 + z_16*z_5*z_37 + z_16*z_6*z_45 ,
z_18*z_34*z_16*z_6*z_46 + z_16*z_3*z_12 + z_16*z_6*z_46 ,
z_18*z_34*z_18*z_32*z_4 ,
z_18*z_34*z_18*z_32*z_5 + z_18*z_33*z_13 ,
z_18*z_34*z_18*z_32*z_6 ,
z_18*z_34*z_18*z_33*z_14 ,
z_18*z_34*z_18*z_37*z_26 + z_17*z_29*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_30*z_25 + z_18*z_33*z_13 + z_18*z_35*z_20 + z_18*z_36*z_25 + z_18*z_37*z_26 ,
z_18*z_34*z_18*z_37*z_27 + z_18*z_33*z_14 ,
z_18*z_35*z_20*z_34*z_18 + z_17*z_29*z_16*z_5 + z_18*z_32*z_4*z_18 + z_18*z_34*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_30*z_25 + z_18*z_32*z_5 + z_18*z_33*z_13 + z_18*z_36*z_25 ,
z_18*z_35*z_21*z_45*z_26 + z_17*z_29*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_30*z_25 + z_18*z_35*z_20 + z_18*z_36*z_25 + z_18*z_37*z_26 ,
z_18*z_35*z_21*z_45*z_27 + z_18*z_33*z_14 ,
z_18*z_36*z_25*z_34*z_15 + z_18*z_34*z_15 ,
z_18*z_36*z_25*z_34*z_17 + z_17*z_29*z_17 + z_18*z_34*z_17 + z_18*z_36*z_24 ,
z_18*z_36*z_25*z_34*z_18 + z_16*z_6*z_44*z_20 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_29*z_18 + z_17*z_30*z_25 + z_18*z_33*z_13 + z_18*z_35*z_20 + z_18*z_36*z_25 + z_18*z_37*z_26 ,
z_18*z_36*z_25*z_35*z_20 + z_16*z_6*z_44*z_20 + z_18*z_34*z_16*z_5 + z_17*z_29*z_18 + z_17*z_30*z_25 + z_18*z_33*z_13 + z_18*z_34*z_18 + z_18*z_35*z_20 + z_18*z_36*z_25 + z_18*z_37*z_26 ,
z_18*z_36*z_25*z_35*z_21 + z_18*z_37*z_27*z_46*z_40 + z_16*z_6*z_44*z_21 + z_16*z_6*z_46*z_40 + z_17*z_29*z_16*z_6 + z_18*z_34*z_15*z_2 + z_18*z_34*z_16*z_6 + z_18*z_33*z_14 ,
z_18*z_37*z_26*z_34*z_18 + z_17*z_29*z_16*z_5 + z_18*z_32*z_4*z_18 + z_17*z_30*z_25 + z_18*z_32*z_5 + z_18*z_34*z_18 + z_18*z_36*z_25 ,
z_20*z_36*z_25*z_34*z_15 ,
z_20*z_36*z_25*z_34*z_17 ,
z_20*z_36*z_25*z_34*z_18 + z_19*z_7*z_20 + z_20*z_36*z_25 ,
z_21*z_45*z_27*z_43*z_13 ,
z_25*z_34*z_15*z_2*z_45 ,
z_25*z_34*z_15*z_2*z_46 + z_24*z_30*z_22*z_9 + z_23*z_12 ,
z_25*z_34*z_18*z_35*z_20 ,
z_25*z_34*z_18*z_37*z_26 ,
z_25*z_34*z_18*z_37*z_27 ,
z_25*z_35*z_20*z_34*z_18 ,
z_26*z_34*z_15*z_2*z_45 + z_27*z_44*z_20*z_37 + z_27*z_44*z_21*z_45 ,
z_26*z_34*z_15*z_2*z_46 + z_27*z_46*z_40*z_46 ,
z_26*z_34*z_16*z_3*z_12 + z_27*z_45*z_27*z_46 + z_27*z_46*z_39*z_12 ,
z_26*z_34*z_18*z_34*z_15 + z_27*z_46*z_40*z_41 + z_26*z_34*z_15 ,
z_26*z_34*z_18*z_34*z_16 + z_26*z_34*z_16 + z_26*z_32 + z_27*z_42 ,
z_26*z_34*z_18*z_34*z_17 + z_27*z_46*z_39*z_11*z_24 ,
z_26*z_34*z_18*z_34*z_18 + z_27*z_44*z_20*z_34*z_18 + z_27*z_45*z_26 ,
z_26*z_34*z_18*z_37*z_26 + z_27*z_44*z_20*z_34*z_18 + z_27*z_44*z_21*z_45*z_26 + z_27*z_46*z_40*z_42*z_5 + z_27*z_46*z_40*z_45*z_26 + z_26*z_32*z_5 + z_27*z_42*z_5 + z_27*z_43*z_13 + z_27*z_44*z_20 ,
z_26*z_34*z_18*z_37*z_27 + z_26*z_32*z_6 + z_27*z_42*z_6 + z_27*z_43*z_14 + z_27*z_45*z_27 ,
z_27*z_42*z_4*z_18*z_37 + z_27*z_44*z_20*z_37 + z_26*z_37 ,
z_27*z_42*z_5*z_34*z_16 + z_26*z_34*z_16 + z_27*z_42 ,
z_27*z_44*z_20*z_34*z_17 ,
z_27*z_44*z_21*z_43*z_13 ,
z_27*z_45*z_27*z_46*z_39 ,
z_27*z_45*z_27*z_46*z_40 + z_26*z_32*z_6 ,
z_27*z_46*z_39*z_11*z_25 + z_27*z_46*z_40*z_42*z_5 + z_27*z_46*z_40*z_45*z_26 + z_27*z_42*z_5 + z_27*z_43*z_13 ,
z_27*z_46*z_40*z_41*z_1 + z_27*z_44*z_20*z_34 + z_27*z_42*z_4 ,
z_27*z_46*z_40*z_41*z_2 + z_26*z_34*z_15*z_2 + z_27*z_45*z_27 ,
z_27*z_46*z_40*z_42*z_4 + z_26*z_34*z_18*z_34 + z_27*z_42*z_5*z_34 + z_27*z_44*z_20*z_34 ,
z_27*z_46*z_40*z_45*z_27 + z_26*z_34*z_15*z_2 ,
z_27*z_46*z_40*z_46*z_39 + z_26*z_34*z_16*z_3 + z_27*z_46*z_39 ,
z_27*z_46*z_40*z_46*z_40 + z_27*z_43*z_14 + z_27*z_44*z_21 ,
z_28*z_30*z_25*z_35*z_20 ,
z_29*z_18*z_34*z_16*z_4 ,
z_29*z_18*z_34*z_16*z_5 + z_30*z_25*z_34*z_18 + z_31*z_28*z_30*z_25 + z_29*z_16*z_5 + z_29*z_18 ,
z_29*z_18*z_34*z_16*z_6 ,
z_29*z_18*z_35*z_21*z_42 ,
z_29*z_18*z_35*z_21*z_45 ,
z_30*z_25*z_34*z_18*z_35 ,
z_30*z_25*z_34*z_18*z_37 + z_29*z_16*z_5*z_37 + z_29*z_18*z_37 ,
z_30*z_25*z_35*z_20*z_34 + z_30*z_25*z_32*z_4 + z_29*z_17*z_29 + z_29*z_18*z_34 + z_30*z_25*z_34 ,
z_31*z_28*z_30*z_25*z_35 + z_29*z_18*z_35 ,
z_33*z_14*z_45*z_27*z_43 + z_34*z_18*z_34*z_18*z_33 + z_33*z_13*z_33 ,
z_34*z_16*z_6*z_44*z_20 + z_32*z_6*z_45*z_26 + z_33*z_14*z_45*z_26 + z_34*z_15*z_1*z_18 + z_34*z_16*z_4*z_18 + z_34*z_18*z_34*z_18 + z_37*z_27*z_42*z_5 + z_37*z_27*z_43*z_13 ,
z_34*z_16*z_6*z_44*z_21 + z_34*z_18*z_34*z_15*z_2 + z_34*z_18*z_34*z_16*z_6 + z_34*z_18*z_33*z_14 ,
z_34*z_16*z_6*z_46*z_40 + z_34*z_18*z_34*z_16*z_6 + z_34*z_18*z_32*z_6 + z_37*z_27*z_43*z_14 + z_37*z_27*z_44*z_21 ,
z_34*z_18*z_32*z_4*z_18 + z_32*z_6*z_45*z_26 + z_33*z_14*z_45*z_26 + z_34*z_15*z_1*z_18 + z_34*z_16*z_4*z_18 + z_34*z_18*z_32*z_5 + z_34*z_18*z_35*z_20 + z_34*z_18*z_37*z_26 + z_35*z_20*z_34*z_18 + z_35*z_21*z_43*z_13 + z_35*z_21*z_45*z_26 + z_36*z_25*z_32*z_5 + z_36*z_25*z_35*z_20 + z_37*z_26*z_34*z_18 + z_37*z_27*z_43*z_13 + z_37*z_27*z_44*z_20 ,
z_34*z_18*z_32*z_6*z_41 + z_34*z_18*z_34*z_15 ,
