/* Group 448.284 downloaded from the LMFDB on 06 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, -7, 1568, 339, 4602, 1641, 80, 8404, 3651, 102, 8748, 124, 9421]); a,b,c,d := Explode([GPC.1, GPC.2, GPC.3, GPC.4]); AssignNames(~GPC, ["a", "b", "c", "d", "d2", "d4", "d8"]);
GPerm := PermutationGroup< 23 | (1,2)(3,6)(4,7)(5,8)(9,11)(10,13)(12,14)(15,16)(18,19)(20,21)(22,23), (1,3,2,6)(4,11,7,9)(5,13,8,10)(12,15,14,16), (1,4,5,12,2,7,8,14)(3,9,10,15,6,11,13,16), (1,5,2,8)(3,10,6,13)(4,12,7,14)(9,15,11,16), (4,7)(9,11)(12,14)(15,16), (1,2)(3,6)(4,7)(5,8)(9,11)(10,13)(12,14)(15,16), (17,18,20,22,23,21,19) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_448_284 := 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, d^28>,< 2, 2, c>,< 2, 7, b>,< 2, 7, b*d^4>,< 2, 14, b*c>,< 4, 2, d^14>,< 4, 2, c*d^42>,< 4, 4, a*d^28>,< 4, 4, a*d^14>,< 4, 14, b*d^2>,< 4, 14, b*c*d^2>,< 4, 28, a*b*c*d^20>,< 4, 28, a*b*d^30>,< 7, 2, d^16>,< 7, 2, d^32>,< 7, 2, d^48>,< 8, 4, d^7>,< 8, 4, d^49>,< 8, 4, a*c*d^7>,< 8, 4, a*d^49>,< 8, 28, a*b*c*d^9>,< 8, 28, a*b*d^51>,< 8, 28, b*d^35>,< 8, 28, b*d^21>,< 14, 2, d^44>,< 14, 2, d^20>,< 14, 2, d^52>,< 14, 4, c*d^8>,< 14, 4, c*d^4>,< 14, 4, c*d^16>,< 28, 4, d^2>,< 28, 4, d^6>,< 28, 4, d^10>,< 28, 4, c*d^30>,< 28, 4, c*d^34>,< 28, 4, c*d^38>,< 28, 8, a*d^8>,< 28, 8, a*d^4>,< 28, 8, a*d^16>,< 28, 8, a*d^2>,< 28, 8, a*d^6>,< 28, 8, a*d^10>,< 56, 8, d>,< 56, 8, d^27>,< 56, 8, d^3>,< 56, 8, d^17>,< 56, 8, d^9>,< 56, 8, d^19>,< 56, 8, a*d>,< 56, 8, a*d^27>,< 56, 8, a*d^3>,< 56, 8, a*d^17>,< 56, 8, a*d^9>,< 56, 8, a*d^19>]); 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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]; 
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*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,-1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.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,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.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*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.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*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.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,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.1,-1*K.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,K.1,-1*K.1,K.1,-1*K.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,K.1,K.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]; 
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*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,-1,K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.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,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.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*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,-1*K.1,K.1,K.1,-1*K.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*K.1,K.1,-1*K.1,K.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*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,K.1,K.1,-1*K.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,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,-1*K.1,K.1,K.1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-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*K.1,-1*K.1,K.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, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 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]; 
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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 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]; 
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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 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]; 
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, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 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]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,0,0,0,2,2,2,2,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,2,2,2,2,0,0,0,0,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,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+K.1^-1,K.1^3+K.1^-3,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+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.1^3+K.1^-3,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+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 |2,2,2,0,0,0,2,2,2,2,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,2,2,2,2,0,0,0,0,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,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.1^3+K.1^-3,K.1^2+K.1^-2,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.1^3+K.1^-3,K.1+K.1^-1,K.1^3+K.1^-3,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.1^2+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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,0,0,0,2,2,2,2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,2,2,2,2,0,0,0,0,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,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.1^2+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.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1^2+K.1^-2,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+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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,0,0,0,2,2,-2,-2,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,-2,-2,2,2,0,0,0,0,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,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+K.1^-1,K.1^3+K.1^-3,-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.1^2-K.1^-2,-1*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,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,K.1^3+K.1^-3,-1*K.1^3-K.1^-3,K.1^2+K.1^-2,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 |2,2,2,0,0,0,2,2,-2,-2,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,-2,-2,2,2,0,0,0,0,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,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.1^3+K.1^-3,K.1^2+K.1^-2,-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-K.1^-1,-1*K.1^3-K.1^-3,K.1+K.1^-1,-1*K.1^3-K.1^-3,-1*K.1-K.