/* Group 640.19151 downloaded from the LMFDB on 13 November 2025. */
 
/* Various presentations of this group are stored in this file: 
	 GPC is polycyclic presentation GPerm is permutation group 
	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
 Many characteristics of the group are stored as booleans in a record: 
	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
	 solvable, supersolvable 
 
 The character table is stored as chartbl_n_i where n is the order of 
 the group and i is which group of that order it is. Conjugacy classes 
 are stored in the variable 'C' with elements from the group 'G'. 
*/
 
/* Constructions */
GPC := PCGroup([8, 2, 2, 2, 2, 2, 2, 2, 5, 5259, 91, 7021, 2525, 901, 141, 16142, 1374, 2054, 166, 16399, 3103, 2087]); a,b,c,d,e := Explode([GPC.1, GPC.2, GPC.3, GPC.4, GPC.6]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "e", "e2", "e4"]);
GPerm := PermutationGroup< 15 | (2,3,5,4)(6,7)(9,11)(13,15), (2,4,5,3)(6,7)(12,13,14,15), (6,7)(8,9)(10,11)(12,13,14,15), (6,7)(8,10)(9,11)(12,14)(13,15), (12,14)(13,15), (8,10)(9,11)(12,14)(13,15), (2,5)(3,4), (1,2,3,4,5) >;
GLZN := MatrixGroup< 2, Integers(40) | [[11, 30, 30, 1], [1, 20, 0, 1], [11, 35, 30, 1], [21, 10, 10, 31], [21, 0, 0, 21], [1, 0, 0, 9], [1, 8, 0, 1], [11, 12, 20, 7]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_640_19151 := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := false,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true>; 

 
/* Character Table */
G:= GLZN;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Matrix(2, [1, 0, 0, 1])>,< 2, 1, Matrix(2, [21, 0, 0, 21])>,< 2, 1, Matrix(2, [11, 20, 0, 11])>,< 2, 1, Matrix(2, [31, 20, 0, 31])>,< 2, 1, Matrix(2, [1, 20, 0, 1])>,< 2, 1, Matrix(2, [21, 20, 0, 21])>,< 2, 1, Matrix(2, [31, 0, 0, 31])>,< 2, 1, Matrix(2, [11, 0, 0, 11])>,< 2, 4, Matrix(2, [31, 25, 0, 1])>,< 2, 4, Matrix(2, [31, 5, 0, 1])>,< 2, 5, Matrix(2, [1, 36, 0, 9])>,< 2, 5, Matrix(2, [11, 20, 0, 19])>,< 2, 5, Matrix(2, [21, 20, 0, 29])>,< 2, 5, Matrix(2, [31, 16, 0, 39])>,< 2, 5, Matrix(2, [11, 0, 0, 19])>,< 2, 5, Matrix(2, [1, 16, 0, 9])>,< 2, 5, Matrix(2, [21, 24, 0, 29])>,< 2, 5, Matrix(2, [31, 12, 0, 39])>,< 2, 20, Matrix(2, [31, 1, 0, 9])>,< 2, 20, Matrix(2, [31, 21, 0, 9])>,< 4, 2, Matrix(2, [11, 30, 30, 1])>,< 4, 2, Matrix(2, [31, 30, 30, 21])>,< 4, 2, Matrix(2, [11, 10, 30, 1])>,< 4, 2, Matrix(2, [31, 10, 30, 21])>,< 4, 4, Matrix(2, [11, 35, 30, 1])>,< 4, 4, Matrix(2, [11, 15, 30, 1])>,< 4, 10, Matrix(2, [11, 4, 20, 23])>,< 4, 10, Matrix(2, [11, 12, 20, 7])>,< 4, 10, Matrix(2, [11, 38, 30, 9])>,< 4, 10, Matrix(2, [31, 22, 30, 29])>,< 4, 10, Matrix(2, [1, 6, 30, 23])>,< 4, 10, Matrix(2, [21, 38, 30, 27])>,< 4, 10, Matrix(2, [21, 24, 20, 33])>,< 4, 10, Matrix(2, [21, 32, 20, 17])>,< 4, 10, Matrix(2, [11, 24, 20, 23])>,< 4, 10, Matrix(2, [11, 32, 20, 7])>,< 4, 10, Matrix(2, [21, 30, 30, 3])>,< 4, 10, Matrix(2, [1, 14, 30, 7])>,< 4, 10, Matrix(2, [11, 18, 30, 9])>,< 4, 10, Matrix(2, [31, 2, 30, 29])>,< 4, 10, Matrix(2, [1, 26, 30, 23])>,< 4, 10, Matrix(2, [21, 18, 30, 27])>,< 4, 10, Matrix(2, [21, 4, 20, 33])>,< 4, 10, Matrix(2, [21, 12, 20, 17])>,< 4, 10, Matrix(2, [21, 10, 30, 3])>,< 4, 10, Matrix(2, [1, 34, 30, 7])>,< 4, 20, Matrix(2, [11, 3, 30, 9])>,< 4, 20, Matrix(2, [11, 23, 30, 9])>,< 4, 20, Matrix(2, [1, 27, 20, 7])>,< 4, 20, Matrix(2, [1, 19, 20, 23])>,< 4, 20, Matrix(2, [21, 9, 30, 7])>,< 4, 20, Matrix(2, [21, 1, 30, 23])>,< 4, 20, Matrix(2, [1, 7, 20, 7])>,< 4, 20, Matrix(2, [1, 39, 20, 23])>,< 4, 20, Matrix(2, [21, 29, 30, 7])>,< 4, 20, Matrix(2, [21, 21, 30, 23])>,< 5, 4, Matrix(2, [1, 16, 0, 1])>,< 10, 4, Matrix(2, [31, 28, 0, 31])>,< 10, 4, Matrix(2, [1, 28, 0, 1])>,< 10, 4, Matrix(2, [21, 4, 0, 21])>,< 10, 4, Matrix(2, [31, 8, 0, 31])>,< 10, 4, Matrix(2, [11, 24, 0, 11])>,< 10, 4, Matrix(2, [21, 24, 0, 21])>,< 10, 4, Matrix(2, [11, 4, 0, 11])>,< 10, 8, Matrix(2, [31, 33, 0, 1])>,< 10, 8, Matrix(2, [31, 1, 0, 1])>,< 10, 8, Matrix(2, [31, 13, 0, 1])>,< 10, 8, Matrix(2, [31, 21, 0, 1])>,< 20, 8, Matrix(2, [11, 22, 30, 1])>,< 20, 8, Matrix(2, [31, 6, 30, 21])>,< 20, 8, Matrix(2, [11, 2, 30, 1])>,< 20, 8, Matrix(2, [31, 26, 30, 21])>,< 20, 8, Matrix(2, [11, 27, 30, 1])>,< 20, 8, Matrix(2, [11, 11, 30, 1])>,< 20, 8, Matrix(2, [11, 7, 30, 1])>,< 20, 8, Matrix(2, [11, 31, 30, 1])>]); 