z_34*z_18*z_32*z_6*z_45 + z_34*z_15*z_2*z_45 + z_34*z_16*z_5*z_37 + z_34*z_16*z_6*z_45 + z_37*z_27*z_45 ,
z_34*z_18*z_34*z_16*z_4 + z_32*z_5*z_34 + z_33*z_13*z_34 + z_35*z_20*z_34 + z_37*z_26*z_34 ,
z_34*z_18*z_34*z_16*z_5 + z_32*z_6*z_45*z_26 + z_33*z_14*z_45*z_26 + z_34*z_15*z_1*z_18 + z_34*z_16*z_4*z_18 + z_34*z_18*z_35*z_20 + z_34*z_18*z_36*z_25 + z_34*z_18*z_37*z_26 + z_35*z_21*z_43*z_13 + z_35*z_21*z_45*z_26 + z_36*z_25*z_32*z_5 + z_36*z_25*z_34*z_18 + z_36*z_25*z_35*z_20 + z_37*z_27*z_43*z_13 + z_37*z_27*z_44*z_20 ,
z_34*z_18*z_34*z_17*z_29 + z_34*z_18*z_37*z_26*z_34 + z_36*z_25*z_32*z_4 + z_34*z_15*z_1 + z_34*z_16*z_4 + z_34*z_17*z_29 + z_35*z_20*z_34 + z_37*z_26*z_34 ,
z_34*z_18*z_34*z_18*z_32 + z_33*z_14*z_42 ,
z_34*z_18*z_34*z_18*z_37 + z_34*z_18*z_35*z_21*z_45 + z_34*z_15*z_2*z_45 + z_37*z_27*z_45 ,
z_34*z_18*z_35*z_20*z_34 + z_36*z_25*z_32*z_4 + z_34*z_15*z_1 + z_34*z_16*z_4 + z_34*z_17*z_29 + z_35*z_20*z_34 + z_37*z_26*z_34 ,
z_34*z_18*z_35*z_21*z_42 + z_34*z_16*z_5*z_32 + z_33*z_14*z_42 ,
z_34*z_18*z_36*z_23*z_12 + z_34*z_16*z_3*z_12 + z_34*z_16*z_6*z_46 ,
z_34*z_18*z_36*z_25*z_34 + z_34*z_18*z_37*z_26*z_34 + z_34*z_16*z_5*z_34 + z_34*z_18*z_32*z_4 + z_33*z_13*z_34 + z_34*z_18*z_34 ,
z_34*z_18*z_36*z_25*z_35 + z_35*z_19*z_7 + z_36*z_25*z_35 ,
z_34*z_18*z_37*z_27*z_46 + z_34*z_16*z_6*z_46 + z_32*z_6*z_46 + z_35*z_21*z_46 + z_36*z_22*z_9 + z_36*z_23*z_12 ,
z_35*z_21*z_45*z_27*z_43 + z_37*z_27*z_44*z_21*z_43 + z_35*z_20*z_33 + z_35*z_21*z_43 ,
z_36*z_25*z_34*z_15*z_2 + z_32*z_6*z_45*z_27 + z_33*z_14*z_45*z_27 + z_34*z_18*z_33*z_14 + z_34*z_18*z_37*z_27 + z_35*z_21*z_46*z_40 + z_37*z_27*z_46*z_40 + z_34*z_16*z_6 + z_32*z_6 + z_33*z_14 ,
z_36*z_25*z_34*z_18*z_35 + z_35*z_19*z_7 + z_36*z_25*z_35 ,
z_36*z_25*z_34*z_18*z_37 + z_32*z_5*z_37 + z_32*z_6*z_45 ,
z_36*z_25*z_35*z_20*z_34 + z_34*z_16*z_5*z_34 + z_34*z_18*z_32*z_4 + z_36*z_25*z_32*z_4 + z_34*z_15*z_1 + z_34*z_16*z_4 + z_34*z_17*z_29 + z_34*z_18*z_34 + z_35*z_20*z_34 + z_37*z_26*z_34 ,
z_37*z_26*z_34*z_18*z_34 + z_36*z_25*z_32*z_4 + z_37*z_27*z_42*z_4 + z_32*z_5*z_34 + z_33*z_13*z_34 + z_34*z_17*z_29 ,
z_37*z_26*z_34*z_18*z_37 + z_34*z_15*z_2*z_45 + z_32*z_5*z_37 + z_32*z_6*z_45 + z_35*z_20*z_37 ,
z_37*z_27*z_42*z_4*z_17 + z_34*z_18*z_34*z_17 + z_34*z_18*z_36*z_24 + z_36*z_25*z_34*z_17 ,
z_37*z_27*z_42*z_4*z_18 + z_32*z_6*z_45*z_26 + z_33*z_14*z_45*z_26 + z_34*z_18*z_34*z_18 + z_34*z_18*z_35*z_20 + z_34*z_18*z_36*z_25 + z_34*z_18*z_37*z_26 + z_35*z_20*z_34*z_18 + z_35*z_21*z_45*z_26 + z_36*z_25*z_34*z_18 + z_37*z_26*z_34*z_18 + z_37*z_27*z_42*z_5 + z_37*z_27*z_43*z_13 + z_37*z_27*z_44*z_20 ,
z_37*z_27*z_42*z_5*z_34 + z_33*z_13*z_34 ,
z_37*z_27*z_44*z_20*z_34 + z_36*z_25*z_32*z_4 + z_37*z_27*z_42*z_4 + z_32*z_5*z_34 + z_34*z_17*z_29 ,
z_37*z_27*z_44*z_20*z_35 + z_35*z_21*z_44 ,
z_37*z_27*z_44*z_20*z_37 + z_35*z_20*z_37 + z_35*z_21*z_45 ,
z_37*z_27*z_44*z_21*z_45 + z_35*z_20*z_37 + z_35*z_21*z_45 ,
z_37*z_27*z_46*z_40*z_41 + z_32*z_6*z_41 ,
z_37*z_27*z_46*z_40*z_42 + z_33*z_14*z_42 ,
z_37*z_27*z_46*z_40*z_45 + z_34*z_15*z_2*z_45 + z_34*z_16*z_6*z_45 + z_32*z_6*z_45 + z_33*z_14*z_45 ,
z_37*z_27*z_46*z_40*z_46 + z_32*z_6*z_46 + z_36*z_23*z_12 ,
z_38*z_8*z_24*z_30*z_22 + z_39*z_12*z_38 ,
z_39*z_12*z_38*z_9*z_39 ,
z_40*z_41*z_1*z_18*z_34 + z_39*z_10*z_5*z_34 ,
z_40*z_41*z_1*z_18*z_36 + z_38*z_8*z_24*z_30 + z_39*z_11 ,
z_40*z_41*z_1*z_18*z_37 + z_40*z_46*z_40*z_45 ,
z_40*z_42*z_5*z_34*z_16 + z_40*z_46*z_40*z_42 ,
z_40*z_42*z_6*z_41*z_1 + z_39*z_10*z_5*z_34 + z_40*z_42*z_5*z_34 ,
z_40*z_44*z_20*z_34*z_17 ,
z_40*z_44*z_20*z_34*z_18 + z_38*z_8*z_25 + z_40*z_44*z_20 ,
z_40*z_44*z_21*z_42*z_4 ,
z_40*z_44*z_21*z_42*z_5 ,
z_40*z_44*z_21*z_42*z_6 + z_39*z_10*z_6 + z_40*z_41*z_2 + z_40*z_42*z_6 + z_40*z_44*z_21 + z_40*z_45*z_27 ,
z_40*z_45*z_26*z_34*z_18 + z_40*z_46*z_40*z_45*z_26 + z_38*z_8*z_25 + z_39*z_10*z_5 + z_39*z_11*z_25 + z_40*z_44*z_20 ,
z_40*z_46*z_40*z_42*z_4 + z_39*z_10*z_5*z_34 + z_40*z_42*z_5*z_34 ,
z_40*z_46*z_40*z_42*z_5 + z_40*z_46*z_40*z_45*z_26 + z_39*z_10*z_5 + z_40*z_42*z_5 ,
z_40*z_46*z_40*z_45*z_27 ,
z_41*z_1*z_18*z_34*z_15 + z_42*z_6*z_41 ,
z_41*z_1*z_18*z_36*z_24 + z_46*z_40*z_41*z_1*z_17 + z_44*z_20*z_34*z_17 + z_42*z_4*z_17 ,
z_41*z_1*z_18*z_36*z_25 + z_46*z_40*z_41*z_1*z_18 + z_44*z_20*z_34*z_18 + z_44*z_21*z_44*z_20 + z_45*z_27*z_43*z_13 + z_46*z_38*z_8*z_25 + z_46*z_39*z_11*z_25 + z_46*z_40*z_42*z_5 + z_46*z_40*z_45*z_26 + z_42*z_4*z_18 + z_42*z_5 + z_43*z_13 ,
z_41*z_1*z_18*z_37*z_26 + z_46*z_40*z_41*z_1*z_18 + z_44*z_20*z_34*z_18 + z_44*z_21*z_42*z_5 + z_45*z_26*z_34*z_18 + z_45*z_27*z_43*z_13 + z_42*z_4*z_18 ,
z_42*z_6*z_41*z_1*z_17 ,
z_42*z_6*z_41*z_1*z_18 + z_46*z_40*z_41*z_1*z_18 + z_44*z_20*z_34*z_18 + z_44*z_21*z_42*z_5 + z_45*z_26*z_34*z_18 + z_45*z_27*z_42*z_5 + z_42*z_4*z_18 ,
z_42*z_6*z_46*z_40*z_41 + z_46*z_40*z_42*z_6*z_41 ,