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,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1+K.1^-1,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 |2,2,2,0,0,0,2,2,-2,-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,-2,-2,2,2,0,0,0,0,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,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.1^2+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.1^3-K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,K.1^3+K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,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,K.1+K.1^-1,-1*K.1-K.1^-1,K.1^3+K.1^-3,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 |2,2,2,0,0,0,2,2,-2,-2,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,2,2,-2,-2,0,0,0,0,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,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+K.1^-1,K.1^3+K.1^-3,-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.1^2-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,K.1^3+K.1^-3,K.1^2+K.1^-2,-1*K.1^3-K.1^-3,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,0,0,0,2,2,-2,-2,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,2,2,-2,-2,0,0,0,0,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,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.1^3+K.1^-3,K.1^2+K.1^-2,-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-K.1^-1,-1*K.1^3-K.1^-3,-1*K.1-K.1^-1,K.1^3+K.1^-3,K.1+K.1^-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,-1*K.1^2-K.1^-2,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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,0,0,0,2,2,-2,-2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,2,2,-2,-2,0,0,0,0,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,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.1^2+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.1^3-K.1^-3,-1*K.1^3-K.1^-3,-1*K.1^2-K.1^-2,-1*K.1^3-K.1^-3,K.1^2+K.1^-2,K.1^3+K.1^-3,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1+K.1^-1,K.1^3+K.1^-3,-1*K.1-K.1^-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]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |2,2,2,0,0,0,2,2,2,2,0,0,0,0,K.1^3+K.1^-3,K.1+K.1^-1,K.1^2+K.1^-2,-2,-2,-2,-2,0,0,0,0,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,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+K.1^-1,K.1^3+K.1^-3,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+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.1^3-K.1^-3,-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-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 |2,2,2,0,0,0,2,2,2,2,0,0,0,0,K.1^2+K.1^-2,K.1^3+K.1^-3,K.1+K.1^-1,-2,-2,-2,-2,0,0,0,0,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,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.1^3+K.1^-3,K.1^2+K.1^-2,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.1^3+K.1^-3,-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,-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.1^2-K.1^-2,-1*K.1-K.1^-1,-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 |2,2,2,0,0,0,2,2,2,2,0,0,0,0,K.1+K.1^-1,K.1^2+K.1^-2,K.1^3+K.1^-3,-2,-2,-2,-2,0,0,0,0,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,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.1^2+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.1^3+K.1^-3,K.1^3+K.1^-3,K.1^2+K.1^-2,-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,-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-K.1^-1,-1*K.1^3-K.1^-3,-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(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,-2,2,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-2*K.1^7,2*K.1^7,2*K.1^7,-2*K.1^7,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^6+K.1^-6,-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.1^4+K.1^-4,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^4-K.1^-4,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3+K.1^11,K.1^3+K.1^11,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,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,-2,2,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,2*K.1^7,-2*K.1^7,-2*K.1^7,2*K.1^7,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^6+K.1^-6,-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.1^4+K.1^-4,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^4-K.1^-4,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^3-K.1^11,-1*K.1^3-K.1^11,-1*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,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3+K.1^11,K.1^5+K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,-2,2,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-2*K.1^7,2*K.1^7,2*K.1^7,-2*K.1^7,0,0,0,0,-1*K.1^6-K.1^-6,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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-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,K.1^6+K.1^-6,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,K.1^3+K.1^11,K.1^5+K.1^9,K.1^3+K.1^11,-1*K.1^5-K.1^9,-1*K.1^5-K.1^9,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.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,-2,2,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,2*K.1^7,-2*K.1^7,-2*K.1^7,2*K.1^7,0,0,0,0,-1*K.1^6-K.1^-6,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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-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,K.1^6+K.1^-6,K.1^6+K.1^-6,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,K.1^2+K.1^-2,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9,-1*K.1^3-K.1^11,K.1^5+K.1^9,K.1^5+K.1^9,-1*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.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,-2,2,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-2*K.1^7,2*K.1^7,2*K.1^7,-2*K.1^7,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,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,K.1^6+K.1^-6,K.1^6+K.1^-6,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^6+K.1^-6,-1*K.1^5-K.1^9,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.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11,K.1^5+K.1^9,-1*K.1^3-K.1^11,K.1^3+K.1^11,K.1^5+K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,-2,2,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,2*K.1^7,-2*K.1^7,-2*K.1^7,2*K.1^7,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,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,K.1^6+K.1^-6,K.1^6+K.1^-6,-1*K.1^4-K.1^-4,-1*K.1^4-K.1^-4,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,K.1^2+K.1^-2,-1*K.1^2-K.1^-2,K.1^6+K.1^-6,K.1^5+K.1^9,-1*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.1^5+K.1^7-K.1^9+K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11,-1*K.1^5-K.1^9,K.1^3+K.1^11,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,2,-2,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-2*K.1^7,2*K.1^7,-2*K.1^7,2*K.1^7,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^6+K.1^-6,-1*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.