//Standard generators of U4(3) are a, b where a has order 2,
//b is in class 6A, ab has order 7 and abababbababb has order 5.
//dfh - standard generators of 12_1.U43 are preimages of standard generators
//of 3_1.U43 and 4.U43.
//i.e. a and b where a,b,ab,abab^2, ab^3, abababbababb have orders
//2, 6, 28, 7, 5 and 20

_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [
      [ a*(a*b)^14,
 b^-2*a*b*a*b^-1*a*b^-1*a*b^-2*a*b^-1*a*b^-2*a*(a*b^-1*a*b^-2*a*b^-3)^35 ],
       //U43.2_1 - order 2 -  not same as in Online ATLAS.
      [ a, b^-1],
 [ a*(a*b)^14,
    b^2*a*b^-1*a*b*a*b*a*b^2*a*b*a*b^2*a*(a*b*a*b^2*a*b^3)^-21 ]]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//Four constituents

_LR`G :=
/*
Original group: c9Group("12au43p")
From DB /nb/reps/d84.12aU43.nfdeg4.M
Schur index: 1
Character: ( 84, -84, 0, -84*zeta(12)_3 - 84, 84*zeta(12)_3, -15, 15*zeta(12)_3 
+ 15, -15*zeta(12)_3, -6*zeta(12)_3 - 6, 6*zeta(12)_3, 6, 0, 0, 84*zeta(12)_4, 
-84*zeta(12)_4, 0, -2, -2*zeta(12)_4, 2*zeta(12)_4, 2, -1, 84*zeta(12)_3 + 84, 
-84*zeta(12)_3, 15, -15*zeta(12)_3 - 15, 15*zeta(12)_3, -6, 6*zeta(12)_3 + 6, 
-6*zeta(12)_3, 0, 0, 0, 3*zeta(12)_3, -3, 3*zeta(12)_3 + 3, -3*zeta(12)_3, 3, 
-3*zeta(12)_3 - 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, zeta(12)_4 - 1, -zeta(12)_4 - 1, 
zeta(12)_4 + 1, -zeta(12)_4 + 1, 0, -zeta(12)_3 + 1, zeta(12)_3 + 2, 
-2*zeta(12)_3 - 1, zeta(12)_3 - 1, -zeta(12)_3 - 2, 2*zeta(12)_3 + 1, 0, 0, 1, 
-84*zeta(12)_4*zeta(12)_3, 84*zeta(12)_4*zeta(12)_3 + 84*zeta(12)_4, 
84*zeta(12)_4*zeta(12)_3, -84*zeta(12)_4*zeta(12)_3 - 84*zeta(12)_4, 
-15*zeta(12)_4*zeta(12)_3, -15*zeta(12)_4*zeta(12)_3 - 15*zeta(12)_4, 
15*zeta(12)_4, 15*zeta(12)_4*zeta(12)_3, -15*zeta(12)_4, 
15*zeta(12)_4*zeta(12)_3 + 15*zeta(12)_4, 6*zeta(12)_4*zeta(12)_3, 6*zeta(12)_4,
-6*zeta(12)_4*zeta(12)_3 - 6*zeta(12)_4, -6*zeta(12)_4*zeta(12)_3, 
-6*zeta(12)_4, 6*zeta(12)_4*zeta(12)_3 + 6*zeta(12)_4, 0, 0, 0, 0, -2*zeta(12)_3
- 2, -2*zeta(12)_4*zeta(12)_3, 2*zeta(12)_4*zeta(12)_3 + 2*zeta(12)_4, 
2*zeta(12)_3 + 2, 2*zeta(12)_4*zeta(12)_3, -2*zeta(12)_3, 
-2*zeta(12)_4*zeta(12)_3 - 2*zeta(12)_4, 2*zeta(12)_3, 3*zeta(12)_4, 
-3*zeta(12)_4*zeta(12)_3, 3*zeta(12)_4*zeta(12)_3, -3*zeta(12)_4, 
-3*zeta(12)_4*zeta(12)_3 - 3*zeta(12)_4, 3*zeta(12)_4*zeta(12)_3 + 3*zeta(12)_4,
0, 0, 0, 0, 0, 0, 0, 0, zeta(12)_4*zeta(12)_3, -1, zeta(12)_3 + 1, -zeta(12)_3, 