z_42*z_6*z_46*z_40*z_45 + z_42*z_5*z_37 + z_42*z_6*z_45 + z_45*z_27*z_45 ,
z_42*z_6*z_46*z_40*z_46 + z_46*z_40*z_46*z_39*z_12 ,
z_44*z_21*z_45*z_27*z_43 + z_42*z_4*z_18*z_33 + z_43*z_13*z_33 ,
z_45*z_26*z_34*z_18*z_34 + z_43*z_13*z_34 ,
z_45*z_26*z_34*z_18*z_37 + z_42*z_6*z_45 + z_43*z_14*z_45 + z_44*z_20*z_37 + z_44*z_21*z_45 ,
z_45*z_27*z_42*z_5*z_34 + z_42*z_6*z_41*z_1 ,
z_45*z_27*z_44*z_20*z_34 + z_43*z_13*z_34 ,
z_45*z_27*z_44*z_20*z_35 + z_44*z_21*z_44 ,
z_45*z_27*z_44*z_20*z_37 + z_42*z_4*z_18*z_37 + z_42*z_6*z_45 + z_44*z_20*z_37 + z_44*z_21*z_45 ,
z_45*z_27*z_44*z_21*z_43 + z_43*z_13*z_33 + z_44*z_20*z_33 + z_44*z_21*z_43 ,
z_45*z_27*z_44*z_21*z_45 + z_42*z_4*z_18*z_37 + z_42*z_6*z_45 + z_44*z_20*z_37 + z_44*z_21*z_45 ,
z_45*z_27*z_46*z_39*z_11 ,
z_45*z_27*z_46*z_39*z_12 + z_46*z_40*z_46*z_39*z_12 + z_42*z_6*z_46 + z_44*z_21*z_46 + z_46*z_38*z_9 + z_46*z_39*z_12 ,
z_45*z_27*z_46*z_40*z_41 ,
z_45*z_27*z_46*z_40*z_42 + z_42*z_5*z_34*z_16 + z_46*z_39*z_10 + z_46*z_40*z_42 ,
z_45*z_27*z_46*z_40*z_45 + z_41*z_1*z_18*z_37 + z_42*z_4*z_18*z_37 + z_42*z_6*z_45 ,
z_45*z_27*z_46*z_40*z_46 ,
z_46*z_39*z_10*z_5*z_34 + z_42*z_4*z_18*z_34 + z_42*z_6*z_41*z_1 + z_44*z_21*z_42*z_4 + z_43*z_13*z_34 ,
z_46*z_40*z_42*z_5*z_34 + z_42*z_4*z_18*z_34 + z_42*z_6*z_41*z_1 ,
z_46*z_40*z_42*z_6*z_45 + z_42*z_4*z_18*z_37 + z_42*z_5*z_37 ,
z_46*z_40*z_44*z_20*z_34 + z_46*z_40*z_45*z_26*z_34 + z_41*z_1*z_18*z_34 + z_42*z_5*z_34 ,
z_46*z_40*z_44*z_20*z_35 + z_44*z_19*z_7 + z_46*z_40*z_44 ,
z_46*z_40*z_44*z_21*z_42 + z_42*z_3*z_10 + z_46*z_39*z_10 ,
z_46*z_40*z_45*z_27*z_45 + z_42*z_4*z_18*z_37 + z_42*z_6*z_45 ,
z_46*z_40*z_46*z_40*z_42 + z_42*z_5*z_32 ,
z_46*z_40*z_46*z_40*z_45 + z_43*z_14*z_45 + z_44*z_21*z_45 ,
z_1*z_17*z_29*z_15 ,
z_1*z_17*z_29*z_16 + z_1*z_18*z_32 ,
z_1*z_17*z_29*z_17 + z_1*z_18*z_36*z_24 ,
z_1*z_17*z_29*z_18 + z_2*z_42*z_5 ,
z_1*z_18*z_32*z_3 + z_2*z_46*z_39 ,
z_1*z_18*z_32*z_4 + z_2*z_42*z_5*z_34 ,
z_1*z_18*z_32*z_5 + z_1*z_18*z_37*z_26 ,
z_1*z_18*z_34*z_16 + z_1*z_18*z_32 + z_2*z_42 ,
z_1*z_18*z_34*z_17 ,
z_1*z_18*z_34*z_18 ,
z_1*z_18*z_36*z_22 ,
z_1*z_18*z_36*z_23 + z_2*z_46*z_39 ,
z_1*z_18*z_37*z_27 ,
z_2*z_42*z_5*z_32 ,
z_2*z_42*z_5*z_37 + z_2*z_45 ,
z_2*z_42*z_6*z_41 ,
z_2*z_42*z_6*z_45 ,
z_2*z_42*z_6*z_46 + z_2*z_46*z_39*z_12 ,
z_2*z_46*z_39*z_10 + z_1*z_18*z_32 + z_2*z_42 ,
z_2*z_46*z_39*z_11 ,
z_2*z_46*z_40*z_41 ,
z_2*z_46*z_40*z_42 + z_1*z_18*z_32 + z_2*z_42 ,
z_2*z_46*z_40*z_44 ,
z_2*z_46*z_40*z_45 + z_1*z_18*z_37 + z_2*z_45 ,
z_2*z_46*z_40*z_46 ,
z_3*z_10*z_4*z_17 + z_3*z_11*z_24 + z_5*z_36*z_24 ,
z_3*z_11*z_25*z_32 + z_4*z_16 + z_6*z_42 ,
z_3*z_11*z_25*z_34 + z_3*z_10*z_4 + z_4*z_17*z_29 + z_6*z_41*z_1 + z_5*z_34 ,
z_3*z_12*z_40*z_41 + z_6*z_46*z_40*z_41 ,
z_3*z_12*z_40*z_44 + z_5*z_35 ,
z_3*z_12*z_40*z_45 + z_4*z_18*z_37 + z_5*z_37 ,
z_3*z_12*z_40*z_46 + z_6*z_46*z_40*z_46 ,
z_4*z_17*z_29*z_15 + z_6*z_41 ,
z_4*z_17*z_29*z_16 + z_5*z_34*z_16 + z_4*z_16 + z_6*z_42 ,
z_4*z_17*z_29*z_17 + z_6*z_41*z_1*z_17 + z_3*z_11*z_24 + z_5*z_36*z_24 ,
z_4*z_17*z_29*z_18 + z_6*z_41*z_1*z_18 + z_5*z_36*z_25 + z_6*z_42*z_5 + z_6*z_44*z_20 + z_6*z_45*z_26 ,
z_4*z_18*z_33*z_13 + z_6*z_42*z_5 ,
z_4*z_18*z_33*z_14 ,
z_4*z_18*z_34*z_15 + z_6*z_46*z_40*z_41 ,
z_4*z_18*z_34*z_16 + z_4*z_16 ,
z_4*z_18*z_34*z_17 + z_6*z_41*z_1*z_17 ,
z_4*z_18*z_34*z_18 + z_6*z_41*z_1*z_18 + z_5*z_32*z_5 ,
z_4*z_18*z_37*z_26 + z_6*z_45*z_26 ,
z_4*z_18*z_37*z_27 + z_6*z_45*z_27 ,
z_5*z_32*z_4*z_17 + z_5*z_36*z_24 ,
z_5*z_32*z_4*z_18 + z_5*z_32*z_5 + z_5*z_36*z_25 + z_6*z_42*z_5 ,
z_5*z_32*z_5*z_32 ,
z_5*z_32*z_5*z_34 + z_6*z_44*z_20*z_34 + z_3*z_10*z_4 + z_4*z_17*z_29 + z_4*z_18*z_34 + z_5*z_32*z_4 + z_5*z_34 ,
z_5*z_32*z_5*z_37 + z_4*z_18*z_37 + z_6*z_45 ,
z_5*z_34*z_16*z_3 + z_3*z_11*z_23 ,
z_5*z_34*z_16*z_4 + z_6*z_44*z_20*z_34 + z_3*z_10*z_4 + z_4*z_17*z_29 + z_4*z_18*z_34 + z_5*z_32*z_4 + z_6*z_41*z_1 + z_5*z_34 ,
z_5*z_34*z_16*z_5 + z_6*z_41*z_1*z_18 + z_5*z_36*z_25 + z_6*z_44*z_20 + z_6*z_45*z_26 ,
z_5*z_34*z_16*z_6 + z_3*z_12*z_40 + z_5*z_35*z_21 + z_5*z_37*z_27 + z_6*z_41*z_2 + z_6*z_44*z_21 + z_6*z_46*z_40 ,
z_5*z_34*z_18*z_32 + z_5*z_32 ,
z_5*z_34*z_18*z_33 ,
z_5*z_34*z_18*z_34 + z_3*z_10*z_4 + z_4*z_17*z_29 + z_4*z_18*z_34 + z_5*z_34 ,
z_5*z_34*z_18*z_35 + z_5*z_35 ,
z_5*z_34*z_18*z_36 + z_5*z_36 ,
z_5*z_34*z_18*z_37 + z_4*z_18*z_37 + z_5*z_37 ,
z_5*z_35*z_21*z_42 + z_4*z_16 + z_5*z_32 ,
z_5*z_35*z_21*z_43 ,
z_5*z_35*z_21*z_44 ,
z_5*z_35*z_21*z_45 ,
z_5*z_35*z_21*z_46 ,
z_5*z_36*z_24*z_30 ,
z_5*z_36*z_24*z_31 ,
z_5*z_36*z_25*z_32 + z_4*z_16 + z_5*z_32 ,
z_5*z_36*z_25*z_34 + z_6*z_44*z_20*z_34 + z_3*z_10*z_4 + z_4*z_17*z_29 + z_4*z_18*z_34 + z_5*z_32*z_4 + z_5*z_34 ,
z_5*z_36*z_25*z_35 ,
z_5*z_37*z_27*z_42 ,
z_5*z_37*z_27*z_43 + z_4*z_18*z_33 ,
z_5*z_37*z_27*z_44 ,
z_5*z_37*z_27*z_45 ,
z_5*z_37*z_27*z_46 + z_3*z_12 + z_6*z_46 ,
