/* Group 2304.vz downloaded from the LMFDB on 11 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([10, -2, -2, -2, -3, -2, -2, 2, -3, -2, 2, 19401, 51, 6362, 82, 39043, 3014, 24924, 2584, 144, 47046, 65536, 11786, 15996, 1446, 206, 153607, 53777, 38427, 13477, 1327, 77778, 25948, 19478, 6528, 1148, 888, 28819, 43229, 7239, 1869, 379]); a,b,c,d,e,f := Explode([GPC.1, GPC.2, GPC.5, GPC.7, GPC.9, GPC.10]); AssignNames(~GPC, ["a", "b", "b2", "b4", "c", "c2", "d", "d2", "e", "f"]);
GPerm := PermutationGroup< 15 | (1,2)(4,6)(5,7)(8,14)(9,11)(10,12)(13,15), (1,2), (1,3)(4,7,5)(8,10,9,13)(11,15,14,12), (4,5,7), (1,2,3)(8,11)(9,14)(10,15)(12,13), (4,5)(6,7), (4,7)(5,6), (1,3,2), (6,7)(8,13)(9,12)(10,11)(14,15), (5,6,7)(8,14)(9,11) >;

 
/* Booleans */
RF := recformat< Agroup, Zgroup, abelian, almost_simple, cyclic, metabelian, metacyclic, monomial, nilpotent, perfect, quasisimple, rational, solvable, supersolvable  : BoolElt >; 
booleans_2304_vz := rec< RF |  
Agroup := false,
Zgroup := false,
abelian := false,
cyclic := false,
metabelian := false,
metacyclic := false,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := false>; 

 
/* Character Table */
G:= GPerm;
C := SequenceToConjugacyClasses([car<Integers(), Integers(), G> |< 1, 1, Id(G)>,< 2, 1, G!(8,14)(9,11)(10,12)(13,15)>,< 2, 2, G!(8,9)(10,13)(11,14)(12,15)>,< 2, 2, G!(8,9)(10,15)(11,14)(12,13)>,< 2, 2, G!(10,12)(13,15)>,< 2, 3, G!(2,3)>,< 2, 3, G!(2,3)(8,14)(9,11)(10,12)(13,15)>,< 2, 3, G!(4,6)(5,7)>,< 2, 3, G!(4,6)(5,7)(8,14)(9,11)(10,12)(13,15)>,< 2, 6, G!(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)>,< 2, 6, G!(4,5)(6,7)(8,9)(10,15)(11,14)(12,13)>,< 2, 6, G!(2,3)(8,9)(10,13)(11,14)(12,15)>,< 2, 6, G!(2,3)(10,12)(13,15)>,< 2, 6, G!(2,3)(8,9)(10,15)(11,14)(12,13)>,< 2, 6, G!(4,6)(5,7)(10,12)(13,15)>,< 2, 9, G!(2,3)(4,5)(6,7)>,< 2, 9, G!(2,3)(4,5)(6,7)(8,14)(9,11)(10,12)(13,15)>,< 2, 18, G!(2,3)(4,5)(6,7)(10,12)(13,15)>,< 2, 18, G!(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)>,< 2, 18, G!(2,3)(4,5)(6,7)(8,9)(10,15)(11,14)(12,13)>,< 2, 24, G!(6,7)(8,10)(9,15)(11,13)(12,14)>,< 2, 72, G!(2,3)(5,7)(8,10)(9,15)(11,13)(12,14)>,< 3, 2, G!(1,3,2)>,< 3, 8, G!(5,7,6)>,< 3, 16, G!(1,3,2)(5,7,6)>,< 4, 4, G!(8,13,9,10)(11,12,14,15)>,< 4, 4, G!(8,10,9,13)(11,15,14,12)>,< 4, 12, G!(4,5)(6,7)(8,13,9,10)(11,12,14,15)>,< 4, 12, G!(4,5)(6,7)(8,10,9,13)(11,15,14,12)>,< 4, 12, G!(2,3)(8,13,9,10)(11,12,14,15)>,< 4, 12, G!(2,3)(8,10,9,13)(11,15,14,12)>,< 4, 24, G!(6,7)(8,12,14,10)(9,13,11,15)>,< 4, 24, G!(4,7,6,5)(8,10)(9,15)(11,13)(12,14)>,< 4, 24, G!(4,7,6,5)(8,12,14,10)(9,13,11,15)>,< 4, 24, G!(6,7)(9,11)(10,15,12,13)>,< 4, 24, G!(6,7)(9,11)(10,13,12,15)>,< 4, 24, G!(4,7,6,5)(9,11)(10,15,12,13)>,< 4, 24, G!(4,5,6,7)(9,11)(10,13,12,15)>,< 4, 36, G!(2,3)(4,5)(6,7)(8,10,9,13)(11,15,14,12)>,< 4, 36, G!(2,3)(4,5)(6,7)(8,10,11,15)(9,13,14,12)>,< 4, 72, G!(1,3)(4,6,5,7)(8,12,14,10)(9,13,11,15)>,< 4, 72, G!(2,3)(5,6)(8,15,14,13)(9,10,11,12)>,< 4, 72, G!(1,2)(4,5,6,7)(8,13)(9,12)(10,11)(14,15)>,< 4, 72, G!(2,3)(4,5)(8,11,14,9)(10,12)>,< 4, 72, G!(2,3)(4,5)(8,9,14,11)(10,12)>,< 4, 72, G!(2,3)(4,5,6,7)(8,14)(10,13,12,15)>,< 4, 72, G!(2,3)(4,7,6,5)(8,14)(10,15,12,13)>,< 6, 2, G!(1,3,2)(8,14)(9,11)(10,12)(13,15)>,< 6, 4, G!(1,2,3)(8,9)(10,15)(11,14)(12,13)>,< 6, 4, G!(1,3,2)(8,9)(10,13)(11,14)(12,15)>,< 6, 4, G!(1,3,2)(10,12)(13,15)>,< 6, 6, G!(1,3,2)(4,6)(5,7)>,< 6, 6, G!(1,3,2)(4,6)(5,7)(8,14)(9,11)(10,12)(13,15)>,< 6, 8, G!(5,6,7)(8,14)(9,11)(10,12)(13,15)>,< 6, 8, G!(5,7,6)(8,9)(10,13)(11,14)(12,15)>,< 6, 8, G!