CR := CharacterRing(G);
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,-1*K.1,-1*K.1,1,K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1,K.1,-1*K.1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1*K.1,K.1,-1,K.1,-1*K.1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,K.1,K.1,1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1,-1*K.1,K.1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,K.1,-1*K.1,-1,-1*K.1,K.1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1*K.1,-1*K.1,-1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,1,-1*K.1,K.1,-1,K.1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,-1,-1*K.1,-1*K.1,1,K.1,-1*K.1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,K.1,K.1,-1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,1,K.1,-1*K.1,-1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1,K.1,K.1,1,-1*K.1,K.1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,-1*K.1,-1*K.1,1,K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1,K.1,-1*K.1,1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1,K.1,-1*K.1,1,-1*K.1,K.1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,K.1,K.1,1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1,-1*K.1,K.1,1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1,-1*K.1,K.1,1,K.1,-1*K.1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1*K.1,-1*K.1,-1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,1,-1*K.1,K.1,-1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,1,K.1,K.1,-1,-1*K.1,K.1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,1,K.1,K.1,-1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,1,K.1,-1*K.1,-1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,1,-1*K.1,-1*K.1,-1,K.1,-1*K.1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,-1*K.1,-1*K.1,1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,1,-1*K.1,K.1,1,K.1,K.1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1,-1*K.1,-1*K.1,-1,-1*K.1,K.1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,K.1,K.1,1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,1,K.1,-1*K.1,1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1,K.1,K.1,-1,K.1,-1*K.1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1*K.1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,K.1,-1,K.1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,1,-1*K.1,K.1,1,-1*K.1,K.1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,K.1,K.1,-1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1,-1*K.1,K.1,-1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,1,K.1,-1*K.1,1,K.1,-1*K.1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1*K.1,-1*K.1,1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,1,-1*K.1,K.1,1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1*K.1,K.1,1,K.1,K.1,1,K.1,-1*K.1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,K.1,K.1,1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,1,K.1,-1*K.1,1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.1,-1*K.1,1,-1*K.1,-1*K.1,1,-1*K.1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1*K.1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,K.1,K.1,-1,K.1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1,K.1,-1*K.1,-1,K.1,-1*K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,K.1,K.1,-1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,-1,-1*K.1,K.1,-1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1,-1*K.1,K.1,-1,-1*K.1,K.1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, -2, 2, 2, 2, -2, 0, 0, -2, 2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 