z_6*z_42*z_3*z_10 + z_4*z_16 + z_5*z_32 ,
z_6*z_42*z_5*z_32 ,
z_6*z_42*z_5*z_34 ,
z_6*z_42*z_5*z_37 ,
z_6*z_44*z_20*z_33 + z_4*z_18*z_33 ,
z_6*z_44*z_20*z_35 ,
z_6*z_44*z_20*z_37 + z_4*z_18*z_37 + z_6*z_45 ,
z_6*z_44*z_21*z_42 + z_4*z_16 + z_5*z_32 + z_6*z_42 ,
z_6*z_44*z_21*z_43 + z_4*z_18*z_33 ,
z_6*z_44*z_21*z_44 ,
z_6*z_44*z_21*z_45 + z_4*z_18*z_37 + z_6*z_45 ,
z_6*z_44*z_21*z_46 + z_6*z_46*z_38*z_9 ,
z_6*z_45*z_26*z_34 ,
z_6*z_45*z_27*z_42 ,
z_6*z_45*z_27*z_43 + z_4*z_18*z_33 ,
z_6*z_45*z_27*z_44 ,
z_6*z_45*z_27*z_45 ,
z_6*z_45*z_27*z_46 + z_6*z_46*z_40*z_46 + z_3*z_12 + z_6*z_46 ,
z_6*z_46*z_38*z_8 + z_5*z_36 ,
z_6*z_46*z_40*z_42 ,
z_6*z_46*z_40*z_44 + z_5*z_35 ,
z_7*z_20*z_35*z_19 ,
z_8*z_25*z_34*z_15 ,
z_8*z_25*z_34*z_16 + z_9*z_40*z_42 ,
z_8*z_25*z_34*z_17 ,
z_8*z_25*z_34*z_18 + z_7*z_20 + z_8*z_25 ,
z_9*z_40*z_42*z_4 ,
z_9*z_40*z_42*z_5 ,
z_9*z_40*z_42*z_6 + z_7*z_21 + z_9*z_40 ,
z_10*z_4*z_17*z_29 + z_12*z_40*z_41*z_1 + z_10*z_5*z_34 ,
z_10*z_5*z_34*z_16 + z_11*z_25*z_32 ,
z_10*z_5*z_34*z_18 + z_12*z_40*z_44*z_20 ,
z_10*z_6*z_42*z_3 ,
z_10*z_6*z_42*z_5 ,
z_11*z_25*z_32*z_4 + z_12*z_40*z_41*z_1 ,
z_11*z_25*z_32*z_5 + z_11*z_25*z_34*z_18 ,
z_11*z_25*z_32*z_6 + z_12*z_40*z_46*z_40 ,
z_11*z_25*z_34*z_15 + z_12*z_40*z_41 ,
z_11*z_25*z_34*z_16 + z_10*z_6*z_42 + z_11*z_25*z_32 ,
z_11*z_25*z_34*z_17 + z_10*z_4*z_17 + z_11*z_24 ,
z_12*z_38*z_8*z_24 + z_10*z_4*z_17 + z_11*z_24 ,
z_12*z_38*z_8*z_25 + z_12*z_40*z_44*z_20 ,
z_12*z_40*z_41*z_2 + z_12*z_40*z_45*z_27 + z_10*z_6 + z_12*z_40 ,
z_12*z_40*z_44*z_21 + z_10*z_6 + z_12*z_40 ,
z_12*z_40*z_45*z_26 ,
z_12*z_40*z_46*z_39 ,
z_13*z_34*z_18*z_32 ,
z_13*z_34*z_18*z_33 + z_14*z_43*z_13*z_33 ,
z_13*z_34*z_18*z_34 + z_14*z_42*z_4 ,
z_13*z_34*z_18*z_35 + z_14*z_44*z_21*z_44 + z_13*z_35 + z_14*z_44 ,
z_13*z_34*z_18*z_36 ,
z_13*z_34*z_18*z_37 + z_14*z_44*z_21*z_45 + z_13*z_37 + z_14*z_45 ,
z_13*z_35*z_20*z_33 + z_14*z_43*z_13*z_33 + z_13*z_33 ,
z_13*z_35*z_20*z_34 + z_14*z_42*z_4 + z_13*z_34 ,
z_13*z_35*z_20*z_37 + z_14*z_44*z_21*z_45 ,
z_13*z_35*z_21*z_42 + z_14*z_42 ,
z_13*z_35*z_21*z_43 + z_14*z_43*z_13*z_33 + z_14*z_44*z_20*z_33 ,
z_13*z_35*z_21*z_44 + z_14*z_44*z_21*z_44 ,
z_13*z_35*z_21*z_45 + z_14*z_44*z_21*z_45 + z_13*z_37 + z_14*z_45 ,
z_13*z_35*z_21*z_46 ,
z_13*z_37*z_26*z_34 + z_14*z_42*z_4 + z_13*z_34 ,
z_13*z_37*z_27*z_42 + z_14*z_42 ,
z_13*z_37*z_27*z_43 + z_14*z_44*z_20*z_33 + z_14*z_45*z_27*z_43 + z_13*z_33 ,
z_13*z_37*z_27*z_44 + z_13*z_35 + z_14*z_44 ,
z_13*z_37*z_27*z_45 ,
z_13*z_37*z_27*z_46 ,
z_14*z_42*z_4*z_17 ,
z_14*z_42*z_4*z_18 + z_13*z_34*z_18 + z_13*z_37*z_26 + z_14*z_43*z_13 + z_14*z_45*z_26 ,
z_14*z_42*z_5*z_32 ,
z_14*z_42*z_5*z_34 ,
z_14*z_42*z_5*z_37 + z_13*z_37 + z_14*z_45 ,
z_14*z_42*z_6*z_41 ,
z_14*z_42*z_6*z_45 + z_13*z_37 + z_14*z_45 ,
z_14*z_42*z_6*z_46 ,
z_14*z_43*z_13*z_34 + z_14*z_42*z_4 ,
z_14*z_44*z_20*z_34 + z_13*z_34 ,
z_14*z_44*z_20*z_35 + z_14*z_44*z_21*z_44 + z_13*z_35 + z_14*z_44 ,
z_14*z_44*z_20*z_37 + z_14*z_44*z_21*z_45 + z_13*z_37 + z_14*z_45 ,
z_14*z_44*z_21*z_42 + z_14*z_42 ,
z_14*z_44*z_21*z_43 + z_13*z_33 ,
z_14*z_44*z_21*z_46 ,
z_14*z_45*z_26*z_34 + z_14*z_42*z_4 + z_13*z_34 ,
z_14*z_45*z_27*z_42 + z_14*z_42 ,
z_14*z_45*z_27*z_44 + z_13*z_35 + z_14*z_44 ,
z_14*z_45*z_27*z_45 ,
z_14*z_45*z_27*z_46 ,
z_15*z_1*z_18*z_32 + z_18*z_34*z_18*z_32 + z_18*z_35*z_21*z_42 + z_16*z_3*z_10 + z_17*z_29*z_16 + z_18*z_32 ,
z_15*z_1*z_18*z_34 + z_17*z_30*z_25*z_34 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_18*z_35*z_20*z_34 + z_18*z_36*z_25*z_34 + z_18*z_37*z_26*z_34 ,
z_15*z_1*z_18*z_36 + z_17*z_30 + z_18*z_36 ,
z_15*z_1*z_18*z_37 + z_18*z_34*z_18*z_37 + z_16*z_6*z_45 ,
z_15*z_2*z_46*z_39 + z_17*z_30*z_23 + z_18*z_36*z_23 ,
z_15*z_2*z_46*z_40 + z_17*z_29*z_15*z_2 + z_17*z_29*z_16*z_6 + z_18*z_34*z_15*z_2 + z_18*z_34*z_16*z_6 + z_18*z_35*z_21 + z_18*z_37*z_27 + z_16*z_6 ,
z_16*z_3*z_10*z_4 + z_17*z_30*z_25*z_34 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_18*z_35*z_20*z_34 + z_18*z_36*z_25*z_34 + z_18*z_32*z_4 + z_15*z_1 + z_16*z_4 ,
z_16*z_3*z_11*z_23 + z_17*z_30*z_23 + z_18*z_32*z_3 ,
z_16*z_3*z_11*z_24 + z_17*z_29*z_17 + z_17*z_30*z_24 + z_18*z_34*z_17 ,
z_16*z_3*z_11*z_25 + z_16*z_6*z_44*z_20 + z_18*z_34*z_16*z_5 + z_17*z_29*z_18 + z_18*z_33*z_13 + z_18*z_34*z_18 + z_18*z_35*z_20 + z_18*z_37*z_26 ,
z_16*z_3*z_12*z_40 + z_16*z_6*z_44*z_21 + z_16*z_6*z_46*z_40 + z_18*z_33*z_14 ,
z_16*z_4*z_17*z_29 + z_17*z_30*z_25*z_34 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_15*z_1 + z_16*z_4 + z_18*z_34 ,
z_16*z_4*z_18*z_33 + z_18*z_34*z_18*z_33 ,
z_16*z_4*z_18*z_34 + z_18*z_35*z_20*z_34 + z_18*z_36*z_25*z_34 + z_16*z_5*z_34 + z_18*z_32*z_4 + z_18*z_34 ,
z_16*z_4*z_18*z_37 + z_15*z_2*z_45 + z_16*z_6*z_45 ,
z_16*z_5*z_32*z_4 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_18*z_35*z_20*z_34 + z_18*z_37*z_26*z_34 ,