(5,6,7)(8,9)(10,13)(11,14)(12,15)>,< 6, 12, G!(1,2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)>,< 6, 12, G!(1,2,3)(4,5)(6,7)(8,9)(10,15)(11,14)(12,13)>,< 6, 12, G!(1,3,2)(4,6)(5,7)(10,12)(13,15)>,< 6, 16, G!(5,6,7)(10,12)(13,15)>,< 6, 16, G!(5,6,7)(8,9)(10,15)(11,14)(12,13)>,< 6, 16, G!(1,2,3)(5,6,7)(8,14)(9,11)(10,12)(13,15)>,< 6, 16, G!(1,3,2)(5,7,6)(8,9)(10,13)(11,14)(12,15)>,< 6, 16, G!(1,2,3)(5,6,7)(8,9)(10,13)(11,14)(12,15)>,< 6, 24, G!(2,3)(5,6,7)>,< 6, 24, G!(2,3)(5,6,7)(8,14)(9,11)(10,12)(13,15)>,< 6, 24, G!(2,3)(5,6,7)(8,9)(10,13)(11,14)(12,15)>,< 6, 24, G!(2,3)(5,6,7)(8,11)(9,14)(10,15)(12,13)>,< 6, 32, G!(1,2,3)(5,6,7)(10,12)(13,15)>,< 6, 32, G!(1,2,3)(5,6,7)(8,9)(10,15)(11,14)(12,13)>,< 6, 48, G!(2,3)(5,6,7)(10,12)(13,15)>,< 6, 48, G!(2,3)(5,6,7)(8,9)(10,15)(11,14)(12,13)>,< 6, 48, G!(1,2,3)(6,7)(8,10)(9,15)(11,13)(12,14)>,< 12, 8, G!(1,2,3)(8,10,9,13)(11,15,14,12)>,< 12, 8, G!(1,2,3)(8,10,11,15)(9,13,14,12)>,< 12, 16, G!(5,6,7)(8,10,9,13)(11,15,14,12)>,< 12, 16, G!(5,6,7)(8,10,11,15)(9,13,14,12)>,< 12, 16, G!(5,6,7)(8,13,11,12)(9,10,14,15)>,< 12, 16, G!(5,6,7)(8,13,9,10)(11,12,14,15)>,< 12, 24, G!(1,2,3)(4,5)(6,7)(8,10,9,13)(11,15,14,12)>,< 12, 24, G!(1,2,3)(4,5)(6,7)(8,10,11,15)(9,13,14,12)>,< 12, 32, G!(1,2,3)(5,6,7)(8,10,9,13)(11,15,14,12)>,< 12, 32, G!(1,2,3)(5,6,7)(8,10,11,15)(9,13,14,12)>,< 12, 32, G!(1,2,3)(5,6,7)(8,13,11,12)(9,10,14,15)>,< 12, 32, G!(1,2,3)(5,6,7)(8,13,9,10)(11,12,14,15)>,< 12, 48, G!(1,2,3)(6,7)(8,10,14,12)(9,15,11,13)>,< 12, 48, G!(1,2,3)(4,5,6,7)(8,10)(9,15)(11,13)(12,14)>,< 12, 48, G!(1,2,3)(4,5,6,7)(8,10,14,12)(9,15,11,13)>,< 12, 48, G!(1,2,3)(6,7)(9,11)(10,13,12,15)>,< 12, 48, G!(1,2,3)(6,7)(9,11)(10,15,12,13)>,< 12, 48, G!(1,2,3)(4,5,6,7)(9,11)(10,13,12,15)>,< 12, 48, G!(1,2,3)(4,5,6,7)(9,11)(10,15,12,13)>,< 12, 48, G!(2,3)(5,6,7)(8,10,9,13)(11,15,14,12)>,< 12, 48, G!(2,3)(5,6,7)(8,10,11,15)(9,13,14,12)>,< 12, 48, G!(2,3)(5,6,7)(8,13,11,12)(9,10,14,15)>,< 12, 48, G!(2,3)(5,6,7)(8,13,9,10)(11,12,14,15)>]); 
CR := CharacterRing(G);
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |1,1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1,1,-1*K.1,1,-1*K.1,K.1,K.1,-1,1,K.1,-1*K.1,-1,-1*K.1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,-1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1,K.1,-1*K.1,1,-1*K.1,K.1,-1*K.1,K.1,1,-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,-1,1,1,-1,-1,1,1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,-1,1,K.1,1,K.1,-1*K.1,-1*K.1,-1,1,-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,-1,1,1,-1,1,-1,-1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1,-1*K.1,K.1,1,K.1,-1*K.1,K.1,-1*K.1,1,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,-1,1,1,-1,1,-1,1,1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1*K.1,1,-1,K.1,-1,-1*K.1,K.1,-1*K.1,1,-1,-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,-1,1,1,-1,1,-1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1*K.1,K.1,-1,K.1,K.1,-1*K.1,-1*K.1,-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,-1,1,1,-1,1,-1,1,1,1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,K.1,1,-1,-1*K.1,-1,K.1,-1*K.1,K.1,1,-1,K.1,-1*K.1,1,-1*K.1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,1,1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,K.1,-1*K.1,-1,-1*K.1,-1*K.1,K.1,K.1,-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,-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,K.1,-1,1,-1*K.1,1,K.1,-1*K.1,-1*K.1,1,-1,-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,-1,-1,-1,1,1,-1,-1