/* Group 448.327 downloaded from the LMFDB on 27 October 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, -7, 56, 645, 36, 254, 58, 1684, 851, 102, 1210]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.5, GPC.7]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "c2", "d"]);
GPerm := PermutationGroup< 27 | (17,18,20,19)(22,23)(24,25)(26,27), (1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(17,19,20,18), (1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(18,19), (1,4,5,14)(2,7,8,12)(3,10,11,13)(6,9,15,16)(17,20)(18,19), (17,20)(18,19), (1,5)(2,8)(3,11)(4,14)(6,15)(7,12)(9,16)(10,13), (21,22,24,26,27,25,23) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_448_327 := 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, b^4>,< 2, 1, b^4*c^2>,< 4, 2, b^6*c^2>,< 4, 2, b^6>,< 4, 4, a*b^5*c^2>,< 4, 4, a*b>,< 4, 8, a*b^4>,< 4, 14, c>,< 4, 14, b^4*c>,< 4, 28, a*b^7*c^3*d^4>,< 4, 28, a*b^5*c*d^6>,< 4, 28, b^2*c^3*d^2>,< 4, 56, a*b^2*c^3>,< 7, 2, d^2>,< 7, 2, d^4>,< 7, 2, d^6>,< 8, 4, b^7>,< 8, 4, b^5>,< 8, 28, b^3*c^3>,< 8, 28, b*c^3>,< 14, 2, c^2*d>,< 14, 2, c^2*d^3>,< 14, 2, c^2*d^2>,< 14, 2, b^4*d^2>,< 14, 2, b^4*d^6>,< 14, 2, b^4*d^3>,< 14, 2, b^4*c^2*d^2>,< 14, 2, b^4*c^2*d^6>,< 14, 2, b^4*c^2*d^3>,< 28, 4, b^2*c^2*d>,< 28, 4, b^2*c^2*d^3>,< 28, 4, b^2*c^2*d^2>,< 28, 4, b^2*d^2>,< 28, 4, b^6*d^6>,< 28, 4, b^2*d^3>,< 28, 8, a*d>,< 28, 8, a*d^6>,< 28, 8, a*d^3>,< 28, 8, a*d^4>,< 28, 8, a*d^5>,< 28, 8, a*d^2>,< 28, 8, a*b*d>,< 28, 8, a*b*c^2*d>,< 28, 8, a*b*c^2*d^3>,< 28, 8, a*b*d^3>,< 28, 8, a*b*d^2>,< 28, 8, a*b*c^2*d^2>,< 56, 4, b*d>,< 56, 4, b^3*d^3>,< 56, 4, b^3*d^2>,< 56, 4, b*d^2>,< 56, 4, b^5*d^3>,< 56, 4, b^3*d>,< 56, 4, b*d^6>,< 56, 4, b*d^3>,< 56, 4, b^5*d^2>,< 56, 4, b*d^5>,< 56, 4, b*d^4>,< 56, 4, b^5*d>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 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, 0, 0, 0, -2, -2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 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, 0, 0, 0, 2, 2, 0, 0, -2, 0, 2, 2, 2, 0, 0, 0, 0, 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(4: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1,2*K.1,0,0,0,0,0,0,0,2,2,2,0,0,0,0,2,-2,-2,2,-2,-2,-2,2,-2,-2,2,-2,2,-2,2,2*K.1,0,0,0,0,-2*K.1,0,0,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
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*K.1,-2*K.1,0,0,0,0,0,0,0,2,2,2,0,0,0,0,2,-2,-2,2,-2,-2,-2,2,-2,-2,2,-2,2,-2,2,-2*K.1,0,0,0,0,2*K.1,0,0,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,0,-2,2,0,0,0,0,2,2,2,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-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,-1*K.1-K.1^-1,K.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^-1,-1*K.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^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,0,-2,2,0,0,0,0,2,2,2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-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,K.1+K.1^-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,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*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,0,2,-2,0,0,0,0,2,2,2,-1*K.1-K.1^-1,K.1+K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,-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,-1*K.1-K.1^-1,K.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^-1,-1*K.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^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(8: Sparse := true);
S := [ K |2,2,-2,-2,0,0,0,0,0,2,-2,0,0,0,0,2,2,2,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-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,K.1+K.1^-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,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*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,2,2,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,2,2,0,0,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,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.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,2,2,0,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,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.1^3+K.1^-3,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,2,2,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-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.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,2,2,0,0,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,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.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1-K.1^-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.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,-2,-2,-2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,2,2,0,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,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.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,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.1^3+K.1^-3,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,-2,-2,2,0,0,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,-2,-2,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,-2,-2,2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,-2,-2,0,0,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-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.