2, 0, -2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, -2, 2, 2, 2, -2, 0, 0, -2, 2, -2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -2, 0, 2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, -2, -2, 2, 2, 0, 0, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, -2, -2, 2, 2, 0, 0, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 2, -2, -2, 2, 0, 0, -2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 2, 2, 0, 0, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, 2, -2, -2, 2, 0, 0, -2, -2, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, -2, -2, 0, 0, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, 2, -2, 2, -2, -2, 0, 0, -2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, -2, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, 2, -2, 2, -2, -2, 0, 0, -2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,-2,2,2,2,-2,0,0,2,-2,2,-2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,0,0,0,0,2*K.1,-2*K.1,0,2*K.1,-2*K.1,0,0,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,0,2,-2,-2,-2,2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,-2,2,2,2,-2,0,0,2,-2,2,-2,-2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,0,0,0,0,-2*K.1,2*K.1,0,-2*K.1,2*K.1,0,0,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,0,2,-2,-2,-2,2,-2,2,2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,2,-2,-2,2,2,0,0,2,-2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,2*K.1,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,-2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,2,-2,-2,2,2,0,0,2,-2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,-2*K.1,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,2,-2,-2,-2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2,2,0,0,2,2,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,-2*K.1,0,0,0,0,2*K.1,2*K.1,0,-2*K.1,2*K.1,0,0,-2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,0,2,2,-2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2,2,0,0,2,2,-2,-2,2,2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1,0,0,0,0,-2*K.1,-2*K.1,0,2*K.1,-2*K.1,0,0,2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,0,2,2,-2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,2,2,-2,2,-2,-2,2,-2,0,0,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,2*K.1,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,2,-2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,2,2,-2,2,-2,-2,2,-2,0,0,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,-2*K.1,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,2,-2,-2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,0,0,-2,2,2,2,-2,2,-2,-2,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,-2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-2,2,2,-2,0,0,0,0,0,-2*K.1,0,2*K.1,2*K.1,0,-2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,0,0,-2,2,2,2,-2,2,-2,-2,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,-2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-2,2,2,-2,0,0,0,0,0,2*K.1,0,-2*K.1,-2*K.1,0,2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,0,0,2,-2,-2,-2,2,-2,2,2,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,-2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-2,2,2,-2,0,0,0,0,0,-2*K.1,0,2*K.1,2*K.1,0,-2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,-2,-2,2,-2,2,0,0,2,-2,-2,-2,2,-2,2,2,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,-2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,-2,-2,-2,2,2,-2,0,0,0,0,0,2*K.1,0,-2*K.1,-2*K.1,0,2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,2,-2,0,0,-2,-2,-2,2,2,2,2,-2,0,0,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,-2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,2,-2,2,0,0,0,0,0,2*K.1,0,2*K.1,-2*K.1,0,-2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,2,-2,0,0,-2,-2,-2,2,2,2,2,-2,0,0,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,2,-2,2,0,0,0,0,0,-2*K.1,0,-2*K.1,2*K.1,0,2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,2,-2,0,0,2,2,2,-2,-2,-2,-2,2,0,0,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,2,-2,2,0,0,0,0,0,2*K.1,0,2*K.1,-2*K.1,0,-2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,2,-2,0,0,2,2,2,-2,-2,-2,-2,2,0,0,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,-2*K.1,0,0,2*K.1,0,0,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,-2,2,-2,2,0,0,0,0,0,-2*K.1,0,-2*K.1,2*K.1,0,2*K.1,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 