1, -zeta(12)_3 - 1, zeta(12)_3, -zeta(12)_4, zeta(12)_4*zeta(12)_3 + zeta(12)_4,
-zeta(12)_4*zeta(12)_3, zeta(12)_4, -zeta(12)_4*zeta(12)_3 - zeta(12)_4, 0, 0, 
-zeta(12)_3, zeta(12)_3 + 1, zeta(12)_3 - 1, -zeta(12)_3 - 2, 2*zeta(12)_3 + 1, 
-zeta(12)_3 + 1, zeta(12)_3 + 2, -2*zeta(12)_3 - 1, 0, 0, -zeta(12)_4, 
zeta(12)_4, 0, 0, 0, 0, zeta(12)_4*zeta(12)_3 + zeta(12)_3, 
zeta(12)_4*zeta(12)_3 + zeta(12)_4 - zeta(12)_3 - 1, -zeta(12)_4*zeta(12)_3 + 
zeta(12)_3, -zeta(12)_4*zeta(12)_3 - zeta(12)_4 + zeta(12)_3 + 1, 
zeta(12)_4*zeta(12)_3 - zeta(12)_3, zeta(12)_4*zeta(12)_3 + zeta(12)_4 + 
zeta(12)_3 + 1, -zeta(12)_4*zeta(12)_3 - zeta(12)_4 - zeta(12)_3 - 1, 
-zeta(12)_4*zeta(12)_3 - zeta(12)_3, 0, 0, 0, 0, 0, 0, zeta(12)_3, -zeta(12)_3 -
1, -zeta(12)_4*zeta(12)_3 + zeta(12)_4, zeta(12)_4*zeta(12)_3 - zeta(12)_4, 
-zeta(12)_4*zeta(12)_3 - 2*zeta(12)_4, 2*zeta(12)_4*zeta(12)_3 + zeta(12)_4, 
zeta(12)_4*zeta(12)_3 + 2*zeta(12)_4, -2*zeta(12)_4*zeta(12)_3 - zeta(12)_4, 
zeta(12)_4*zeta(12)_3 - zeta(12)_4, -zeta(12)_4*zeta(12)_3 - 2*zeta(12)_4, 
2*zeta(12)_4*zeta(12)_3 + zeta(12)_4, -zeta(12)_4*zeta(12)_3 + zeta(12)_4, 
zeta(12)_4*zeta(12)_3 + 2*zeta(12)_4, -2*zeta(12)_4*zeta(12)_3 - zeta(12)_4, 0, 
0, 0, 0, 0, 0, 0, 0, -zeta(12)_4*zeta(12)_3, zeta(12)_4*zeta(12)_3, 
zeta(12)_4*zeta(12)_3 + zeta(12)_4, -zeta(12)_4*zeta(12)_3 - zeta(12)_4, 0, 0, 
0, 0, 0, 0, 0, 0 )
*/

MatrixGroup<84,K | [
Matrix(K,84,84,
[[1/27,0,-2/27,0],[0,0,0,0],[0,2/27,0,2/27],
[0,0,0,0],[8/27,0,-4/27,0],[0,0,0,0],[0,
-2/27,0,4/27],[0,0,0,0],[0,-5/27,0,10/27],[0,
10/27,0,-20/27],[0,-4/9,0,2/9],[-5/27,-1/27,-5/27,
2/27],[0,1/27,0,1/27],[2/27,-5/27,-1/27,-5/27],[
0,-4/27,0,8/27],[-4/27,0,2/27,0],[2/27,4/27,-1/27,
4/27],[-4/9,-4/27,2/9,-4/27],[2/27,-2/27,2/27,4/27],
[-4/27,4/27,2/27,4/27],[8/27,-1/27,-4/27,-1/27],[
0,2/27,0,2/27],[0,-2/27,0,4/27],[2/27,1/27,-1/27,
1/27],[-2/27,0,1/27,0],[-1/27,0,-1/27,0],[-2/27,
0,4/27,0],[-2/27,-4/27,4/27,2/27],[2/27,0,-1/27,
0],[0,1/27,0,1/27],[2/27,4/27,-4/27,-2/27],[1/9,
2/9,-2/9,-1/9],[1/9,0,1/9,0],[0,2/27,0,-1/27],
[1/27,4/27,-2/27,-2/27],[8/27,-1/27,-4/27,-1/27],
[1/9,2/9,-2/9,-1/9],[-1/27,-2/27,2/27,1/27],[0,0,
0,0],[-2/27,0,-2/27,0],[2/27,4/27,-4/27,-2/27],[
0,1/27,0,1/27],[-8/27,0,4/27,0],[-1/27,4/27,-1/27,
-8/27],[1/27,2/27,-2/27,-1/27],[1/27,0,-2/27,0],
[-1/27,0,-1/27,0],[-4/27,0,-4/27,0],[-2/27,2/27,
-2/27,-4/27],[1/27,-8/27,-2/27,4/27],[-4/27,0,2/27,