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,-2,-2,2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,-2,-2,0,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,-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-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,0,0,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,-2,-2,0,0,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,0,0,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,-2,-2,0,0,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^2-K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1+K.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.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,2,2,2,2,2,-2,0,0,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,-2,-2,0,0,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1+K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^3+K.1^-3,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.1^3-K.1^-3,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^3-K.1^-3,-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-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1^7,2*K.1^7,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,0,0,0,0,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.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^5-K.1^9,-1*K.1^4-K.1^10,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^6+K.1^8,K.1^4+K.1^10,-1*K.1^3-K.1^11,-1*K.1^6-K.1^8,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^5+K.1^9,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,K.1^3+K.1^-3,K.1^5+K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2*K.1^7,-2*K.1^7,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,0,0,0,0,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.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,K.1^5+K.1^9,K.1^4+K.1^10,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^6-K.1^8,-1*K.1^4-K.1^10,K.1^3+K.1^11,K.1^6+K.1^8,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^5-K.1^9,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,K.1^3+K.1^-3,K.1^5+K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1^7,2*K.1^7,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,0,0,0,0,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.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^5-K.1^9,K.1^4+K.1^10,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^6-K.1^8,-1*K.1^4-K.1^10,-1*K.1^3-K.1^11,K.1^6+K.1^8,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^5+K.1^9,K.1^5+K.1^-5,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2*K.1^7,-2*K.1^7,0,0,0,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,0,0,0,0,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.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,K.1^5+K.1^9,-1*K.1^4-K.1^10,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^6+K.1^8,K.1^4+K.1^10,K.1^3+K.1^11,-1*K.1^6-K.1^8,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^5-K.1^9,K.1^5+K.1^-5,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1^7,2*K.1^7,0,0,0,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^6+K.1^-6,-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^-4,-1*K.1^6-K.1^-6,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,-1*K.1^6-K.1^8,-1*K.1^4-K.1^10,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,K.1^5+K.1^9,K.1^4+K.1^10,K.1^6+K.1^8,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9,K.1^3+K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^5+K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^5-K.1^-5,-1*K.1^3-K.1^-3,K.1^5+K.1^-5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2*K.1^7,-2*K.1^7,0,0,0,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^6+K.1^-6,-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^-4,-1*K.1^6-K.1^-6,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,K.1^6+K.1^8,K.1^4+K.1^10,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,-1*K.1^5-K.1^9,-1*K.1^4-K.1^10,-1*K.1^6-K.1^8,K.1^3+K.1^11,K.1^5+K.1^9,-1*K.1^3-K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^5+K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^5-K.1^-5,-1*K.1^3-K.1^-3,K.1^5+K.1^-5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1^7,2*K.1^7,0,0,0,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^6+K.1^-6,-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^-4,-1*K.1^6-K.1^-6,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,K.1^6+K.1^8,K.1^4+K.1^10,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^5+K.1^9,-1*K.1^4-K.1^10,-1*K.1^6-K.1^8,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9,K.1^3+K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,K.1^5+K.1^-5,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^5+K.1^-5,K.1^3+K.1^-3,-1*K.1^5-K.1^-5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2*K.1^7,-2*K.1^7,0,0,0,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,0,0,0,0,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^4-K