4, 4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 4, 4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 4, 4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, -4, 4, 4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,-4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,-4*K.1^5,4*K.1^5,4*K.1^5,-4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,1,-1,-1,1,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,2*K.1^3-K.1^5+2*K.1^7,K.1^5,-2*K.1^3+K.1^5-2*K.1^7,-1*K.1^5,-1*K.1^5,-2*K.1^3+K.1^5-2*K.1^7,K.1^5,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,-4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1^5,-4*K.1^5,-4*K.1^5,4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,1,-1,-1,1,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,-2*K.1^3+K.1^5-2*K.1^7,-1*K.1^5,2*K.1^3-K.1^5+2*K.1^7,K.1^5,K.1^5,2*K.1^3-K.1^5+2*K.1^7,-1*K.1^5,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,-4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,-4*K.1^5,4*K.1^5,4*K.1^5,-4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,1,-1,-1,1,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,-2*K.1^3+K.1^5-2*K.1^7,K.1^5,2*K.1^3-K.1^5+2*K.1^7,-1*K.1^5,-1*K.1^5,2*K.1^3-K.1^5+2*K.1^7,K.1^5,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,-4,-4,-4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1^5,-4*K.1^5,-4*K.1^5,4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,-1,1,1,1,-1,-1,1,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,2*K.1^3-K.1^5+2*K.1^7,-1*K.1^5,-2*K.1^3+K.1^5-2*K.1^7,K.1^5,K.1^5,-2*K.1^3+K.1^5-2*K.1^7,-1*K.1^5,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,4,-4,-4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,-4*K.1^5,4*K.1^5,-4*K.1^5,4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,-1,1,-1,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,2*K.1^3-K.1^5+2*K.1^7,-1*K.1^5,2*K.1^3-K.1^5+2*K.1^7,-1*K.1^5,K.1^5,-2*K.1^3+K.1^5-2*K.1^7,K.1^5,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,4,-4,-4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1^5,-4*K.1^5,4*K.1^5,-4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,-1,1,-1,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,-2*K.1^3+K.1^5-2*K.1^7,K.1^5,-2*K.1^3+K.1^5-2*K.1^7,K.1^5,-1*K.1^5,2*K.1^3-K.1^5+2*K.1^7,-1*K.1^5,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,4,-4,-4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,-4*K.1^5,4*K.1^5,-4*K.1^5,4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,-1,1,-1,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,-2*K.1^3+K.1^5-2*K.1^7,-1*K.1^5,-2*K.1^3+K.1^5-2*K.1^7,-1*K.1^5,K.1^5,2*K.1^3-K.1^5+2*K.1^7,K.1^5,2*K.1^3-K.1^5+2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |4,4,4,-4,-4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1^5,-4*K.1^5,4*K.1^5,-4*K.1^5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,1,-1,1,-1,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,1+2*K.1^4-2*K.1^6,-1-2*K.1^4+2*K.1^6,2*K.1^3-K.1^5+2*K.1^7,K.1^5,2*K.1^3-K.1^5+2*K.1^7,K.1^5,-1*K.1^5,-2*K.1^3+K.1^5-2*K.1^7,-1*K.1^5,-2*K.1^3+K.1^5-2*K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, -8, -8, -8, 8, 8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, -8, 8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 8, -8, 8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[8, -8, 8, 8, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_640_19151:= KnownIrreducibles(CR);