z_16*z_5*z_32*z_5 + z_16*z_6*z_44*z_20 + z_17*z_29*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_30*z_25 + z_18*z_35*z_20 + z_18*z_36*z_25 + z_18*z_37*z_26 ,
z_16*z_5*z_34*z_16 + z_18*z_34*z_18*z_32 + z_16*z_3*z_10 + z_17*z_29*z_16 + z_18*z_32 ,
z_16*z_5*z_34*z_18 + z_18*z_34*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_29*z_18 + z_17*z_30*z_25 + z_18*z_32*z_5 + z_18*z_34*z_18 + z_18*z_36*z_25 ,
z_16*z_5*z_37*z_27 + z_16*z_6*z_44*z_21 + z_16*z_6*z_46*z_40 + z_17*z_29*z_16*z_6 + z_18*z_32*z_6 ,
z_16*z_6*z_45*z_26 + z_18*z_34*z_16*z_5 + z_15*z_1*z_18 + z_16*z_4*z_18 + z_17*z_29*z_18 + z_17*z_30*z_25 + z_18*z_35*z_20 + z_18*z_36*z_25 + z_18*z_37*z_26 ,
z_16*z_6*z_45*z_27 + z_18*z_33*z_14 ,
z_16*z_6*z_46*z_38 ,
z_17*z_29*z_16*z_3 + z_17*z_30*z_23 + z_18*z_32*z_3 + z_18*z_36*z_23 ,
z_17*z_29*z_16*z_4 + z_17*z_30*z_25*z_34 + z_18*z_34*z_16*z_4 + z_18*z_34*z_17*z_29 + z_18*z_35*z_20*z_34 + z_18*z_36*z_25*z_34 + z_15*z_1 + z_16*z_4 ,
z_17*z_29*z_17*z_29 + z_17*z_30*z_25*z_34 + z_18*z_34*z_17*z_29 + z_18*z_35*z_20*z_34 + z_18*z_36*z_25*z_34 + z_16*z_5*z_34 + z_18*z_32*z_4 + z_18*z_34 ,
z_17*z_29*z_18*z_32 + z_18*z_34*z_18*z_32 + z_18*z_35*z_21*z_42 + z_16*z_5*z_32 ,
z_17*z_29*z_18*z_34 + z_17*z_30*z_25*z_34 + z_18*z_35*z_20*z_34 + z_18*z_36*z_25*z_34 + z_18*z_37*z_26*z_34 ,
z_17*z_29*z_18*z_35 ,
z_17*z_29*z_18*z_37 + z_18*z_32*z_6*z_45 + z_15*z_2*z_45 + z_16*z_5*z_37 + z_16*z_6*z_45 ,
z_17*z_30*z_23*z_11 + z_16*z_3*z_11 + z_17*z_30 + z_18*z_36 ,
z_17*z_30*z_23*z_12 + z_18*z_36*z_23*z_12 + z_16*z_3*z_12 + z_16*z_6*z_46 ,
z_17*z_30*z_25*z_32 + z_18*z_34*z_18*z_32 + z_18*z_35*z_21*z_42 + z_16*z_3*z_10 + z_17*z_29*z_16 + z_18*z_34*z_16 + z_18*z_32 ,
z_17*z_30*z_25*z_35 + z_18*z_36*z_25*z_35 ,
z_18*z_32*z_4*z_17 + z_17*z_29*z_17 + z_18*z_36*z_24 ,
z_18*z_32*z_5*z_32 + z_18*z_34*z_18*z_32 + z_18*z_35*z_21*z_42 + z_16*z_5*z_32 ,
z_18*z_32*z_5*z_34 + z_18*z_35*z_20*z_34 + z_18*z_37*z_26*z_34 ,
z_18*z_32*z_5*z_37 + z_18*z_34*z_18*z_37 + z_18*z_35*z_21*z_45 + z_15*z_2*z_45 + z_16*z_5*z_37 + z_16*z_6*z_45 ,
z_18*z_32*z_6*z_46 + z_18*z_36*z_23*z_12 + z_16*z_3*z_12 + z_16*z_6*z_46 ,
z_18*z_33*z_13*z_33 ,
z_18*z_33*z_13*z_34 ,
z_18*z_33*z_14*z_42 ,
z_18*z_33*z_14*z_44 ,
z_18*z_33*z_14*z_45 ,
z_18*z_34*z_15*z_1 + z_18*z_34*z_16*z_4 ,
z_18*z_34*z_16*z_3 + z_17*z_30*z_23 + z_18*z_36*z_23 ,
z_18*z_34*z_18*z_34 ,
z_18*z_34*z_18*z_35 + z_16*z_6*z_44 ,
z_18*z_34*z_18*z_36 + z_16*z_3*z_11 + z_17*z_30 + z_18*z_36 ,
z_18*z_35*z_20*z_33 + z_18*z_33 ,
z_18*z_35*z_20*z_37 + z_18*z_35*z_21*z_45 + z_15*z_2*z_45 ,
z_18*z_35*z_21*z_43 + z_18*z_33 ,
z_18*z_35*z_21*z_44 ,
z_18*z_35*z_21*z_46 + z_18*z_36*z_22*z_9 ,
z_18*z_36*z_23*z_11 + z_16*z_3*z_11 + z_17*z_30 + z_18*z_36 ,
z_18*z_36*z_24*z_30 ,
z_18*z_36*z_24*z_31 ,
z_18*z_36*z_25*z_32 + z_16*z_3*z_10 + z_17*z_29*z_16 + z_18*z_34*z_16 + z_18*z_32 ,
z_18*z_37*z_27*z_42 ,
z_18*z_37*z_27*z_43 + z_18*z_33 ,
z_18*z_37*z_27*z_44 + z_16*z_6*z_44 ,
z_18*z_37*z_27*z_45 + z_15*z_2*z_45 ,
z_19*z_7*z_20*z_35 + z_20*z_35*z_19*z_7 ,
z_20*z_34*z_16*z_3 + z_21*z_46*z_39 ,
z_20*z_34*z_16*z_4 + z_21*z_42*z_4 ,
z_20*z_34*z_16*z_5 + z_21*z_42*z_5 ,
z_20*z_34*z_16*z_6 + z_19*z_7*z_21 + z_21*z_42*z_6 + z_21*z_46*z_40 ,
z_20*z_34*z_17*z_29 ,
z_20*z_34*z_18*z_32 + z_20*z_34*z_16 + z_21*z_42 ,
z_20*z_34*z_18*z_33 + z_21*z_45*z_27*z_43 + z_20*z_33 + z_21*z_43 ,
z_20*z_34*z_18*z_34 + z_21*z_42*z_4 ,
z_20*z_34*z_18*z_35 + z_20*z_35*z_19*z_7 + z_20*z_35 ,
z_20*z_34*z_18*z_36 + z_20*z_36*z_24*z_30 ,
z_20*z_34*z_18*z_37 + z_20*z_37 ,
z_20*z_36*z_25*z_32 + z_20*z_34*z_16 + z_21*z_42 ,
z_21*z_42*z_4*z_17 ,
z_21*z_42*z_4*z_18 + z_21*z_42*z_5 + z_21*z_43*z_13 ,
z_21*z_42*z_5*z_32 ,
z_21*z_42*z_5*z_34 ,
z_21*z_42*z_5*z_37 + z_20*z_37 + z_21*z_45 ,
z_21*z_42*z_6*z_41 ,
z_21*z_42*z_6*z_45 + z_20*z_37 + z_21*z_45 ,
z_21*z_42*z_6*z_46 + z_21*z_46*z_39*z_12 ,
z_21*z_43*z_13*z_33 + z_20*z_33 + z_21*z_43 ,
z_21*z_43*z_13*z_34 ,
z_21*z_44*z_20*z_33 + z_20*z_33 + z_21*z_43 ,
z_21*z_44*z_20*z_34 ,
z_21*z_44*z_20*z_35 ,
z_21*z_44*z_20*z_37 ,
z_21*z_44*z_21*z_42 ,
z_21*z_44*z_21*z_43 + z_20*z_33 + z_21*z_43 ,
z_21*z_44*z_21*z_44 ,
z_21*z_44*z_21*z_45 ,
z_21*z_44*z_21*z_46 ,
z_21*z_45*z_26*z_34 + z_21*z_42*z_4 ,
z_21*z_45*z_27*z_42 ,
z_21*z_45*z_27*z_44 + z_21*z_44 ,
z_21*z_45*z_27*z_45 ,
z_21*z_45*z_27*z_46 ,
z_21*z_46*z_39*z_10 + z_20*z_34*z_16 + z_21*z_42 ,
z_21*z_46*z_40*z_41 ,
z_21*z_46*z_40*z_42 + z_20*z_34*z_16 + z_21*z_42 ,
z_21*z_46*z_40*z_45 ,
z_21*z_46*z_40*z_46 ,
z_24*z_31*z_28*z_30 + z_24*z_30 ,
z_25*z_32*z_4*z_17 + z_25*z_34*z_17 ,
z_25*z_32*z_4*z_18 + z_25*z_32*z_5 + z_25*z_35*z_20 ,
z_25*z_32*z_5*z_32 ,
z_25*z_32*z_5*z_34 + z_25*z_35*z_20*z_34 ,
z_25*z_32*z_5*z_37 + z_25*z_34*z_18*z_37 ,
z_25*z_32*z_6*z_41 ,
z_25*z_32*z_6*z_45 + z_25*z_34*z_18*z_37 ,
z_25*z_32*z_6*z_46 ,