0],[-1/27,2/27,2/27,-1/27],[2/27,1/27,2/27,-2/27],
[1/27,0,1/27,0],[-1/27,2/27,2/27,-1/27],[2/27,-1/27,
2/27,2/27],[1/27,0,-2/27,0],[-2/27,1/27,1/27,1/27
],[4/27,1/27,-2/27,1/27],[-2/27,-2/27,-2/27,4/27],
[2/27,1/27,-1/27,1/27],[-1/27,-8/27,2/27,4/27],[
-2/27,2/27,4/27,-1/27],[2/27,0,-1/27,0],[0,4/27,
0,-8/27],[-2/27,4/27,1/27,4/27],[-1/27,0,2/27,0],
[2/27,2/27,2/27,-4/27],[1/27,-2/27,-2/27,1/27],[
1/27,0,-2/27,0],[-1/27,1/27,-1/27,-2/27],[-1/27,0,
2/27,0],[0,2/27,0,2/27],[0,-2/27,0,4/27],[1/27,
-1/27,1/27,2/27],[2/27,0,-1/27,0],[-2/9,1/9,1/9,
1/9],[-4/27,1/27,-4/27,-2/27],[4/27,0,-2/27,0],
[0,1/27,0,1/27],[0,2/9,0,-1/9],[0,2/27,0,-1/27
],[-2/27,2/27,1/27,2/27],[0,-2/27,0,1/27],[2/27,
4/27,-4/27,-2/27],[-2/27,-2/27,4/27,1/27],[0,2/27,
0,2/27],[0,4/27,0,-2/27],[-2/27,-1/27,1/27,-1/27],
[10/27,1/27,-5/27,1/27],[-2/27,0,-2/27,0],[0,-2/27,
0,-2/27],[-1/27,-5/27,-1/27,10/27],[1/27,5/27,1/27,
-10/27],[2/27,-4/27,-4/27,2/27],[-2/27,0,-2/27,0],
[0,1/27,0,1/27],[10/27,-1/27,-5/27,-1/27],[-4/27,
-2/27,-4/27,4/27],[-2/27,-1/9,1/27,-1/9],[0,5/27,0,
5/27],[-10/27,-1/3,5/27,-1/3],[2/27,-4/27,2/27,8/27],
[-8/27,4/27,4/27,4/27],[10/27,-1/27,-5/27,-1/27],[
-4/9,2/9,2/9,2/9],[2/27,2/27,2/27,-4/27],[2/9,1/9,
-1/9,1/9],[-2/27,-2/27,1/27,-2/27],[-1/9,-1/27,-1/9,
2/27],[-2/27,0,4/27,0],[-1/27,-4/27,2/27,2/27],
[0,1/27,0,1/27],[0,0,0,0],[-1/27,4/27,2/27,
-2/27],[0,2/27,0,-1/27],[1/27,-1/27,1/27,2/27],
[-1/27,2/27,2/27,-1/27],[-1/27,0,2/27,0],[0,1/9,
0,1/9],[0,2/27,0,-1/27],[2/27,-2/9,-4/27,1/9],
[2/27,1/27,-1/27,1/27],[-1/27,2/27,-1/27,-4/27],
[0,-2/27,0,1/27],[-4/27,2/27,2/27,2/27],[-8/27,
-4/27,4/27,-4/27],[2/27,1/9,2/27,-2/9],[-1/27,4/27,
2/27,-2/27],[2/27,2/9,-4/27,-1/9],[1/27,1/27,1/27,
-2/27],[-2/27,1/9,-2/27,-2/9],[0,-1/27,0,2/27],
[1/9,-4/27,-2/9,2/27],[0,0,0,0],[-4/27,0,8/27,
0],[1/27,-1/27,1/27,2/27],[-1/27,-1/9,-1/27,2/9],
[-2/27,2/27,4/27,-1/27],[1/27,-2/27,1/27,4/27],
[1/9,4/27,-2/9,-2/27],[-2/9,2/27,1/9,2/27],[2/27,
1/27,-1/27,1/27],[-2/27,-2/27,-2/27,4/27],[0,2/27,0,
2/27],[1/27,-2/9,-2/27,1/9],[-2/27,-2/27,4/27,1/27],
[4/27,1/27,-2/27,1/27],[2/27,1/9,2/27,-2/9],[-2/9,
1/27,1/9,1/27],[-1/27,2/27,2/27,-1/27],[2/27,-2/27,
2/27,4/27],[1/27,4/27,-2/27,-2/27],[0,2/27,0,-1/27],
[0,0,0,0],[1/27,2/27,-2/27,-1/27],[-4/27,0,2/27,
0],[-1/27,-2/27,-1/27,4/27],[2/27,-1/27,2/27,2/27
],[2/27,0,-1/27,0],[-8/27,0,4/27,0],[-1/9,0,
