//Standard generators of U3(4) are a and b where a has order 2, b has order 3
//and ab has order 13.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
_LR`AI := [ [a, b*a*b^-1*a*b*a*b^-1*a*b^-1*a*b*a], [a,b^-1] ]
                  where a is (_LR`F).1 where b is (_LR`F).2;
//second automorphism is square of first - must handle that somehow!

//four constituents
_LR`G :=
/*
Original group: c9Group("u34p")
From DB /nb/reps/d75.U34.nfdeg4.M
Schur index: 1
Character: ( 75, -5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(13)_13^9 - 
zeta(13)_13^3 - zeta(13)_13, -zeta(13)_13^6 - zeta(13)_13^5 - zeta(13)_13^2, 
zeta(13)_13^11 + zeta(13)_13^9 + zeta(13)_13^8 + zeta(13)_13^7 + zeta(13)_13^6 +
zeta(13)_13^5 + zeta(13)_13^3 + zeta(13)_13^2 + zeta(13)_13 + 1, -zeta(13)_13^11
- zeta(13)_13^8 - zeta(13)_13^7, 0, 0, 0, 0 )
*/

MatrixGroup<75,K | [
Matrix(SparseMatrix(K,75,75,[<1,1,-1>,<2,2,-1>,<3,3,
-1>,<4,4,-1>,<5,5,-1>,<6,6,1>,<7,7,-1>,<8,8,1>,
<9,9,1>,<10,10,-1>,<11,11,1>,<12,12,-1>,<13,17,-1>,
<13,18,1>,<14,15,1>,<14,51,-1>,<15,14,1>,<15,51,-1>,
<16,34,-1>,<16,36,1>,<17,17,-1>,<18,13,1>,<18,17,-1>,
<19,19,-1>,<20,21,1>,<20,22,-1>,<21,20,1>,<21,22,-1>,
<22,22,-1>,<23,19,-1>,<23,24,1>,<24,19,-1>,<24,23,1>,
<25,28,-1>,<25,29,1>,<26,27,1>,<26,30,-1>,<27,26,1>,
<27,30,-1>,<28,28,-1>,<29,25,1>,<29,28,-1>,<30,30,
-1>,<31,32,-1>,<31,33,1>,<32,32,-1>,<33,31,1>,<33,
32,-1>,<34,34,-1>,<35,49,1>,<35,58,-1>,<36,16,1>,
<36,34,-1>,<37,37,-1>,<38,39,1>,<38,54,-1>,<39,38,
1>,<39,54,-1>,<40,40,-1>,<41,37,-1>,<41,42,1>,<42,
37,-1>,<42,41,1>,<43,52,-1>,<43,53,1>,<44,40,-1>,
<44,45,1>,<45,40,-1>,<45,44,1>,<46,46,-1>,<47,46,
-1>,<47,48,1>,<48,46,-1>,<48,47,1>,<49,35,1>,<49,58,
-1>,<50,50,-1>,<51,51,-1>,<52,52,-1>,<53,43,1>,<53,
52,-1>,<54,54,-1>,<55,50,-1>,<55,59,1>,<56,57,1>,
<56,60,-1>,<57,56,1>,<57,60,-1>,<58,58,-1>,<59,50,
-1>,<59,55,1>,<60,60,-1>,<61,61,1>,<62,62,1>,<63,
63,1>,<64,64,1>,<65,65,1>,<66,66,1>,<67,67,1>,<68,
68,1>,<69,69,1>,<70,70,1>,<71,71,1>,<72,72,1>,<73,
73,1>,<74,74,1>,<75,75,1>])),Matrix(K,75,75,
[[9/20,-49/120,-9/40,-17/120],[3/20,3/40,3/40,1/40],
[1/10,-1/24,-1/20,-1/30],[2/5,-1/24,-3/40,-7/120],
[1/60,-31/120,-17/120,-1/15],[1/8,-19/120,1/5,-1/24
],[-3/40,1/20,1/40,0],[1/30,-1/20,-1/30,1/40],
[-3/40,9/40,1/20,-3/40],[1/12,-1/4,-2/15,-3/40],
[1/15,1/24,-11/120,-1/60],[-7/40,1/30,-1/40,1/60],
[1/10,-1/15,0,1/24],[3/20,-37/120,1/20,1/30],[-1/8,
1/120,-1/40,-19/120],[-1/10,29/120,-1/20,1/12],[-3/40,