z_25*z_34*z_15*z_1 + z_25*z_32*z_4 ,
z_25*z_34*z_16*z_3 ,
z_25*z_34*z_16*z_4 + z_25*z_32*z_4 ,
z_25*z_34*z_16*z_5 + z_25*z_32*z_5 ,
z_25*z_34*z_16*z_6 + z_25*z_32*z_6 ,
z_25*z_34*z_17*z_29 + z_25*z_35*z_20*z_34 ,
z_25*z_34*z_18*z_32 ,
z_25*z_34*z_18*z_33 ,
z_25*z_34*z_18*z_34 + z_25*z_35*z_20*z_34 ,
z_25*z_34*z_18*z_36 ,
z_25*z_35*z_20*z_33 ,
z_25*z_35*z_20*z_37 ,
z_25*z_35*z_21*z_42 + z_25*z_34*z_16 + z_25*z_32 ,
z_25*z_35*z_21*z_43 ,
z_25*z_35*z_21*z_44 ,
z_25*z_35*z_21*z_45 ,
z_26*z_32*z_4*z_17 ,
z_26*z_32*z_4*z_18 + z_26*z_32*z_5 ,
z_26*z_32*z_5*z_32 ,
z_26*z_32*z_5*z_34 ,
z_26*z_32*z_5*z_37 + z_27*z_44*z_20*z_37 + z_27*z_44*z_21*z_45 ,
z_26*z_32*z_6*z_41 ,
z_26*z_32*z_6*z_45 + z_27*z_44*z_20*z_37 + z_27*z_44*z_21*z_45 ,
z_26*z_32*z_6*z_46 ,
z_26*z_34*z_15*z_1 + z_27*z_44*z_20*z_34 + z_26*z_32*z_4 + z_27*z_42*z_4 ,
z_26*z_34*z_16*z_4 + z_27*z_42*z_4 ,
z_26*z_34*z_16*z_5 + z_26*z_32*z_5 + z_27*z_42*z_5 + z_27*z_45*z_26 ,
z_26*z_34*z_16*z_6 + z_27*z_42*z_6 + z_27*z_45*z_27 ,
z_26*z_34*z_18*z_32 + z_27*z_46*z_40*z_42 + z_26*z_32 ,
z_26*z_34*z_18*z_33 + z_27*z_44*z_21*z_43 ,
z_26*z_34*z_18*z_35 + z_27*z_44 ,
z_26*z_34*z_18*z_36 + z_27*z_46*z_39*z_11 ,
z_27*z_42*z_5*z_32 + z_26*z_32 ,
z_27*z_42*z_5*z_37 + z_27*z_44*z_21*z_45 + z_27*z_45 ,
z_27*z_42*z_6*z_41 ,
z_27*z_42*z_6*z_45 + z_27*z_44*z_21*z_45 + z_26*z_37 ,
z_27*z_42*z_6*z_46 + z_27*z_45*z_27*z_46 + z_27*z_46*z_39*z_12 ,
z_27*z_43*z_13*z_33 ,
z_27*z_43*z_13*z_34 ,
z_27*z_43*z_14*z_45 + z_27*z_44*z_21*z_45 + z_26*z_37 ,
z_27*z_44*z_20*z_33 + z_27*z_44*z_21*z_43 ,
z_27*z_44*z_21*z_42 + z_26*z_32 ,
z_27*z_44*z_21*z_44 ,
z_27*z_44*z_21*z_46 ,
z_27*z_45*z_26*z_34 + z_26*z_32*z_4 ,
z_27*z_45*z_27*z_42 ,
z_27*z_45*z_27*z_43 ,
z_27*z_45*z_27*z_44 ,
z_27*z_45*z_27*z_45 ,
z_27*z_46*z_39*z_10 + z_27*z_46*z_40*z_42 + z_26*z_34*z_16 + z_27*z_42 ,
z_27*z_46*z_40*z_44 ,
z_28*z_30*z_25*z_32 ,
z_28*z_30*z_25*z_34 ,
z_29*z_15*z_2*z_45 ,
z_29*z_16*z_3*z_10 + z_29*z_18*z_32 + z_30*z_25*z_32 ,
z_29*z_16*z_3*z_11 + z_30*z_23*z_11 ,
z_29*z_16*z_3*z_12 + z_30*z_23*z_12 ,
z_29*z_16*z_4*z_17 + z_30*z_25*z_34*z_17 + z_29*z_17 + z_30*z_24 ,
z_29*z_16*z_5*z_32 + z_29*z_18*z_32 ,
z_29*z_16*z_5*z_34 + z_30*z_25*z_32*z_4 + z_29*z_17*z_29 + z_30*z_25*z_34 ,
z_29*z_16*z_6*z_44 ,
z_29*z_16*z_6*z_45 + z_29*z_18*z_37 ,
z_29*z_16*z_6*z_46 + z_30*z_23*z_12 ,
z_29*z_17*z_29*z_15 + z_30*z_25*z_34*z_15 ,
z_29*z_17*z_29*z_16 + z_29*z_18*z_34*z_16 + z_30*z_25*z_32 ,
z_29*z_17*z_29*z_17 ,
z_29*z_17*z_29*z_18 + z_31*z_28*z_30*z_25 + z_29*z_16*z_5 + z_29*z_18 ,
z_29*z_18*z_32*z_3 ,
z_29*z_18*z_32*z_4 ,
z_29*z_18*z_32*z_5 ,
z_29*z_18*z_32*z_6 ,
z_29*z_18*z_34*z_15 ,
z_29*z_18*z_34*z_17 ,
z_29*z_18*z_34*z_18 + z_30*z_25*z_35*z_20 + z_31*z_28*z_30*z_25 + z_29*z_16*z_5 + z_29*z_18 ,
z_29*z_18*z_35*z_20 ,
z_29*z_18*z_37*z_26 + z_30*z_25*z_34*z_18 + z_31*z_28*z_30*z_25 + z_29*z_16*z_5 + z_29*z_18 ,
z_29*z_18*z_37*z_27 ,
z_30*z_23*z_11*z_23 + z_29*z_16*z_3 + z_30*z_23 ,
z_30*z_25*z_32*z_5 + z_30*z_25*z_34*z_18 ,
z_30*z_25*z_34*z_16 + z_29*z_18*z_32 + z_30*z_25*z_32 ,
z_32*z_4*z_17*z_29 + z_34*z_16*z_5*z_34 + z_34*z_18*z_32*z_4 + z_36*z_25*z_32*z_4 + z_34*z_15*z_1 + z_34*z_16*z_4 + z_34*z_18*z_34 + z_35*z_20*z_34 + z_37*z_26*z_34 ,
z_32*z_4*z_18*z_33 + z_33*z_13*z_33 ,
z_32*z_4*z_18*z_34 + z_34*z_16*z_5*z_34 + z_34*z_18*z_32*z_4 + z_32*z_5*z_34 + z_33*z_13*z_34 + z_34*z_15*z_1 + z_34*z_16*z_4 + z_34*z_18*z_34 + z_35*z_20*z_34 + z_37*z_26*z_34 ,
z_32*z_4*z_18*z_37 + z_32*z_6*z_45 ,
z_32*z_5*z_32*z_4 ,
z_32*z_5*z_32*z_5 + z_37*z_27*z_45*z_26 ,
z_32*z_5*z_34*z_16 + z_32*z_5*z_32 + z_33*z_14*z_42 + z_35*z_21*z_42 + z_37*z_27*z_42 ,
z_32*z_5*z_34*z_18 + z_32*z_6*z_45*z_26 + z_33*z_14*z_45*z_26 + z_34*z_18*z_34*z_18 + z_34*z_18*z_35*z_20 + z_34*z_18*z_36*z_25 + z_34*z_18*z_37*z_26 + z_35*z_20*z_34*z_18 + z_35*z_21*z_43*z_13 + z_35*z_21*z_45*z_26 + z_36*z_25*z_32*z_5 + z_36*z_25*z_34*z_18 + z_36*z_25*z_35*z_20 + z_37*z_26*z_34*z_18 + z_37*z_27*z_43*z_13 + z_37*z_27*z_44*z_20 + z_37*z_27*z_45*z_26 ,
z_32*z_5*z_37*z_27 + z_32*z_6*z_45*z_27 ,
z_32*z_6*z_41*z_1 + z_36*z_25*z_32*z_4 + z_32*z_5*z_34 + z_34*z_17*z_29 ,
z_32*z_6*z_41*z_2 + z_32*z_6*z_45*z_27 + z_33*z_14*z_45*z_27 + z_34*z_18*z_33*z_14 ,
z_32*z_6*z_46*z_38 ,
z_32*z_6*z_46*z_40 + z_36*z_25*z_32*z_6 + z_37*z_27*z_43*z_14 + z_37*z_27*z_44*z_21 ,
z_33*z_13*z_34*z_18 + z_37*z_27*z_45*z_26 ,
z_33*z_14*z_42*z_4 ,
z_33*z_14*z_42*z_5 + z_37*z_27*z_45*z_26 ,
z_33*z_14*z_42*z_6 ,
z_33*z_14*z_44*z_20 + z_33*z_14*z_45*z_26 + z_34*z_18*z_34*z_18 + z_34*z_18*z_35*z_20 + z_34*z_18*z_36*z_25 + z_34*z_18*z_37*z_26 + z_35*z_20*z_34*z_18 + z_35*z_21*z_43*z_13 + z_35*z_21*z_45*z_26 + z_36*z_25*z_34*z_18 + z_37*z_26*z_34*z_18 + z_37*z_27*z_43*z_13 + z_37*z_27*z_44*z_20 ,
z_33*z_14*z_44*z_21 + z_33*z_14*z_45*z_27 + z_34*z_18*z_33*z_14 ,