-1/9,0],[2/27,1/27,-1/27,1/27],[0,1/27,0,1/27],
[-2/27,4/27,4/27,-2/27],[0,0,0,0],[0,1/27,0,
1/27],[1/27,-2/27,-2/27,1/27],[0,2/27,0,-4/27],
[0,0,0,0],[-1/27,0,2/27,0],[0,0,0,0],[0,
-2/27,0,1/27],[0,0,0,0],[4/27,0,-2/27,0],[0,
0,0,0],[-2/27,0,1/27,0],[4/27,0,-2/27,0],[0,
0,0,0],[2/27,-1/27,-1/27,-1/27],[4/27,0,-8/27,
0],[1/27,10/27,-2/27,-5/27],[-4/27,0,2/27,0],
[1/9,-2/27,-2/9,1/27],[-5/27,10/27,10/27,-5/27],
[5/27,-2/3,-10/27,1/3],[-8/27,4/27,4/27,4/27],[
-5/27,-2/27,10/27,1/27],[5/27,10/27,-10/27,-5/27],
[-10/27,0,20/27,0],[4/27,0,-2/27,0],[1/27,10/27,
-2/27,-5/27],[0,-4/27,0,2/27],[0,-2/27,0,-2/27],
[0,-1/27,0,2/27],[2/27,-1/27,2/27,2/27],[0,-2/27,
0,1/27],[1/27,0,-2/27,0],[1/27,-2/27,1/27,4/27],
[0,0,0,0],[0,0,0,0],[5/27,0,5/27,0],[1/27,
-1/27,1/27,2/27],[-1/27,4/27,2/27,-2/27],[0,0,0,
0],[-2/27,-2/27,-2/27,4/27],[0,2/9,0,-1/9],[0,
-1/27,0,-1/27],[-2/27,1/27,-2/27,-2/27],[-2/27,0,
4/27,0],[0,-10/27,0,5/27],[4/27,1/27,-2/27,1/27],
[2/27,2/27,2/27,-4/27],[0,5/27,0,-10/27],[0,1/27,
0,1/27],[0,-5/27,0,-5/27],[2/27,2/27,-1/27,2/27],
[-2/27,-1/27,-2/27,2/27],[0,-2/27,0,1/27],[2/27,
-2/27,2/27,4/27],[-2/27,1/27,1/27,1/27],[0,2/27,
0,2/27],[2/27,-2/27,2/27,4/27],[2/27,1/27,-1/27,
1/27],[0,5/27,0,-10/27],[-2/27,-4/27,4/27,2/27],
[1/27,2/27,-2/27,-1/27],[-2/27,2/27,1/27,2/27],
[-2/27,4/27,4/27,-2/27],[-2/27,1/27,-2/27,-2/27],
[-1/27,-1/27,-1/27,2/27],[0,4/27,0,-2/27],[10/27,
0,-5/27,0],[-2/27,2/27,4/27,-1/27],[0,1/27,0,
-2/27],[-4/27,1/27,2/27,1/27],[-2/27,2/27,-2/27,
-4/27],[0,2/27,0,-4/27],[4/27,-2/27,-2/27,-2/27],
[0,1/27,0,-2/27],[-1/27,0,2/27,0],[-2/27,0,1/27,
0],[-4/27,2/27,2/27,2/27],[0,4/27,0,-2/27],[0,0,
0,0],[-2/27,-2/27,1/27,-2/27],[0,2/27,0,-1/27],
[1/27,0,-2/27,0],[1/9,0,1/9,0],[2/27,0,2/27,
0],[-1/27,2/27,2/27,-1/27],[-2/27,0,-2/27,0],
[2/27,-4/27,-4/27,2/27],[-2/27,2/9,4/27,-1/9],
[2/27,-1/27,-1/27,-1/27],[2/27,2/27,-4/27,-1/27],
[-2/27,1/27,1/27,1/27],[4/27,0,-2/27,0],[-2/27,0,
-2/27,0],[2/27,-1/27,-1/27,-1/27],[5/27,0,5/27,0],
[-1/27,-5/27,-1/27,10/27],[2/27,0,-4/27,0],[2/27,
0,2/27,0],[-8/27,4/27,4/27,4/27],[2/9,-1/3,-1/9,
-1/3],[-2/27,-4/27,-2/27,8/27],[-4/9,0,2/9,0],
[10/27,-4/27,-5/27,-4/27],[-10/27,1/3,5/27,1/3],
[2/27,4/27,2/27,-8/27],[10/27,1/27,-5/27,1/27],
[-10/27,-1/27,5/27,-1/27],[10/27,1/27,-5/27,1/27],
[-2/27,2/27,-2/27,-4/27],[0,-2/27,0,-2/27],[0,
1/27,0,1/27],[2/27,-1/9,2/27,2/9],[1/27,2/27,-2/27,