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1,K.1,-1*K.1,1,-1*K.1,-1*K.1,K.1,K.1,1,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,-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,-1*K.1,-1,1,K.1,1,-1*K.1,K.1,K.1,1,-1,K.1,-1*K.1,1,-1*K.1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1,-1*K.1,K.1,1,K.1,K.1,-1*K.1,-1*K.1,1,-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,-1,1,1,1,1,1,1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,1,-1,K.1,-1,K.1,-1*K.1,K.1,-1,1,K.1,-1*K.1,-1,-1*K.1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,K.1,-1*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,-1*K.1,K.1,-1,K.1,-1*K.1,K.1,-1*K.1,-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,-1,1,1,1,1,1,1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,-1*K.1,K.1,1,-1,-1*K.1,-1,-1*K.1,K.1,-1*K.1,-1,1,-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,-1,-1,-1,1,1,1,-1,-1*K.1,K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,K.1,-1*K.1,-1,-1*K.1,K.1,-1*K.1,K.1,-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, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 2, -1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, -1, -1, 0, -1, 0, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, -1, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 0, 0, 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, 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, -2, 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, -2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 0, 0, 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, 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, 2, 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, 2, -2, -2, 2, 2, -2, -2, 2, -2, 2, 0, 0, 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, 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, 2, 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, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, 0, 0, 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, 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, -2, 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, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 2, -1, -1, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 0, 1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, -1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 2, -1, -1, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 0, 1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 2, -1, -2, -2, -2, -2, 0, 0, 2, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, -1, -1, 0, 1, 0, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 0, 0, -1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 2, -1, 2, 2, 2, 2, 0, 0, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, -1, -1, 0, 1, 0, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 2, -1, -2, -2, -2, -2, 0, 0, -2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 0, 0, 0, 0, -1, -1, 0, -1, 0, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 0, 0, 