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,K.1^4+K.1^-4,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-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.1^3-K.1^11,K.1^3+K.1^11,K.1^5+K.1^9,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.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3+K.1^11,K.1^5+K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,2,-2,0,0,0,0,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,2*K.1^7,-2*K.1^7,2*K.1^7,-2*K.1^7,0,0,0,0,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,K.1^2+K.1^-2,K.1^6+K.1^-6,K.1^6+K.1^-6,-1*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.1^2+K.1^-2,-1*K.1^4-K.1^-4,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,K.1^4+K.1^-4,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3+K.1^11,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.1^11,-1*K.1^5-K.1^9,-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.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,2,-2,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,-2*K.1^7,2*K.1^7,-2*K.1^7,2*K.1^7,0,0,0,0,-1*K.1^6-K.1^-6,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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-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,K.1^6+K.1^-6,-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.1^2-K.1^-2,-1*K.1^3-K.1^11,K.1^5+K.1^9,K.1^3+K.1^11,K.1^5+K.1^9,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-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.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3+K.1^11,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,2,-2,0,0,0,0,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,K.1^4+K.1^-4,2*K.1^7,-2*K.1^7,2*K.1^7,-2*K.1^7,0,0,0,0,-1*K.1^6-K.1^-6,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,-1*K.1^6-K.1^-6,K.1^6+K.1^-6,-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,K.1^6+K.1^-6,-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.1^2-K.1^-2,K.1^3+K.1^11,-1*K.1^5-K.1^9,-1*K.1^3-K.1^11,-1*K.1^5-K.1^9,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3+K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^3-K.1^11,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,2,-2,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-2*K.1^7,2*K.1^7,-2*K.1^7,2*K.1^7,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,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,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,-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,-1*K.1^6-K.1^-6,K.1^5+K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^5-K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11,K.1^5+K.1^9,K.1^3+K.1^11,K.1^3+K.1^11,-1*K.1^5-K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,-1*K.1^3-K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(28: Sparse := true);
S := [ K |2,2,2,0,0,0,-2,-2,2,-2,0,0,0,0,K.1^4+K.1^-4,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,2*K.1^7,-2*K.1^7,2*K.1^7,-2*K.1^7,0,0,0,0,K.1^4+K.1^-4,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,-1*K.1^2-K.1^-2,-1*K.1^6-K.1^-6,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,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,-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,-1*K.1^6-K.1^-6,-1*K.1^5-K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^5+K.1^9,-1*K.1^3+K.1^5-K.1^7+K.1^9-K.1^11,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11,-1*K.1^5-K.1^9,-1*K.1^3-K.1^11,-1*K.1^3-K.1^11,K.1^5+K.1^9,K.1^3-K.1^5+K.1^7-K.1^9+K.1^11,K.1^3+K.1^11]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
x := CR!\[4, -4, 0, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -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]; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,-4,0,0,0,-4,4,0,0,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1^2-2*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+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^-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,-4,0,0,0,-4,4,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,2*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*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+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^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,-4,0,0,0,-4,4,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,-2*K.1^3-2*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.1^3+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^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,-4,0,0,0,4,-4,0,0,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,0,0,0,0,0,0,0,0,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,2*K.1+2*K.1^-1,-2*K.1^2-2*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.1^2-2*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^-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,-4,0,0,0,4,-4,0,0,0,0,0,0,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,2*K.1+2*K.1^-1,0,0,0,0,0,0,0,0,2*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*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.1-2*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^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |4,4,-4,0,0,0,4,-4,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^2+2*K.1^-2,2*K.1^3+2*K.1^-3,0,0,0,0,0,0,0,0,2*K.1+2*K.1^-1,2*K.1^3+2*K.1^-3,2*K.1^2+2*K.1^-2,-2*K.1^3-2*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.1^3-2*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^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1^3+4*K.1^-3,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,0,0,0,0,0,0,0,0,-4*K.1^3-4*K.1^-3,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1^2+4*K.1^-2,4*K.1^3+4*K.1^-3,4*K.1+4*K.1^-1,0,0,0,0,0,0,0,0,-4*K.1^2-4*K.1^-2,-4*K.1-4*K.1^-1,-4*K.1^3-4*K.1^-3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
K := CyclotomicField(7: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,0,0,0,0,0,0,0,4*K.1+4*K.1^-1,4*K.1^2+4*K.1^-2,4*K.1^3+4*K.1^-3,0,0,0,0,0,0,0,0,-4*K.1-4*K.1^-1,-4*K.1^3-4*K.1^-3,-4*K.1^2-4*K.1^-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := -1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_448_284:= KnownIrreducibles(CR);