-1/27],[2/27,2/27,-4/27,-1/27],[0,1/27,0,1/27],
[-4/27,-1/27,2/27,-1/27],[0,8/27,0,-4/27],[-2/27,
4/27,4/27,-2/27],[0,-1/27,0,2/27],[1/9,-2/27,-2/9,
1/27],[-1/27,2/27,2/27,-1/27],[2/27,1/9,-1/27,1/9],
[-2/27,-2/27,4/27,1/27],[-2/27,-2/9,4/27,1/9],[0,
-2/27,0,-2/27],[-2/27,1/27,-2/27,-2/27],[-4/27,0,
8/27,0],[4/27,2/27,-2/27,2/27],[-4/27,1/9,2/27,1/9],
[-2/27,1/9,-2/27,-2/9],[0,0,0,0],[0,-2/9,0,1/9],
[-1/27,2/27,-1/27,-4/27],[0,0,0,0],[1/27,0,1/27,
0],[-1/27,-2/27,2/27,1/27],[4/27,-1/27,-2/27,-1/27],
[0,2/27,0,-1/27],[0,0,0,0],[0,-1/9,0,2/9],[
2/27,2/27,-4/27,-1/27],[0,0,0,0],[1/27,-2/9,-2/27,
1/9],[8/27,4/27,-4/27,4/27],[-2/27,1/27,1/27,1/27],
[-1/27,0,-1/27,0],[4/27,-1/27,-2/27,-1/27],[-1/27,
2/27,2/27,-1/27],[-2/27,2/27,4/27,-1/27],[2/27,-1/27,
-1/27,-1/27],[-1/9,-2/27,-1/9,4/27],[-2/9,-1/27,1/9,
-1/27],[0,2/27,0,-1/27],[2/27,1/27,2/27,-2/27],[
-1/27,0,2/27,0],[0,2/27,0,-1/27],[1/9,-2/27,1/9,
4/27],[1/27,-2/27,-2/27,1/27],[-4/27,0,2/27,0],[
2/27,0,2/27,0],[2/27,2/27,2/27,-4/27],[-4/27,-2/27,
2/27,-2/27],[-4/27,1/27,2/27,1/27],[1/9,-2/27,1/9,
4/27],[2/27,-1/27,-1/27,-1/27],[-2/27,1/27,1/27,1/27
],[1/27,0,-2/27,0],[1/27,-2/27,-2/27,1/27],[2/27,
-2/27,-1/27,-2/27],[-1/9,-4/27,2/9,2/27],[4/27,0,
4/27,0],[0,0,0,0],[0,-4/27,0,2/27],[0,0,0,0],
[-1/27,0,2/27,0],[0,0,0,0],[0,-2/27,0,-2/27],
[0,0,0,0],[0,-5/27,0,-5/27],[0,10/27,0,10/27],
[0,1/3,0,-2/3],[10/27,-4/27,-5/27,-4/27],[0,4/27,
0,-2/27],[-1/27,-8/27,2/27,4/27],[0,5/27,0,5/27
],[-1/27,2/9,2/27,-1/9],[-1/27,4/27,2/27,-2/27],
[0,-4/27,0,2/27],[-4/27,1/27,2/27,1/27],[-4/27,
4/27,8/27,-2/27],[2/27,2/27,-4/27,-1/27],[0,-4/27,
0,2/27],[0,1/27,0,1/27],[-1/27,4/27,2/27,-2/27],
[1/27,0,-2/27,0],[2/27,0,-1/27,0],[1/27,0,1/27,
0],[-2/27,2/27,-2/27,-4/27],[2/27,0,-4/27,0],[
0,-2/27,0,1/27],[2/27,-2/27,2/27,4/27],[-1/9,1/9,
-1/9,-2/9],[0,0,0,0],[0,-1/27,0,2/27],[4/27,
1/27,4/27,-2/27],[-1/27,-4/27,2/27,2/27],[-1/9,1/9,
-1/9,-2/9],[-1/27,1/27,-1/27,-2/27],[1/9,0,-2/9,0],
[-8/27,0,4/27,0],[2/27,-2/27,2/27,4/27],[0,-2/27,
0,1/27],[-2/27,0,4/27,0],[-4/27,1/27,2/27,1/27],
[1/27,-1/27,1/27,2/27],[1/27,0,1/27,0],[2/27,0,
-1/27,0],[-4/27,0,2/27,0],[4/27,2/27,-2/27,2/27],
[-2/27,1/27,-2/27,-2/27],[-4/27,0,8/27,0],[-1/27,
-1/27,-1/27,2/27],[2/27,4/27,-1/27,4/27],[-2/27,0,
1/27,0],[-1/27,-1/27,-1/27,2/27],[2/27,-4/27,-1/27,
-4/27],[1/27,0,1/27,0],[1/27,-2/27,-2/27,1/27],
[1/27,-8/27,-2/27,4/27],[4/27,-2/27,-2/27,-2/27],