1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, -1, -1, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,2,-2,-2,-2,2,2,2,-2,2,-2,-2,2,-2,-2,2,2,-2,0,0,2,-1,-1,-2*K.1,2*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0,0,0,0,0,2,2,-2,-2,2,2,-1,1,1,2,-2,-2,-1,-1,1,1,1,1,1,-1,-1,1,-1,1,0,-1,2*K.1,-2*K.1,-1*K.1,K.1,K.1,-1*K.1,2*K.1,-2*K.1,K.1,-1*K.1,-1*K.1,K.1,0,0,0,0,0,-1*K.1,K.1,0,0,K.1,-1*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,-2,2,2,2,-2,2,-2,-2,2,-2,-2,2,2,-2,0,0,2,-1,-1,2*K.1,-2*K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0,0,0,0,0,2,2,-2,-2,2,2,-1,1,1,2,-2,-2,-1,-1,1,1,1,1,1,-1,-1,1,-1,1,0,-1,-2*K.1,2*K.1,K.1,-1*K.1,-1*K.1,K.1,-2*K.1,2*K.1,-1*K.1,K.1,K.1,-1*K.1,0,0,0,0,0,K.1,-1*K.1,0,0,-1*K.1,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,-2,0,0,2,2,2,-2,0,-2,0,0,0,0,0,0,0,-2,0,-1,2,-1,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,2*K.1,-2*K.1,2*K.1,-2,2,-2*K.1,2,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,2,-2,-2,-1,1,1,2,-1,1,-2,1,0,0,0,0,1,-1,0,1,0,-1*K.1,K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,1,-1*K.1,K.1,-1,K.1,0,0,-1*K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,2,-2,0,0,2,2,2,-2,0,-2,0,0,0,0,0,0,0,-2,0,-1,2,-1,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,-2*K.1,2*K.1,-2*K.1,-2,2,2*K.1,2,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,2,-2,-2,-1,1,1,2,-1,1,-2,1,0,0,0,0,1,-1,0,1,0,K.1,-1*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,1,K.1,-1*K.1,-1,-1*K.1,0,0,K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,2,-2,0,0,2,2,2,-2,0,-2,0,0,0,0,0,0,0,2,0,-1,2,-1,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,-2*K.1,2*K.1,-2*K.1,2,-2,2*K.1,-2,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,2,-2,-2,-1,1,1,2,-1,1,-2,1,0,0,0,0,1,-1,0,-1,0,-1*K.1,K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,-1*K.1,K.1,K.1,-1*K.1,-1*K.1,K.1,-1,K.1,-1*K.1,1,-1*K.1,0,0,K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,2,-2,0,0,2,2,2,-2,0,-2,0,0,0,0,0,0,0,2,0,-1,2,-1,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,2*K.1,-2*K.1,2*K.1,2,-2,-2*K.1,-2,0,0,0,0,0,0,0,0,0,-1,-1,1,1,-1,-1,2,-2,-2,-1,1,1,2,-1,1,-2,1,0,0,0,0,1,-1,0,-1,0,K.1,-1*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,K.1,-1*K.1,-1*K.1,K.1,K.1,-1*K.1,-1,-1*K.1,K.1,1,K.1,0,0,-1*K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |2,2,-2,2,-2,2,2,2,2,2,-2,-2,-2,2,-2,2,2,-2,-2,2,0,0,2,-1,-1,-2*K.1,2*K.1,-2*K.1,2*K.1,-2*K.1,2*K.1,0,0,0,0,0,0,0,2*K.1,-2*K.1,0,0,0,0,0,0,0,2,2,-2,-2,2,2,-1,1,1,2,-2,-2,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,0,1,2*K.1,-2*K.1,-1*K.1,K.1,K.1,-1*K.1,2*K.1,-2*K.1,K.1,-1*K.1,-1*K.1,K.1,0,0,0,0,0,K.1,-1*K.1,0,0,-1*K.1,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,-2,2,2,2,2,2,-2,-2,-2,2,-2,2,2,-2,-2,2,0,0,2,-1,-1,2*K.1,-2*K.1,2*K.1,-2*K.1,2*K.1,-2*K.1,0,0,0,0,0,0,0,-2*K.1,2*K.1,0,0,0,0,0,0,0,2,2,-2,-2,2,2,-1,1,1,2,-2,-2,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,0,1,-2*K.1,2*K.1,K.1,-1*K.1,-1*K.1,K.1,-2*K.1,2*K.1,-1*K.1,K.1,K.1,-1*K.1,0,0,0,0,0,-1*K.1,K.1,0,0,K.1,-1*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,-2,2,2,-2,-2,2,2,2,-2,-2,-2,-2,2,2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,2,2,-1,1,1,-2,2,-2,1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,0,1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |2,2,-2,-2,2,-2,-2,2,2,-2,-2,2,2,2,-2,-2,-2,-2,2,2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,2,2,-1,1,1,-2,2,-2,1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,0,1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,0,0,-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(12: Sparse := true);
S := [ K |2,2,-2,-2,2,2,2,2,2,-2,-2,-2,2,-2,2,2,2,2,-2,-2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,2,2,-1,1,1,-2,2,-2,1,-1,1,-1,1,-1,-1,1,1,-1,1,1,0,-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,K.1+K.1^-1,K.1+K.1^-1,0,0,-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(12: Sparse := true);