z_34*z_16*z_3*z_10 + z_34*z_16*z_5*z_32 + z_34*z_18*z_34*z_16 + z_34*z_18*z_32 + z_35*z_21*z_42 + z_37*z_27*z_42 ,
z_34*z_16*z_3*z_11 + z_34*z_18*z_36 + z_36*z_23*z_11 + z_36*z_24*z_30 ,
z_34*z_17*z_29*z_15 + z_32*z_6*z_41 ,
z_34*z_17*z_29*z_16 + z_32*z_5*z_32 + z_33*z_14*z_42 + z_35*z_21*z_42 + z_37*z_27*z_42 ,
z_34*z_17*z_29*z_17 + z_34*z_18*z_34*z_17 + z_34*z_18*z_36*z_24 ,
z_34*z_17*z_29*z_18 + z_35*z_21*z_43*z_13 + z_35*z_21*z_45*z_26 + z_37*z_27*z_42*z_5 + z_37*z_27*z_44*z_20 + z_37*z_27*z_45*z_26 ,
z_34*z_18*z_32*z_3 + z_34*z_18*z_36*z_23 ,
z_34*z_18*z_33*z_13 + z_37*z_27*z_45*z_26 ,
z_34*z_18*z_36*z_22 + z_35*z_19 + z_36*z_22 ,
z_35*z_19*z_7*z_20 + z_36*z_25*z_35*z_20 ,
z_35*z_19*z_7*z_21 + z_35*z_21*z_46*z_40 ,
z_35*z_20*z_34*z_16 + z_32*z_5*z_32 + z_33*z_14*z_42 + z_35*z_21*z_42 ,
z_35*z_20*z_34*z_17 ,
z_35*z_21*z_42*z_4 + z_36*z_25*z_32*z_4 + z_37*z_27*z_42*z_4 + z_32*z_5*z_34 + z_34*z_17*z_29 ,
z_35*z_21*z_42*z_5 + z_35*z_21*z_43*z_13 + z_35*z_21*z_45*z_26 + z_37*z_27*z_44*z_20 ,
z_35*z_21*z_42*z_6 + z_37*z_27*z_42*z_6 + z_37*z_27*z_43*z_14 + z_37*z_27*z_44*z_21 ,
z_35*z_21*z_44*z_21 + z_35*z_21*z_45*z_27 + z_37*z_27*z_42*z_6 + z_37*z_27*z_43*z_14 ,
z_35*z_21*z_46*z_39 + z_32*z_3 + z_36*z_23 ,
z_36*z_23*z_11*z_23 + z_32*z_3 + z_36*z_23 ,
z_36*z_24*z_30*z_22 + z_35*z_19 + z_36*z_22 ,
z_36*z_24*z_31*z_28 + z_36*z_25*z_34*z_17 + z_32*z_4*z_17 + z_34*z_17 ,
z_36*z_25*z_34*z_16 + z_32*z_5*z_32 + z_33*z_14*z_42 + z_36*z_25*z_32 ,
z_37*z_26*z_34*z_15 + z_32*z_6*z_41 ,
z_37*z_26*z_34*z_16 + z_33*z_14*z_42 + z_37*z_27*z_42 ,
z_37*z_27*z_45*z_27 ,
z_37*z_27*z_46*z_39 ,
z_38*z_8*z_25*z_34 + z_40*z_44*z_20*z_34 ,
z_38*z_9*z_39*z_12 + z_39*z_12*z_38*z_9 ,
z_39*z_10*z_6*z_42 ,
z_39*z_11*z_25*z_32 + z_40*z_46*z_40*z_42 ,
z_39*z_11*z_25*z_34 + z_40*z_42*z_5*z_34 ,
z_39*z_12*z_38*z_8 ,
z_40*z_42*z_4*z_17 + z_39*z_11*z_24 ,
z_40*z_42*z_4*z_18 + z_39*z_10*z_5 + z_39*z_11*z_25 ,
z_40*z_42*z_5*z_32 ,
z_40*z_42*z_5*z_37 + z_40*z_42*z_6*z_45 + z_40*z_45*z_27*z_45 ,
z_40*z_42*z_6*z_46 ,
z_40*z_44*z_20*z_33 ,
z_40*z_44*z_20*z_37 ,
z_40*z_44*z_21*z_43 ,
z_40*z_44*z_21*z_44 ,
z_40*z_44*z_21*z_45 ,
z_40*z_45*z_27*z_42 + z_39*z_10 + z_40*z_42 ,
z_40*z_45*z_27*z_43 ,
z_40*z_45*z_27*z_44 ,
z_40*z_45*z_27*z_46 + z_40*z_46 ,
z_40*z_46*z_39*z_10 + z_40*z_46*z_40*z_42 ,
z_40*z_46*z_39*z_11 ,
z_40*z_46*z_40*z_41 ,
z_40*z_46*z_40*z_44 ,
z_40*z_46*z_40*z_46 ,
z_41*z_1*z_17*z_29 + z_41*z_1*z_18*z_34 + z_42*z_6*z_41*z_1 + z_44*z_21*z_42*z_4 + z_46*z_40*z_41*z_1 + z_43*z_13*z_34 + z_44*z_20*z_34 + z_45*z_26*z_34 + z_42*z_4 ,
z_41*z_1*z_18*z_32 + z_42*z_5*z_34*z_16 + z_42*z_5*z_32 + z_44*z_21*z_42 + z_45*z_27*z_42 + z_46*z_39*z_10 + z_46*z_40*z_42 ,
z_42*z_3*z_10*z_4 + z_46*z_40*z_42*z_4 ,
z_42*z_4*z_17*z_29 + z_42*z_4*z_18*z_34 + z_46*z_40*z_42*z_4 + z_42*z_5*z_34 ,
z_42*z_5*z_32*z_4 + z_44*z_21*z_42*z_4 + z_43*z_13*z_34 ,
z_42*z_5*z_32*z_5 + z_44*z_21*z_42*z_5 + z_45*z_27*z_43*z_13 ,
z_42*z_5*z_34*z_18 + z_44*z_21*z_42*z_5 + z_45*z_27*z_43*z_13 + z_46*z_39*z_11*z_25 + z_46*z_40*z_42*z_5 ,
z_42*z_5*z_37*z_27 + z_44*z_21*z_44*z_21 + z_44*z_21*z_45*z_27 + z_45*z_27*z_42*z_6 + z_45*z_27*z_44*z_21 + z_46*z_39*z_10*z_6 + z_46*z_40*z_42*z_6 ,
z_42*z_6*z_41*z_2 + z_46*z_39*z_10*z_6 + z_46*z_40*z_42*z_6 + z_46*z_40*z_44*z_21 + z_46*z_40*z_46*z_40 + z_41*z_2 + z_43*z_14 + z_44*z_21 + z_45*z_27 ,
z_42*z_6*z_45*z_26 + z_44*z_21*z_42*z_5 + z_44*z_21*z_43*z_13 + z_44*z_21*z_45*z_26 + z_45*z_27*z_44*z_20 + z_46*z_39*z_10*z_5 + z_46*z_40*z_42*z_5 ,
z_42*z_6*z_45*z_27 + z_44*z_21*z_44*z_21 + z_44*z_21*z_45*z_27 + z_45*z_27*z_42*z_6 + z_45*z_27*z_44*z_21 ,
z_42*z_6*z_46*z_38 + z_44*z_19 + z_46*z_38 ,
z_43*z_13*z_34*z_18 + z_44*z_21*z_43*z_13 + z_45*z_27*z_43*z_13 ,
z_43*z_14*z_45*z_26 + z_44*z_21*z_42*z_5 + z_44*z_21*z_45*z_26 + z_45*z_27*z_43*z_13 + z_46*z_39*z_10*z_5 + z_46*z_40*z_42*z_5 ,
z_43*z_14*z_45*z_27 + z_44*z_21*z_45*z_27 ,
z_44*z_19*z_7*z_20 + z_46*z_40*z_44*z_20 ,
z_44*z_19*z_7*z_21 + z_46*z_39*z_10*z_6 + z_46*z_40*z_41*z_2 + z_46*z_40*z_42*z_6 + z_46*z_40*z_45*z_27 ,
z_44*z_20*z_34*z_16 + z_42*z_3*z_10 + z_44*z_21*z_42 + z_46*z_39*z_10 ,
z_44*z_20*z_35*z_19 + z_44*z_19 + z_46*z_38 ,
z_44*z_21*z_46*z_39 + z_42*z_3 + z_46*z_39 ,
z_44*z_21*z_46*z_40 + z_46*z_40*z_44*z_21 ,
z_45*z_26*z_34*z_15 ,
z_45*z_26*z_34*z_16 + z_45*z_27*z_42 ,
z_45*z_27*z_42*z_4 + z_43*z_13*z_34 ,
z_45*z_27*z_43*z_14 + z_45*z_27*z_44*z_21 ,
z_45*z_27*z_45*z_26 ,
z_45*z_27*z_45*z_27 ,
z_46*z_38*z_9*z_39 + z_42*z_3 + z_46*z_39 ,
z_46*z_39*z_12*z_38 + z_44*z_19 + z_46*z_38 ,
z_1*z_17*z_30 + z_1*z_18*z_36 ,
z_1*z_18*z_33 ,
z_1*z_18*z_35 ,
z_2*z_42*z_3 + z_2*z_46*z_39 ,
z_2*z_42*z_4 ,
z_2*z_45*z_26 ,
z_2*z_45*z_27 ,
z_2*z_46*z_38 ,
z_3*z_10*z_5 + z_3*z_11*z_25 + z_5*z_32*z_5 + z_5*z_34*z_18 + z_5*z_36*z_25 + z_6*z_44*z_20 + z_6*z_45*z_26 ,
z_3*z_10*z_6 + z_3*z_12*z_40 + z_5*z_35*z_21 ,
z_3*z_12*z_38 + z_6*z_46*z_38 ,