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1/27],[-1/27,2/27,2/27,-1/27],[0,-4/27,0,-4/27],
[4/27,2/9,-2/27,2/9],[-1/27,4/27,-1/27,-8/27],[
8/27,-4/27,-4/27,-4/27],[0,1/27,0,-2/27],[0,-1/27,
0,2/27],[-1/27,0,2/27,0],[2/27,1/27,2/27,-2/27],
[-4/27,2/27,2/27,2/27],[0,-4/27,0,-4/27],[0,1/27,
0,-2/27],[-4/27,1/27,2/27,1/27],[4/27,-2/27,-2/27,
-2/27],[-2/27,2/27,1/27,2/27],[-1/27,0,-1/27,0],
[-2/27,0,1/27,0],[0,2/27,0,2/27],[0,0,0,0],
[-1/27,0,-1/27,0],[0,0,0,0],[-2/27,0,1/27,0],
[1/27,-2/27,1/27,4/27],[2/27,-2/27,-4/27,1/27],[
2/27,0,-4/27,0],[2/27,-1/27,-1/27,-1/27],[2/9,0,
-1/9,0],[0,4/27,0,-2/27],[1/27,-2/27,-2/27,1/27],
[0,-1/27,0,2/27],[2/27,0,-4/27,0],[-2/27,2/27,
4/27,-1/27],[0,0,0,0],[1/27,-2/27,-2/27,1/27],
[1/27,2/27,-2/27,-1/27],[0,1/27,0,1/27],[-1/27,0,
-1/27,0],[2/27,2/27,-4/27,-1/27],[-4/27,0,2/27,0],
[0,-1/27,0,-1/27],[1/27,-1/27,1/27,2/27],[0,4/27,
0,-2/27],[1/27,2/27,-2/27,-1/27],[1/27,0,1/27,0],
[2/27,1/27,2/27,-2/27],[1/27,-2/27,1/27,4/27],[1/27,
-2/27,-2/27,1/27],[0,1/9,0,1/9],[1/27,2/27,-2/27,
-1/27],[0,2/27,0,-4/27],[1/27,2/27,1/27,-4/27],[
0,-4/27,0,2/27],[1/27,0,1/27,0],[-1/27,2/27,2/27,
-1/27],[-2/27,1/27,1/27,1/27],[0,-2/27,0,-2/27],
[1/27,0,1/27,0],[-2/27,1/27,1/27,1/27],[-1/27,
-2/27,2/27,1/27],[1/27,0,-2/27,0],[-2/27,0,1/27,
0],[1/27,2/27,1/27,-4/27],[2/27,-1/27,-1/27,-1/27],
[-1/27,0,2/27,0],[0,1/27,0,-2/27],[-2/27,0,4/27,
0],[1/27,4/27,-2/27,-2/27],[0,0,0,0],[0,-4/27,
0,2/27],[-2/27,2/27,1/27,2/27],[0,1/27,0,-2/27],
[2/27,0,2/27,0],[-2/27,2/27,1/27,2/27],[2/27,1/27,
-1/27,1/27],[0,0,0,0],[0,1/27,0,1/27],[2/27,
-1/27,-1/27,-1/27],[1/27,0,-2/27,0],[0,0,0,0],
[-4/27,-1/27,2/27,-1/27],[-2/27,0,4/27,0],[-1/27,
2/27,-1/27,-4/27],[1/27,-1/27,1/27,2/27],[0,2/27,
0,-1/27],[1/27,0,1/27,0],[-2/27,4/27,4/27,-2/27],
[-2/27,-4/27,4/27,2/27],[2/27,0,-1/27,0],[1/27,0,
-2/27,0],[0,-1/27,0,-1/27],[4/27,1/9,-2/27,1/9],
[-4/27,1/27,-4/27,-2/27],[2/27,-1/27,-1/27,-1/27],
[0,4/27,0,-2/27],[-1/9,-4/27,2/9,2/27],[2/27,0,
-1/27,0],[-1/27,4/27,2/27,-2/27],[0,0,0,0],[
1/27,0,-2/27,0],[0,1/27,0,1/27],[-1/27,2/27,2/27,
-1/27],[-1/27,0,2/27,0],[1/27,8/27,-2/27,-4/27],
[-2/27,-4/27,1/27,-4/27],[1/27,-2/9,-2/27,1/9],[
-1/27,0,2/27,0],[-2/27,-1/27,1/27,-1/27],[1/27,0,
1/27,0],[1/27,1/27,1/27,-2/27],[0,2/27,0,-1/27],
[-1/27,4/27,2/27,-2/27],[-1/27,-2/27,-1/27,4/27],
[2/27,0,2/27,0],[2/27,-1/27,-1/27,-1/27],[0,0,0,
0],[0,0,0,0],[0,4/27,0,-2/27],[2/27,0,2/27,0],