S := [ K |2,2,-2,-2,2,2,2,2,2,-2,-2,-2,2,-2,2,2,2,2,-2,-2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,-2,2,2,2,-1,1,1,-2,2,-2,1,-1,1,-1,1,-1,-1,1,1,-1,1,1,0,-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,-1*K.1-K.1^-1,-1*K.1-K.1^-1,0,0,K.1+K.1^-1,K.1+K.1^-1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,-2,2,2,-2,2,-2,-2,2,2,-2,-2,2,-2,2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,2,-1,-1,-1,-2,-2,2,1,-1,-1,1,-1,1,1,1,1,1,1,-1,0,-1,0,0,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,0,0,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,0,0,0,0,0,1+2*K.1,-1-2*K.1,0,0,1+2*K.1,-1-2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,-2,-2,-2,-2,2,2,-2,2,-2,-2,2,2,-2,-2,2,-2,2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,2,-1,-1,-1,-2,-2,2,1,-1,-1,1,-1,1,1,1,1,1,1,-1,0,-1,0,0,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,0,0,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,0,0,0,0,0,-1-2*K.1,1+2*K.1,0,0,-1-2*K.1,1+2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,-2,-2,2,2,2,2,-2,2,2,-2,-2,-2,2,2,-2,2,-2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,2,-1,-1,-1,-2,-2,2,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,1,0,1,0,0,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,0,0,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,0,0,0,0,0,-1-2*K.1,1+2*K.1,0,0,-1-2*K.1,1+2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |2,2,2,-2,-2,2,2,2,2,-2,2,2,-2,-2,-2,2,2,-2,2,-2,0,0,2,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,2,-2,2,2,-1,-1,-1,-2,-2,2,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,1,0,1,0,0,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,0,0,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,0,0,0,0,0,1+2*K.1,-1-2*K.1,0,0,1+2*K.1,-1-2*K.1]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, 1, 1, 3, 0, 0, 3, 3, -1, -1, 3, 3, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 0, 0, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, 3, 0, 0, 3, 3, -1, -1, 3, 3, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, -1, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, -3, -3, -1, -1, -1, -1, -3, -1, -3, -3, 1, 1, 1, 1, 1, -1, 1, 3, 0, 0, -3, -3, 1, 1, 3, 3, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, -1, -1, 1, 1, 0, 0, 1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, -3, -3, -1, -1, -1, -1, -3, -1, -3, -3, 1, 1, 1, 1, 1, -1, 1, 3, 0, 0, 3, 3, -1, -1, -3, -3, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, -1, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, -3, -3, -1, -1, -1, -1, -3, -1, -3, -3, 1, 1, 1, 1, 1, 1, -1, 3, 0, 0, -3, -3, 1, 1, 3, 3, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 1, 1, -1, -1, 0, 0, -1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, -3, -3, -1, -1, -1, -1, -3, -1, -3, -3, 1, 1, 1, 1, 1, 1, -1, 3, 0, 0, 3, 3, -1, -1, -3, -3, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 0, 0, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, -1, -1, 3, 0, 0, -3, -3, 1, 1, -3, -3, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, -1, -1, 1, 1, 0, 0, 1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, 3, -1, 3, 3, -1, -1, -1, -1, -1, 1, 1, 3, 0, 0, -3, -3, 1, 1, -3, -3, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 3, 3, 3, 3, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, 1, 1, -1, -1, 0, 