z_4*z_16*z_3 + z_6*z_42*z_3 ,
z_4*z_16*z_4 + z_5*z_32*z_4 ,
z_4*z_16*z_5 + z_5*z_32*z_5 ,
z_4*z_16*z_6 + z_5*z_35*z_21 + z_6*z_41*z_2 + z_6*z_44*z_21 + z_6*z_45*z_27 ,
z_4*z_17*z_30 + z_3*z_11 + z_5*z_36 ,
z_4*z_18*z_32 + z_5*z_34*z_16 + z_5*z_32 ,
z_4*z_18*z_35 + z_5*z_35 + z_6*z_44 ,
z_4*z_18*z_36 + z_3*z_11 ,
z_5*z_32*z_3 + z_6*z_42*z_3 ,
z_5*z_32*z_6 + z_5*z_35*z_21 + z_6*z_41*z_2 + z_6*z_44*z_21 + z_6*z_45*z_27 ,
z_5*z_34*z_15 + z_6*z_41 ,
z_5*z_34*z_17 + z_5*z_36*z_24 ,
z_5*z_35*z_19 ,
z_5*z_35*z_20 + z_5*z_36*z_25 ,
z_5*z_36*z_22 ,
z_5*z_36*z_23 + z_6*z_42*z_3 ,
z_5*z_37*z_26 + z_6*z_45*z_26 ,
z_6*z_42*z_4 ,
z_6*z_42*z_6 ,
z_6*z_44*z_19 + z_6*z_46*z_38 ,
z_6*z_46*z_39 ,
z_7*z_20*z_33 ,
z_7*z_20*z_34 + z_8*z_25*z_34 ,
z_7*z_20*z_37 ,
z_7*z_21*z_42 + z_9*z_40*z_42 ,
z_7*z_21*z_43 ,
z_7*z_21*z_44 ,
z_7*z_21*z_45 ,
z_8*z_25*z_32 + z_9*z_40*z_42 ,
z_9*z_39*z_10 + z_9*z_40*z_42 ,
z_9*z_40*z_41 ,
z_9*z_40*z_45 ,
z_9*z_40*z_46 ,
z_10*z_4*z_16 + z_10*z_6*z_42 ,
z_10*z_4*z_18 + z_10*z_5 + z_11*z_25 ,
z_10*z_5*z_32 + z_10*z_6*z_42 ,
z_10*z_5*z_35 ,
z_10*z_5*z_36 ,
z_10*z_5*z_37 + z_12*z_40*z_45 ,
z_10*z_6*z_41 + z_12*z_40*z_41 ,
z_10*z_6*z_44 + z_12*z_40*z_44 ,
z_10*z_6*z_45 + z_12*z_40*z_45 ,
z_10*z_6*z_46 + z_12*z_40*z_46 ,
z_11*z_23*z_12 + z_12*z_40*z_46 ,
z_11*z_24*z_30 ,
z_11*z_24*z_31 ,
z_12*z_40*z_42 ,
z_13*z_33*z_13 + z_13*z_34*z_18 + z_13*z_37*z_26 + z_14*z_42*z_5 + z_14*z_43*z_13 + z_14*z_45*z_26 ,
z_13*z_33*z_14 + z_13*z_35*z_21 + z_13*z_37*z_27 + z_14*z_42*z_6 + z_14*z_44*z_21 + z_14*z_45*z_27 ,
z_13*z_34*z_15 ,
z_13*z_34*z_16 + z_14*z_42 ,
z_13*z_34*z_17 ,
z_13*z_35*z_19 ,
z_14*z_42*z_3 ,
z_14*z_43*z_14 + z_14*z_44*z_21 + z_14*z_45*z_27 ,
z_14*z_44*z_19 ,
z_15*z_1*z_17 + z_16*z_4*z_17 + z_17*z_30*z_24 + z_18*z_34*z_17 + z_18*z_36*z_24 ,
z_15*z_2*z_42 + z_16*z_3*z_10 + z_17*z_29*z_16 + z_18*z_32 ,
z_16*z_4*z_16 + z_16*z_5*z_32 ,
z_16*z_5*z_35 ,
z_16*z_5*z_36 ,
z_16*z_6*z_41 ,
z_16*z_6*z_42 ,
z_17*z_30*z_22 + z_18*z_36*z_22 ,
z_18*z_35*z_19 + z_18*z_36*z_22 ,
z_20*z_33*z_13 + z_21*z_43*z_13 ,
z_20*z_33*z_14 + z_21*z_44*z_21 + z_21*z_45*z_27 ,
z_20*z_34*z_15 ,
z_20*z_35*z_20 + z_21*z_42*z_5 + z_21*z_43*z_13 + z_21*z_45*z_26 ,
z_20*z_35*z_21 + z_21*z_42*z_6 + z_21*z_44*z_21 + z_21*z_45*z_27 ,
z_20*z_37*z_26 + z_21*z_44*z_20 + z_21*z_45*z_26 ,
z_20*z_37*z_27 + z_21*z_44*z_21 + z_21*z_45*z_27 ,
z_21*z_42*z_3 + z_21*z_46*z_39 ,
z_21*z_43*z_14 + z_21*z_44*z_21 + z_21*z_45*z_27 ,
z_21*z_44*z_19 ,
z_22*z_9*z_40 + z_25*z_35*z_21 ,
z_23*z_11*z_24 + z_25*z_34*z_17 ,
z_23*z_11*z_25 + z_25*z_35*z_20 ,
z_23*z_12*z_40 + z_25*z_32*z_6 ,
z_24*z_30*z_23 ,
z_24*z_30*z_24 ,
z_24*z_30*z_25 + z_25*z_32*z_5 + z_25*z_34*z_18 ,
z_26*z_32*z_3 ,
z_26*z_34*z_17 ,
z_26*z_37*z_26 + z_27*z_45*z_26 ,
z_26*z_37*z_27 ,
z_27*z_42*z_3 + z_27*z_46*z_39 ,
z_27*z_44*z_19 ,
z_27*z_46*z_38 ,
z_28*z_30*z_23 ,
z_28*z_30*z_24 ,
z_29*z_15*z_1 + z_29*z_16*z_4 + z_29*z_17*z_29 + z_29*z_18*z_34 + z_30*z_25*z_34 ,
z_29*z_17*z_30 + z_30*z_23*z_11 ,
z_29*z_18*z_33 ,
z_29*z_18*z_36 ,
z_30*z_24*z_30 ,
z_30*z_24*z_31 ,
z_32*z_3*z_10 + z_32*z_5*z_32 + z_33*z_14*z_42 + z_36*z_25*z_32 ,
z_32*z_3*z_11 + z_36*z_23*z_11 ,
z_32*z_3*z_12 + z_36*z_23*z_12 ,
z_32*z_4*z_16 + z_32*z_5*z_32 ,
z_32*z_5*z_35 ,
z_32*z_5*z_36 ,
z_32*z_6*z_42 + z_33*z_14*z_42 ,
z_32*z_6*z_44 + z_33*z_14*z_44 ,
z_33*z_13*z_35 + z_33*z_14*z_44 ,
z_33*z_13*z_37 + z_33*z_14*z_45 ,
z_33*z_14*z_43 + z_34*z_18*z_33 ,
z_34*z_17*z_30 + z_36*z_23*z_11 + z_36*z_24*z_30 ,
z_35*z_20*z_35 + z_37*z_27*z_44 ,
z_35*z_20*z_36 + z_36*z_23*z_11 ,
z_37*z_26*z_32 ,
z_37*z_26*z_37 + z_37*z_27*z_45 ,
z_38*z_9*z_40 + z_39*z_10*z_6 + z_40*z_41*z_2 + z_40*z_42*z_6 + z_40*z_45*z_27 ,
z_39*z_10*z_4 + z_40*z_42*z_4 ,
z_39*z_11*z_23 + z_40*z_46*z_39 ,
z_39*z_12*z_40 + z_40*z_41*z_2 + z_40*z_42*z_6 + z_40*z_44*z_21 + z_40*z_45*z_27 ,
z_40*z_42*z_3 + z_40*z_46*z_39 ,
z_40*z_46*z_38 ,
z_41*z_2*z_42 + z_42*z_3*z_10 + z_42*z_5*z_32 + z_44*z_21*z_42 + z_45*z_27*z_42 + z_46*z_39*z_10 ,
z_41*z_2*z_45 + z_45*z_27*z_45 ,
z_41*z_2*z_46 + z_42*z_6*z_46 + z_44*z_21*z_46 + z_45*z_27*z_46 + z_46*z_39*z_12 ,
z_42*z_3*z_11 + z_46*z_39*z_11 ,
z_42*z_3*z_12 + z_44*z_21*z_46 + z_46*z_38*z_9 + z_46*z_39*z_12 ,
z_42*z_4*z_16 + z_42*z_5*z_32 ,
z_42*z_5*z_35 + z_44*z_19*z_7 + z_46*z_40*z_44 ,
z_42*z_5*z_36 ,
z_42*z_6*z_42 ,
z_42*z_6*z_44 + z_44*z_20*z_35 + z_45*z_27*z_44 ,
z_43*z_13*z_35 + z_45*z_27*z_44 ,
z_43*z_13*z_37 + z_43*z_14*z_45 ,
z_43*z_14*z_42 ,
z_43*z_14*z_43 + z_44*z_21*z_43 + z_45*z_27*z_43 ,
z_43*z_14*z_44 + z_44*z_21*z_44 + z_45*z_27*z_44 ,
z_44*z_20*z_36 + z_46*z_38*z_8 ,
z_45*z_26*z_32 ,
z_45*z_26*z_37 ,

The projective resolutions of the simple modules.


Simple Module Number 1 is Projective.



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 not 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.