[-2/27,1/27,-2/27,-2/27],[-2/27,-2/27,4/27,1/27],
[0,2/27,0,2/27],[2/27,0,2/27,0],[1/27,-4/27,
-2/27,2/27],[0,0,0,0],[-2/27,-2/27,1/27,-2/27],
[0,-2/27,0,4/27],[1/27,2/27,1/27,-4/27],[0,1/27,
0,1/27],[-4/27,1/27,2/27,1/27],[4/27,0,-2/27,0],
[-1/27,-1/27,-1/27,2/27],[-1/27,2/27,2/27,-1/27],
[0,-1/27,0,2/27],[0,-1/27,0,-1/27],[-2/27,-1/27,
1/27,-1/27],[-1/27,0,-1/27,0],[4/27,0,-2/27,0],[
-1/27,1/27,-1/27,-2/27],[-1/27,2/27,2/27,-1/27],[1/27,
0,-2/27,0],[-2/27,1/27,1/27,1/27],[0,2/9,0,-1/9],
[1/27,-1/27,1/27,2/27],[0,-1/27,0,2/27],[0,4/27,
0,-2/27],[2/27,-1/27,-1/27,-1/27],[1/27,2/27,-2/27,
-1/27],[1/27,0,1/27,0],[-2/27,-1/27,1/27,-1/27],
[1/27,-2/27,1/27,4/27],[0,1/27,0,-2/27],[-2/27,0,
1/27,0],[1/27,1/27,1/27,-2/27],[1/27,0,-2/27,0],
[0,-1/27,0,-1/27],[-2/27,1/27,1/27,1/27],[2/27,0,
-4/27,0],[0,2/27,0,-1/27],[4/27,0,-2/27,0],[-1/27,
-4/27,2/27,2/27],[0,4/27,0,-2/27],[-2/27,-1/27,-2/27,
2/27],[-2/27,-1/27,-2/27,2/27],[0,2/9,0,-1/9],[0,
0,0,0],[0,-8/27,0,4/27],[2/27,4/9,-4/27,-2/9],
[-2/27,-4/27,1/27,-4/27],[4/27,-8/27,-8/27,4/27],[
0,2/27,0,2/27],[-4/27,-1/9,2/27,-1/9],[2/27,-1/27,
2/27,2/27],[-2/27,1/27,1/27,1/27],[1/27,2/27,1/27,
-4/27],[1/27,-2/27,1/27,4/27],[1/27,0,-2/27,0],[0,
1/27,0,-2/27],[8/27,1/27,-4/27,1/27],[-14/27,2/27,
7/27,2/27],[2/27,2/27,2/27,-4/27],[4/27,1/9,-2/27,
1/9],[2/9,1/9,-1/9,1/9],[-8/27,1/27,4/27,1/27],
[-1/27,1/27,-1/27,-2/27],[0,1/27,0,1/27],[2/27,
-1/27,-1/27,-1/27],[-4/27,0,2/27,0],[2/27,0,2/27,
0],[4/27,1/27,-2/27,1/27],[2/27,2/27,-1/27,2/27],
[-1/27,0,-1/27,0],[1/27,-2/27,-2/27,1/27],[0,-4/27,
0,2/27],[4/27,-1/27,-2/27,-1/27],[4/27,0,-2/27,0],
[-2/27,0,4/27,0],[-1/27,2/27,2/27,-1/27],[0,1/27,
0,-2/27],[1/9,0,-2/9,0],[0,0,0,0],[-4/27,1/27,
2/27,1/27],[-1/27,2/27,2/27,-1/27],[0,-4/27,0,2/27],
[0,-1/27,0,-1/27],[-2/27,-1/27,-2/27,2/27],[-1/27,
-4/27,2/27,2/27],[-4/27,0,2/27,0],[0,-1/9,0,-1/9],
[0,2/27,0,-4/27],[-1/27,-2/27,2/27,1/27],[-1/27,0,
2/27,0],[-1/27,1/27,-1/27,-2/27],[1/27,0,1/27,0],
[-2/27,1/27,-2/27,-2/27],[0,4/27,0,-2/27],[0,1/27,
0,1/27],[1/27,2/27,-2/27,-1/27],[1/27,-1/27,1/27,
2/27],[-1/27,0,-1/27,0],[-1/27,2/27,2/27,-1/27],
[1/27,1/27,1/27,-2/27],[1/27,0,-2/27,0],[0,-2/27,
0,-2/27],[-2/27,1/27,1/27,1/27],[0,-1/27,0,2/27],
[0,0,0,0],[-1/27,0,2/27,0],[1/27,2/27,-2/27,
-1/27],[2/27,-2/27,-1/27,-2/27],[0,1/27,0,-2/27],
[2/27,0,-1/27,0],[1/27,-2/27,-2/27,1/27],[-1/27,
0,-1/27,0],[0,-4/27,0,2/27],[-1/27,4/27,2/27,