0, -1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,-3,-3,-1,-1,-1,1,3,1,-3,3,1,1,-1,-1,1,-1,1,3,0,0,-3*K.1,3*K.1,K.1,-1*K.1,3*K.1,-3*K.1,-1*K.1,K.1,K.1,1,-1,-1*K.1,1,K.1,-1*K.1,K.1,-1,-1,-1*K.1,-1*K.1,1,K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,3*K.1,-3*K.1,0,0,0,0,-1*K.1,K.1,0,0,0,0,1,-1*K.1,K.1,-1,-1*K.1,0,0,K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,-3,-3,-1,-1,-1,1,3,1,-3,3,1,1,-1,-1,1,-1,1,3,0,0,3*K.1,-3*K.1,-1*K.1,K.1,-3*K.1,3*K.1,K.1,-1*K.1,-1*K.1,1,-1,K.1,1,-1*K.1,K.1,-1*K.1,-1,-1,K.1,K.1,1,-1*K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,-3*K.1,3*K.1,0,0,0,0,K.1,-1*K.1,0,0,0,0,1,K.1,-1*K.1,-1,K.1,0,0,-1*K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,-3,-3,-1,-1,-1,1,3,1,-3,3,1,1,-1,-1,1,1,-1,3,0,0,-3*K.1,3*K.1,K.1,-1*K.1,3*K.1,-3*K.1,K.1,-1*K.1,-1*K.1,-1,1,K.1,-1,K.1,-1*K.1,-1*K.1,1,1,K.1,K.1,-1,-1*K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3*K.1,-3*K.1,0,0,0,0,-1*K.1,K.1,0,0,0,0,-1,K.1,-1*K.1,1,K.1,0,0,-1*K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,-3,-3,-1,-1,-1,1,3,1,-3,3,1,1,-1,-1,1,1,-1,3,0,0,3*K.1,-3*K.1,-1*K.1,K.1,-3*K.1,3*K.1,-1*K.1,K.1,K.1,-1,1,-1*K.1,-1,-1*K.1,K.1,K.1,1,1,-1*K.1,-1*K.1,-1,K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-3*K.1,3*K.1,0,0,0,0,K.1,-1*K.1,0,0,0,0,-1,-1*K.1,K.1,1,-1*K.1,0,0,K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,3,3,-1,-1,-1,1,-3,1,3,-3,-1,-1,1,1,-1,-1,-1,3,0,0,-3*K.1,3*K.1,K.1,-1*K.1,-3*K.1,3*K.1,-1*K.1,K.1,K.1,1,-1,-1*K.1,1,-1*K.1,K.1,-1*K.1,1,1,K.1,K.1,-1,-1*K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,3*K.1,-3*K.1,0,0,0,0,-1*K.1,K.1,0,0,0,0,1,-1*K.1,K.1,-1,-1*K.1,0,0,K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,3,3,-1,-1,-1,1,-3,1,3,-3,-1,-1,1,1,-1,-1,-1,3,0,0,3*K.1,-3*K.1,-1*K.1,K.1,3*K.1,-3*K.1,K.1,-1*K.1,-1*K.1,1,-1,K.1,1,K.1,-1*K.1,K.1,1,1,-1*K.1,-1*K.1,-1,K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,-3*K.1,3*K.1,0,0,0,0,K.1,-1*K.1,0,0,0,0,1,K.1,-1*K.1,-1,K.1,0,0,-1*K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,3,3,-1,-1,-1,1,-3,1,3,-3,-1,-1,1,1,-1,1,1,3,0,0,-3*K.1,3*K.1,K.1,-1*K.1,-3*K.1,3*K.1,K.1,-1*K.1,-1*K.1,-1,1,K.1,-1,-1*K.1,K.1,K.1,-1,-1,-1*K.1,-1*K.1,1,K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3*K.1,-3*K.1,0,0,0,0,-1*K.1,K.1,0,0,0,0,-1,K.1,-1*K.1,1,K.1,0,0,-1*K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |3,3,-3,3,-3,3,3,-1,-1,-1,1,-3,1,3,-3,-1,-1,1,1,-1,1,1,3,0,0,3*K.1,-3*K.1,-1*K.1,K.1,3*K.1,-3*K.1,-1*K.1,K.1,K.1,-1,1,-1*K.1,-1,K.1,-1*K.1,-1*K.1,-1,-1,K.1,K.1,1,-1*K.1,3,3,-3,-3,-1,-1,0,0,0,-1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-3*K.1,3*K.1,0,0,0,0,K.1,-1*K.1,0,0,0,0,-1,-1*K.1,K.1,1,-1*K.1,0,0,K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 0, 0, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 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, 0, 0, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 4, -4, 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, -4, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 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; 
x := CR!\[4, -4, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, -4, 4, 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, -4, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -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; 