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^4+K.1^-4,-1*K.1^4-K.1^-4,K.1^6+K.1^-6,-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^-4,-1*K.1^6-K.1^-6,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,-1*K.1^6-K.1^8,-1*K.1^4-K.1^10,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^5-K.1^9,K.1^4+K.1^10,K.1^6+K.1^8,K.1^3+K.1^11,K.1^5+K.1^9,-1*K.1^3-K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,K.1^5+K.1^-5,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^5+K.1^-5,K.1^3+K.1^-3,-1*K.1^5-K.1^-5]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1^7,2*K.1^7,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,0,0,0,0,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^3+K.1^11,-1*K.1^6-K.1^8,K.1^4+K.1^10,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^6+K.1^8,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^4-K.1^10,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^5-K.1^9,-1*K.1^3-K.1^11,K.1^3+K.1^-3,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^5+K.1^-5,-1*K.1-K.1^-1,-1*K.1^5-K.1^-5,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2*K.1^7,-2*K.1^7,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,0,0,0,0,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^3-K.1^11,K.1^6+K.1^8,-1*K.1^4-K.1^10,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^6-K.1^8,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^4+K.1^10,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^5+K.1^9,K.1^3+K.1^11,K.1^3+K.1^-3,K.1^5+K.1^-5,-1*K.1^5-K.1^-5,-1*K.1-K.1^-1,-1*K.1^3-K.1^-3,K.1^3+K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^-3,K.1^5+K.1^-5,-1*K.1-K.1^-1,-1*K.1^5-K.1^-5,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,-2*K.1^7,2*K.1^7,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,0,0,0,0,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,K.1^3+K.1^11,K.1^6+K.1^8,-1*K.1^4-K.1^10,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^6-K.1^8,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^4+K.1^10,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^5-K.1^9,-1*K.1^3-K.1^11,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^5-K.1^-5,K.1+K.1^-1,K.1^5+K.1^-5,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,-2,2,-2,2,-2,2*K.1^7,-2*K.1^7,0,0,0,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,0,0,0,0,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^6+K.1^-6,-1*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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^4+K.1^-4,-1*K.1^3-K.1^11,-1*K.1^6-K.1^8,K.1^4+K.1^10,1-2*K.1^2+K.1^4-K.1^6+K.1^8-K.1^10,K.1^6+K.1^8,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1+2*K.1^2-K.1^4+K.1^6-K.1^8+K.1^10,-1*K.1^4-K.1^10,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^5+K.1^9,K.1^3+K.1^11,-1*K.1^3-K.1^-3,-1*K.1^5-K.1^-5,K.1^5+K.1^-5,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^-3,-1*K.1^5-K.1^-5,K.1+K.1^-1,K.1^5+K.1^-5,-1*K.1-K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,0,0,0,0,0,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1+2*K.1^-1,-2*K.1-2*K.1^-1,-2*K.1^3-2*K.1^-3,2*K.1^3+2*K.1^-3,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,-2*K.1^3-2*K.1^-3,2*K.1^2+2*K.1^-2,-2*K.1^2-2*K.1^-2,2*K.1^3+2*K.1^-3,-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.1^3-2*K.1^-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,0,0,0,0,2*K.1^3+2*K.1^-3,-2*K.1^3-2*K.1^-3,-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.1^3-2*K.1^-3,-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.1^3-2*K.1^-3,2*K.1^3+2*K.1^-3,-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(7: Sparse := true);
S := [ K |4,-4,4,-4,-4,4,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,0,0,0,0,2*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.1^3-2*K.1^-3,-2*K.1^2-2*K.1^-2,-2*K.1-2*K.1^-1,2*K.1^3+2*K.1^-3,-2*K.1^3-2*K.1^-3,2*K.1+2*K.1^-1,-2*K.1^2-2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^3-2*K.1^-3,2*K.1^3+2*K.1^-3,-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(7: Sparse := true);
S := [ K |4,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,2*K.1+2*K.1^-1,2*K.1+2*K.1^-1,2*K.1^3+2*K.1^-3,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,-2*K.1^3-2*K.1^-3,-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.1^3-2*K.1^-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^3+2*K.1^-3,2*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.1^3-2*K.1^-3,-2*K.1^3-2*K.1^-3,-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(7: Sparse := true);
