/* Group 320.586 downloaded from the LMFDB on 14 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([7, -2, -2, -2, -2, -2, -2, -5, 2325, 36, 4707, 346, 80, 1538, 124, 1595]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.4, GPC.6]); AssignNames(~GPC, ["a", "b", "b2", "c", "c2", "d", "d2"]);
GPerm := PermutationGroup< 17 | (2,3)(4,5)(8,9)(10,11)(12,13)(14,15)(16,17), (6,7)(8,9)(10,11)(12,13)(15,16), (6,8)(7,9)(11,13)(14,16,17,15), (6,7)(8,9)(10,12)(11,13)(14,17)(15,16), (14,17)(15,16), (10,12)(11,13)(14,17)(15,16), (1,2,4,5,3) >;
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], [31, 2, 20, 39], [1, 8, 0, 1]] >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_320_586 := 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:= GPC;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, c^2>,< 2, 1, c^2*d^5>,< 2, 1, b^2*d^5>,< 2, 1, b^2*c^2>,< 2, 1, b^2*c^2*d^5>,< 2, 1, b^2>,< 2, 1, d^5>,< 2, 4, a>,< 2, 4, a*c^2>,< 2, 20, a*b^3*c^3*d>,< 2, 20, a*b*c*d>,< 4, 4, b>,< 4, 4, b^3>,< 4, 4, a*b>,< 4, 4, a*b*d^5>,< 4, 20, b^3*c*d^2>,< 4, 20, c^3*d^3>,< 4, 20, b*c*d>,< 4, 20, b^2*c^3*d^9>,< 4, 20, a*b^2*c^3*d^4>,< 4, 20, a*b^2*c*d^9>,< 5, 2, d^4>,< 5, 2, d^8>,< 10, 2, c^2*d^2>,< 10, 2, c^2*d^4>,< 10, 2, c^2*d>,< 10, 2, c^2*d^3>,< 10, 2, b^2*d>,< 10, 2, b^2*d^3>,< 10, 2, b^2*c^2*d^2>,< 10, 2, b^2*c^2*d^4>,< 10, 2, b^2*c^2*d>,< 10, 2, b^2*c^2*d^3>,< 10, 2, b^2*d^4>,< 10, 2, b^2*d^2>,< 10, 2, d^9>,< 10, 2, d^7>,< 10, 4, a*d^2>,< 10, 4, a*d^8>,< 10, 4, a*d^6>,< 10, 4, a*d>,< 10, 4, a*c^2*d^2>,< 10, 4, a*c^2*d^8>,< 10, 4, a*c^2*d^6>,< 10, 4, a*c^2*d>,< 20, 4, b*d^2>,< 20, 4, b*d^3>,< 20, 4, b*d>,< 20, 4, b*d^4>,< 20, 4, b*c^2*d>,< 20, 4, b*d^6>,< 20, 4, b*d^8>,< 20, 4, b^3*d^2>,< 20, 4, a*b*d^2>,< 20, 4, a*b*d^3>,< 20, 4, a*b*d>,< 20, 4, a*b*d^4>,< 20, 4, a*b^3*d^4>,< 20, 4, a*b*d^6>,< 20, 4, a*b*d^8>,< 20, 4, a*b^3*d^2>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 2, 2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 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, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 2, 2, -2, 2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,2,0,0,2,2,2,2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,2,0,0,2,2,2,2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,-2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,-2*K.1,0,0,2*K.1,0,2,2,2,2,2,2,-2,-2,2,-2,-2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,2,0,0,0,0,0,0,0,0,0,2*K.1,0,0,-2*K.1,0,2,2,2,2,2,2,-2,-2,2,-2,-2,2,-2,-2,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
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,-2,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0,0,0,0,2,2,2,-2,-2,-2,2,2,-2,-2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,2*K.1,2*K.1,-2*K.1,0,0,2*K.1,0,-2*K.1,0,0,2*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,-2,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0,0,0,0,2,2,2,-2,-2,-2,2,2,-2,-2,2,2,2,-2,-2,-2,0,0,0,0,0,0,0,0,0,-2*K.1,-2*K.1,2*K.1,0,0,-2*K.1,0,2*K.1,0,0,-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,-2,0,0,0,0,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,2,2,-2,-2,2,2,2,2,-2,-2,-2,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,-2*K.1,0,0,0,-2*K.1,-2*K.1,0,2*K.1,0,2*K.1,2*K.1,0,0,2*K.1,0,-2*K.1]; 
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,-2,0,0,0,0,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,2,2,-2,-2,2,2,2,2,-2,-2,-2,-2,-2,2,-2,2,0,0,0,0,0,0,0,0,2*K.1,0,0,0,2*K.1,2*K.1,0,-2*K.1,0,-2*K.1,-2*K.1,0,0,-2*K.1,0,2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,-2,0,0,-2,-2,2,2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,-2,0,0,-2,-2,2,2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,-2,0,0,2,2,-2,-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,-2,0,0,2,2,-2,-2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,2,0,0,-2,-2,-2,-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,2,0,0,-2,-2,-2,-2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1+K.1^-1,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,-2,2,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1+K.1^-1,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,K.1^2-K.1^-2,-1*K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2,K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |2,-2,2,-2,-2,-2,2,2,2,-2,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1-K.1^-1,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,K.1^2-K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,1+2*K.1+K.1^2+K.1^-2,K.1^2-K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1-2*K.1-K.1^2-K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2,-1*K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^6,K.1^4+K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^3-K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^7,K.1^3+K.1^-3,K.1^3+K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3-K.1^5+K.1^7,K.1^3+K.1^7,K.1+K.1^-1,-1*K.1^3+K.1^5-K.1^7,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^6,-1*K.1^4-K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,-1*K.1^3-K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,K.1^3-K.1^5+K.1^7,