x := CR!\[4, 4, -4, -4, 4, 0, 0, 4, 4, -4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, -2, 4, -4, -4, 2, -2, 2, -4, -2, 2, 4, 2, 0, 0, 0, 0, -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, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, -4, -4, 0, 0, 4, 4, -4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, -2, -2, 4, 4, 4, 2, 2, -2, -4, -2, -2, -4, -2, 0, 0, 0, 0, 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, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[4, 4, 4, 4, 4, 0, 0, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,0,0,-4,4,-4,4,0,0,0,0,0,0,4,-4,0,0,0,0,0,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,4,-4,2,-2-4*K.1,2+4*K.1,0,0,0,0,2,2+4*K.1,0,-2-4*K.1,-2,2,2+4*K.1,-2-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,0,0,-4,4,-4,4,0,0,0,0,0,0,4,-4,0,0,0,0,0,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,4,-4,2,2+4*K.1,-2-4*K.1,0,0,0,0,2,-2-4*K.1,0,2+4*K.1,-2,2,-2-4*K.1,2+4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,0,0,4,-4,-4,4,0,0,0,0,0,0,-4,4,0,0,0,0,0,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,4,-4,2,-2-4*K.1,2+4*K.1,0,0,0,0,2,2+4*K.1,0,-2-4*K.1,2,-2,-2-4*K.1,2+4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,-4,0,0,0,4,-4,-4,4,0,0,0,0,0,0,-4,4,0,0,0,0,0,4,-2,-2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,0,0,0,4,-4,2,2+4*K.1,-2-4*K.1,0,0,0,0,2,-2-4*K.1,0,2+4*K.1,2,-2,2+4*K.1,-2-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,4,4,-4,-4,0,0,4,4,-4,4,0,-4,0,0,0,0,0,0,0,0,0,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,-2,-2,-2,-2,2,2,-2,2,1,1,2,1,0,0,0,0,-1,-1,0,0,0,0,0,-2-4*K.1,-2-4*K.1,2+4*K.1,2+4*K.1,0,0,-1-2*K.1,-1-2*K.1,1+2*K.1,1+2*K.1,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |4,4,4,-4,-4,0,0,4,4,-4,4,0,-4,0,0,0,0,0,0,0,0,0,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,-2,2,-2,-2,-2,-2,-2,2,2,-2,2,1,1,2,1,0,0,0,0,-1,-1,0,0,0,0,0,2+4*K.1,2+4*K.1,-2-4*K.1,-2-4*K.1,0,0,1+2*K.1,1+2*K.1,-1-2*K.1,-1-2*K.1,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,4,-4,0,0,4,4,4,-4,0,-4,0,0,0,0,0,0,0,0,0,-2,-2,1,-4*K.1,4*K.1,-4*K.1,4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,2,-2,-2,-2,2,2,-2,2,2,-2,1,-1,2,-1,0,0,0,0,-1,1,0,0,0,-2*K.1,2*K.1,-2*K.1,2*K.1,2*K.1,-2*K.1,-2*K.1,2*K.1,-1*K.1,K.1,K.1,-1*K.1,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |4,4,-4,4,-4,0,0,4,4,4,-4,0,-4,0,0,0,0,0,0,0,0,0,-2,-2,1,4*K.1,-4*K.1,4*K.1,-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,-2,2,2,-2,-2,-2,2,2,-2,2,2,-2,1,-1,2,-1,0,0,0,0,-1,1,0,0,0,2*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,-1*K.1,K.1,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,4,-4,-4,4,0,0,4,4,-4,-4,0,4,0,0,0,0,0,0,0,0,0,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,-2,-2,2,2,2,-2,2,2,1,-1,-2,-1,0,0,0,0,1,-1,0,0,0,0,0,-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^-1,0,0,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(12: Sparse := true);
S := [ K |4,4,-4,-4,4,0,0,4,4,-4,-4,0,4,0,0,0,0,0,0,0,0,0,-2,-2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-2,2,2,-2,-2,-2,-2,2,2,2,-2,2,2,1,-1,-2,-1,0,0,0,0,1,-1,0,0,0,0,0,2*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^-1,0,0,-1*K.1-K.1^-1,K.1+K.1^-1,-1*K.1-K.1^-1,K.1+K.1^-1,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -6, -6, -6, -6, -2, -2, 2, -2, -6, 2, 6, 6, 2, 2, -2, 2, -2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, 6, -6, -2, -2, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, -6, -6, 6, 6, -2, -2, 2, -2, 6, 2, -6, -6, -2, -2, 2, -2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, 6, -6, -2, -2, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, 6, -6, -6, -2, -2, 2, 2, 6, -2, 6, -6, 2, 2, 2, -2, -2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, -6, 6, -2, -2, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, -6, -6, 6, 6, 6, -2, -2, 2, 2, -6, -2, -6, 6, -2, -2, -2, 2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -6, -6, 6, -2, -2, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 