S := [ K |4,4,4,4,-4,-4,0,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,0,0,0,0,2*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.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,2*K.1^3+2*K.1^-3,2*K.1^3+2*K.1^-3,-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.1^3-2*K.1^-3,-2*K.1^3-2*K.1^-3,-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(56: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,0,0,0,0,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^12+2*K.1^-12,-2*K.1^12-2*K.1^-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,K.1^5+K.1^9-K.1^19-K.1^23,K.1^5+K.1^9-K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,-1*K.1^5-K.1^9+K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,0,0,0,0,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^12+2*K.1^-12,-2*K.1^12-2*K.1^-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23,-1*K.1^5-K.1^9+K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,K.1^5+K.1^9-K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,K.1^5+K.1^9-K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,0,0,0,0,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,-2*K.1^4-2*K.1^-4,-2*K.1^12-2*K.1^-12,-2*K.1^8-2*K.1^-8,2*K.1^8+2*K.1^-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^5-K.1^9+K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23,K.1^5+K.1^9-K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1^5+K.1^9-K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,0,0,0,0,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,-2*K.1^4-2*K.1^-4,-2*K.1^12-2*K.1^-12,-2*K.1^8-2*K.1^-8,2*K.1^8+2*K.1^-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^5+K.1^9-K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1^5+K.1^9-K.1^19-K.1^23,-1*K.1^5-K.1^9+K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,0,0,0,0,2*K.1^12+2*K.1^-12,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,-2*K.1^12-2*K.1^-12,2*K.1^8+2*K.1^-8,2*K.1^4+2*K.1^-4,-2*K.1^4-2*K.1^-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1^5+K.1^9-K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,-1*K.1^5-K.1^9+K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,K.1^5+K.1^9-K.1^19-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,-4,-4,4,0,0,0,0,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,0,0,0,0,2*K.1^12+2*K.1^-12,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,-2*K.1^12-2*K.1^-12,2*K.1^8+2*K.1^-8,2*K.1^4+2*K.1^-4,-2*K.1^4-2*K.1^-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1-K.1^3+K.1^5-K.1^9+K.1^11+K.1^13-2*K.1^17+K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11+K.1^13-2*K.1^15+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,K.1^5+K.1^9-K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11-K.1^13+2*K.1^15-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,K.1^5+K.1^9-K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9-K.1^11-K.1^13+2*K.1^17-K.1^21,-1*K.1^5-K.1^9+K.1^19+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,-2*K.1^7-2*K.1^-7,2*K.1^7+2*K.1^-7,0,0,-2*K.1^8-2*K.1^-8,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^4+2*K.1^-4,-2*K.1^12-2*K.1^-12,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,2*K.1^12+2*K.1^-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23,K.1^5-K.1^9+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,K.1^5-K.1^9+K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,-1*K.1^5+K.1^9-K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,2*K.1^7+2*K.1^-7,-2*K.1^7-2*K.1^-7,0,0,-2*K.1^8-2*K.1^-8,2*K.1^8+2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^4+2*K.1^-4,-2*K.1^12-2*K.1^-12,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,2*K.1^12+2*K.1^-12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,K.1^5-K.1^9+K.1^19-K.1^23,-1*K.1^5+K.1^9-K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,K.1^5-K.1^9+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,-2*K.1^7-2*K.1^-7,2*K.1^7+2*K.1^-7,0,0,2*K.1^4+2*K.1^-4,-2*K.1^4-2*K.1^-4,-2*K.1^12-2*K.1^-12,2*K.1^12+2*K.1^-12,2*K.1^8+2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1^5-K.1^9+K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23,-1*K.1^5+K.1^9-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,K.1^5-K.1^9+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,2*K.1^8+2*K.1^-8,2*K.1^7+2*K.1^-7,-2*K.1^7-2*K.1^-7,0,0,2*K.1^4+2*K.1^-4,-2*K.1^4-2*K.1^-4,-2*K.1^12-2*K.1^-12,2*K.1^12+2*K.1^-12,2*K.1^8+2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,-2*K.1^8-2*K.1^-8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1^5+K.1^9-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,K.1^5-K.1^9+K.1^19-K.1^23,K.1^5-K.1^9+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,-2*K.1^7-2*K.1^-7,2*K.1^7+2*K.1^-7,0,0,2*K.1^12+2*K.1^-12,-2*K.1^12-2*K.1^-12,2*K.1^8+2*K.1^-8,-2*K.1^8-2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,K.1^5-K.1^9+K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,K.1^5-K.1^9+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(56: Sparse := true);
S := [ K |4,4,-4,-4,0,0,0,0,0,0,0,0,0,0,0,2*K.1^8+2*K.1^-8,-2*K.1^12-2*K.1^-12,-2*K.1^4-2*K.1^-4,2*K.1^7+2*K.1^-7,-2*K.1^7-2*K.1^-7,0,0,2*K.1^12+2*K.1^-12,-2*K.1^12-2*K.1^-12,2*K.1^8+2*K.1^-8,-2*K.1^8-2*K.1^-8,-2*K.1^4-2*K.1^-4,2*K.1^12+2*K.1^-12,-2*K.1^8-2*K.1^-8,2*K.1^4+2*K.1^-4,2*K.1^4+2*K.1^-4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,-1*K.1^5+K.1^9-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,-1*K.1-K.1^3+K.1^7-K.1^11+K.1^13-K.1^19+K.1^23,-1*K.1^5+K.1^9-K.1^19+K.1^23,K.1+K.1^3-K.1^7+K.1^11-K.1^13+K.1^19-K.1^23,-1*K.1-K.1^3+K.1^5-K.1^9-K.1^11+K.1^13+K.1^21,K.1^5-K.1^9+K.1^19-K.1^23,K.1+K.1^3-K.1^5+K.1^9+K.1^11-K.1^13-K.1^21,K.1^5-K.1^9+K.1^19-K.1^23]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_448_327:= KnownIrreducibles(CR);