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^7,K.1^3+K.1^-3,-1*K.1^3-K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^7,K.1+K.1^-1,K.1^3-K.1^5+K.1^7,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^6,-1*K.1^4-K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^3+K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^7,-1*K.1^3-K.1^-3,K.1^3+K.1^7,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3-K.1^5+K.1^7,K.1^3+K.1^7,-1*K.1-K.1^-1,-1*K.1^3+K.1^5-K.1^7,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^6,K.1^4+K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,K.1^3+K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^7,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^7,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^7,-1*K.1-K.1^-1,K.1^3-K.1^5+K.1^7,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,K.1+K.1^-1,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,K.1^3+K.1^7,-1*K.1-K.1^-1,K.1^3+K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1-K.1^-1,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^7,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^-3,K.1^3+K.1^7,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,K.1+K.1^-1,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^7,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^3+K.1^5-K.1^7,-1*K.1-K.1^-1,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^7,K.1^3-K.1^5+K.1^7,K.1^3+K.1^-3,-1*K.1^3-K.1^7,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1*K.1-K.1^-1,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,K.1^3+K.1^7,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^3-K.1^5+K.1^7,K.1+K.1^-1,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^7,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^-3,K.1^3+K.1^7,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,-2,2,2,-2,2,-2,-2,0,0,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,-1*K.1-K.1^-1,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^7,K.1+K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1+K.1^-1,K.1^3-K.1^5+K.1^7,K.1^3+K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^7,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^7,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,K.1^3+K.1^7,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^7,K.1^3+K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3-K.1^5+K.1^7,K.1+K.1^-1,-1*K.1^3+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,-1*K.1^3-K.1^7,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^-3,K.1^3+K.1^7,K.1^3+K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1+K.1^-1,K.1^3-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^3+K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^-3,-1*K.1^3-K.1^7,-1*K.1^3-K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1-K.1^-1,-1*K.1^3+K.1^5-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^3-K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,K.1^3+K.1^-3,K.1^3+K.1^7,-1*K.1^3-K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3+K.1^5-K.1^7,-1*K.1-K.1^-1,K.1^3-K.1^5+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,K.1+K.1^-1,K.1^3-K.1^5+K.1^7,-1*K.1-K.1^-1,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^7,K.1^3+K.1^-3,K.1^3+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,K.1^3-K.1^5+K.1^7,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,K.1+K.1^-1,-1*K.1^3+K.1^5-K.1^7,-1*K.1-K.1^-1,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^7,K.1^3+K.1^-3,-1*K.1^3-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,-2*K.1^5,2*K.1^5,0,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1*K.1^3+K.1^5-K.1^7,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^7,-1*K.1-K.1^-1,K.1^3-K.1^5+K.1^7,K.1+K.1^-1,-1*K.1^3-K.1^7,K.1^3-K.1^5+K.1^7,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^7,-1*K.1^3-K.1^-3,K.1^3+K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(20: Sparse := true);
S := [ K |2,2,2,-2,2,-2,-2,-2,0,0,0,0,2*K.1^5,-2*K.1^5,0,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^2-K.1^-2,1-2*K.1^2+K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,K.1^4+K.1^6,-1*K.1^4-K.1^6,-1+2*K.1^2-K.1^4+K.1^6,1-2*K.1^2+K.1^4-K.1^6,-1*K.1^4-K.1^6,K.1^4+K.1^6,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3-K.1^5+K.1^7,-1*K.1^3-K.1^7,-1*K.1-K.1^-1,-1*K.1^3+K.1^5-K.1^7,K.1+K.1^-1,K.1^3+K.1^7,-1*K.1^3+K.1^5-K.1^7,K.1^3+K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^7,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^7]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,-4,4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,-4,4,4,-4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,-4,-4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,-4,-4,-4,4,4,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,-4,4,-4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,4,-4,4,-4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,-4,-4,4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(5: Sparse := true);
S := [ K |4,-4,-4,-4,4,4,-4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^2-2*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_320_586:= KnownIrreducibles(CR);