6, 0, 0, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 6, 6, -2, -2, 0, 0, -2, -2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, -1, 0, 0, -1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 6, 0, 0, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, 6, 6, -2, -2, 0, 0, 2, 2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, -3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 0, 0, 1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 6, 0, 0, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, -6, -6, 2, 2, 0, 0, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 1, 1, -1, -1, 0, 0, -1, 1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[6, 6, 6, 6, 6, 0, 0, -2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, -6, -6, 2, 2, 0, 0, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 3, 3, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, -1, -1, 1, 1, 0, 0, 1, -1, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,6,-6,6,-6,0,0,-2,-2,-2,2,0,2,0,0,0,0,0,0,0,-2,0,-3,0,0,-6*K.1,6*K.1,2*K.1,-2*K.1,0,0,-2*K.1,2*K.1,2*K.1,2,-2,-2*K.1,2,0,0,0,0,0,0,0,0,0,-3,-3,3,3,1,1,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-3*K.1,3*K.1,0,0,0,0,K.1,-1*K.1,0,0,0,0,-1,K.1,-1*K.1,1,K.1,0,0,-1*K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,6,-6,6,-6,0,0,-2,-2,-2,2,0,2,0,0,0,0,0,0,0,-2,0,-3,0,0,6*K.1,-6*K.1,-2*K.1,2*K.1,0,0,2*K.1,-2*K.1,-2*K.1,2,-2,2*K.1,2,0,0,0,0,0,0,0,0,0,-3,-3,3,3,1,1,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,3*K.1,-3*K.1,0,0,0,0,-1*K.1,K.1,0,0,0,0,-1,-1*K.1,K.1,1,-1*K.1,0,0,K.1,-1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,6,-6,6,-6,0,0,-2,-2,-2,2,0,2,0,0,0,0,0,0,0,2,0,-3,0,0,-6*K.1,6*K.1,2*K.1,-2*K.1,0,0,2*K.1,-2*K.1,-2*K.1,-2,2,2*K.1,-2,0,0,0,0,0,0,0,0,0,-3,-3,3,3,1,1,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,-3*K.1,3*K.1,0,0,0,0,K.1,-1*K.1,0,0,0,0,1,-1*K.1,K.1,-1,-1*K.1,0,0,K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(4: Sparse := true);
S := [ K |6,6,-6,6,-6,0,0,-2,-2,-2,2,0,2,0,0,0,0,0,0,0,2,0,-3,0,0,6*K.1,-6*K.1,-2*K.1,2*K.1,0,0,-2*K.1,2*K.1,2*K.1,-2,2,-2*K.1,-2,0,0,0,0,0,0,0,0,0,-3,-3,3,3,1,1,0,0,0,1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,3*K.1,-3*K.1,0,0,0,0,-1*K.1,K.1,0,0,0,0,1,K.1,-1*K.1,-1,K.1,0,0,-1*K.1,1,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -4, 4, -8, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,-4,4,4,-4-8*K.1,4+8*K.1,0,0,0,0,-2,-2-4*K.1,0,2+4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
K := CyclotomicField(3: Sparse := true);
S := [ K |8,-8,0,0,0,0,0,-8,8,0,0,0,0,0,0,0,0,0,0,0,0,0,-4,-4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,-4,4,4,4+8*K.1,-4-8*K.1,0,0,0,0,-2,2+4*K.1,0,-2-4*K.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]; 
x := CR!S; 
x`IsCharacter := true;
x`Schur := 0;
x`IsIrreducible := true; 
x := CR!\[12, -12, 0, 0, 0, -12, 12, 4, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, -12, 0, 0, 0, 12, -12, 4, -4, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, 12, -12, -12, 0, 0, -4, -4, 4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, -6, 6, 2, 2, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[12, 12, -12, -12, 12, 0, 0, -4, -4, 4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 6, 6, -6, 2, 2, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
x := CR!\[24, -24, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; 
x`IsCharacter := true;
x`Schur := 1;
x`IsIrreducible := true; 
_ := CharacterTable(G : Check := 0); 
chartbl_2304_vz:= KnownIrreducibles(CR);