-2/27],[1/27,1/27,1/27,-2/27],[0,2/27,0,-1/27],
[-2/27,1/27,1/27,1/27],[1/27,2/27,1/27,-4/27],[0,
2/27,0,-4/27],[2/27,2/27,-1/27,2/27],[-2/27,-1/27,
1/27,-1/27],[-2/27,1/27,-2/27,-2/27],[0,-2/27,0,
-2/27],[2/27,-2/27,-1/27,-2/27],[-1/27,0,2/27,0],
[2/27,0,-4/27,0],[0,0,0,0],[0,0,0,0]])    ,
Matrix(SparseMatrix(K,84,84,[<1,18,-1>,<1,19,-w^3 + w>,<2,
18,-w^3 - 1>,<2,19,w^2>,<3,17,-w^2 + 1>,<3,18,w^2 - w -
1>,<3,19,w^3 + 1>,<3,20,w>,<4,17,w^3 - 1>,<4,18,-w^3>,
<4,20,-1>,<5,13,-w^2>,<5,14,w^2>,<5,15,-w^2 + 1>,<5,
16,-w^3 + w>,<6,13,-w^2>,<6,14,w^2>,<6,15,-w^2 + 1>,<7,
13,-w^3 - 1>,<7,14,1>,<8,13,w^3 + w^2 - w>,<8,14,-w^3 -
w^2 + w>,<8,15,-w>,<8,16,w^3 - w>,<9,10,-1>,<9,11,w^2>,
<10,9,-w^3 - 1>,<10,10,1>,<10,12,-w^3>,<11,9,-w>,<11,
10,-w^2 + 1>,<11,12,-w>,<12,9,w^3 - 1>,<12,10,-w^3 + 1>,
<12,11,w^3 - w^2 - w>,<12,12,-1>,<13,5,w^3 - w>,<13,6,
-w^3 - w^2 + w>,<13,7,-w>,<13,8,w^3 - w>,<14,5,w^3 - w^2
- w>,<14,6,-2*w^3 + 2*w>,<14,7,-w>,<14,8,w^3 - w^2 - w>,
<15,5,-1>,<15,6,-w^3>,<15,8,-1>,<16,5,w^3 - w>,<16,
6,-w^3 + w>,<17,1,w^3>,<17,2,-w^3>,<17,3,w^3 - w>,<17,
4,-1>,<18,1,w^3>,<18,2,-1>,<19,1,w^2 + w - 1>,<19,2,
-w>,<20,1,-w^3>,<20,2,2*w^3 + 1>,<20,3,-w^3 - w^2 + w>,
<20,4,-w^3>,<21,22,w^2>,<21,23,-w^2 + 1>,<21,24,-w^3 -
w^2 + w>,<22,21,-w^3 - w^2 + w>,<22,22,w^3 + 2*w^2 - w>,
<22,23,-w^2 + w + 1>,<22,24,-2*w^3 + 2*w>,<23,21,-w^3>,
<23,22,2*w^3 + 1>,<23,23,-w^3 - w^2 + w>,<23,24,-w^3 + 1>,
<24,21,w^3 - w^2 - w>,<24,22,-w^3 + w>,<24,24,-w^2>,<25,
74,-w>,<26,65,w^3>,<27,78,-w^3 + w>,<28,84,w^3>,<29,
83,-w^3>,<30,69,w^2 - 1>,<31,82,-w^3>,<32,72,-w^3 +
w>,<33,49,w^2 - 1>,<34,75,-w^3 + w>,<35,73,w^3>,<36,
80,w^3 - w>,<37,79,w>,<38,56,1>,<39,41,1>,<40,54,
-w>,<41,39,-w^2>,<42,77,-w>,<43,68,w^3 - w>,<44,53,
-w^3 + w>,<45,66,w^2>,<46,47,-w^3 + w>,<47,46,w^3 - w>,
<48,64,w>,<49,33,1>,<50,50,w^2>,<51,60,w^3>,<52,81,
-w^2 + 1>,<53,44,w>,<54,40,-w^3>,<55,63,-w^3>,<56,38,
1>,<57,57,w^2 - 1>,<58,62,w^3>,<59,59,w^2 - 1>,<60,
51,w>,<61,70,-w>,<62,58,w>,<63,55,-w>,<64,48,-w>,
<65,26,-w^3>,<66,45,-1>,<67,67,-1>,<68,43,-w>,<69,
30,1>,<70,61,-w^3>,<71,76,w^3>,<72,32,-w^3>,<73,35,
w^3 - w>,<74,25,w^3 - w>,<75,34,-w^3>,<76,71,-w^3>,<77,
42,w^3 - w>,<78,27,w>,<79,37,-w^3 + w>,<80,36,w^3>,
<81,52,-1>,<82,31,-w^3 + w>,<83,29,-w>,<84,28,-w^3>]))
]> where w := K.1 where K := ext<K|Polynomial(K,[1,0,-1,0,1])>
where K is RationalField() ;

return _LR;