1/120,1/20,1/24],[-1/20,1/5,-3/40,-1/40],[0,0,0,
0],[-1/20,1/20,-1/40,0],[3/8,-11/60,-1/40,13/120],
[-3/20,-1/30,1/10,7/120],[0,0,0,0],[0,0,0,0],
[0,-1/24,1/40,-1/120],[-1/4,11/30,0,1/120],[1/8,
-31/120,0,-7/60],[-7/40,3/20,1/20,-3/20],[3/10,
-1/15,1/40,17/120],[9/40,-7/20,3/20,1/40],[-3/40,
1/30,0,1/24],[3/40,7/120,0,1/24],[-3/20,3/40,1/40,
1/20],[-1/10,-11/60,11/40,-1/24],[-11/40,1/4,1/40,
-1/10],[3/20,-1/30,-1/40,-1/60],[1/8,-11/120,-3/40,
-1/12],[0,7/120,1/20,-1/30],[-1/4,2/5,-3/10,3/40],
[-1/40,-7/120,-1/20,1/120],[1/20,1/30,3/20,1/60],
[-1/8,13/120,-1/10,7/60],[-3/20,13/40,1/40,-1/40],
[3/40,-1/40,0,1/20],[1/8,-7/60,3/40,-7/120],[1/10,
1/24,1/40,1/120],[0,-1/120,1/5,7/120],[-13/40,17/60,
-11/40,-7/120],[-1/8,1/6,-1/20,13/120],[1/20,-11/120,
-1/10,-1/30],[-9/40,13/60,-1/40,7/120],[0,-11/120,
0,1/60],[7/40,-13/120,0,1/120],[1/40,1/30,-1/20,
-7/120],[-3/40,1/12,1/10,1/24],[1/10,0,-3/20,-1/20],
[1/10,-3/10,1/10,3/40],[1/20,-1/4,1/40,-1/40],[0,
1/30,-1/20,-1/120],[-1/20,7/40,3/40,0],[0,-13/96,
-3/32,-1/48],[1/4,-7/96,-1/8,-1/12],[3/16,-1/4,-3/16,
-3/32],[1/16,3/32,1/32,1/32],[-3/32,7/48,3/32,1/24],
[-7/32,1/6,3/32,5/96],[3/32,7/48,1/8,1/96],[-1/32,
-1/48,0,1/48],[0,0,0,0],[-5/32,3/32,3/32,1/16],
[-5/32,25/96,3/16,1/12],[-1/32,1/96,0,-1/96],[3/32,
-13/96,-3/32,-5/96],[-3/16,-1/32,0,1/32],[0,-1/6,
-3/32,-5/96],[1/20,-1/5,-1/10,-1/20],[-1/20,1/12,1/5,
1/15],[1/20,1/20,-3/20,-1/20],[7/20,-1/12,-1/20,-1/15
],[3/20,-1/6,-1/20,-1/30],[1/20,-1/15,1/10,-1/30],
[-1/10,1/30,-1/10,-1/12],[1/20,-1/15,-1/10,-1/30],
[-7/20,3/10,0,0],[3/20,-1/15,0,-1/30],[1/20,1/12,
0,1/60],[1/10,-1/15,-1/4,-1/30],[1/40,-1/60,-1/20,
1/15],[1/40,-1/12,-3/40,1/30],[-1/10,1/15,0,7/120],
[3/40,3/40,-7/40,9/40],[-1/10,7/24,0,-1/6],[-3/40,
1/30,-1/40,7/60],[0,0,0,0],[3/10,-13/40,1/20,1/40],
[-3/40,1/40,-1/10,-1/20],[-3/10,71/120,-1/8,1/30],
[0,0,0,0],[0,0,0,0],[0,-23/120,1/20,-13/120],
[-1/5,7/24,-3/20,-1/60],[-3/40,13/60,-3/20,7/120],
[9/40,-4/15,7/40,-1/30],[1/10,-1/30,-1/10,1/120],
[9/40,-29/120,3/20,-1/30],[-3/20,17/120,0,-17/120],
[-1/20,1/10,1/20,9/40],[11/40,-29/60,11/40,1/12],[
3/40,-1/5,1/4,-1/20],[-1/40,17/120,0,-1/60],[-1/40,
1/10,-1/20,-7/40],[1/10,-31/120,7/20,1/30],[13/40,
-13/60,3/20,-7/120],[1/8,1/24,-3/20,7/30],[-1/40,
-1/12,0,5/24],[3/40,11/60,-1/8,1/15],[-1/5,-1/120,
3/40,-1/15],[0,-1/120,-13/40,1/12],[-3/40,7/60,-1/20,
-1/15],[-3/40,9/40,-1/40,-3/40],[1/10,-5/24,-1/20,
2/15],[1/10,1/40,-1/40,0],[7/40,-3/10,1/4,1/20],
[1/40,1/40,-3/40,-3/40],[-3/40,-13/120,1/10,-7/60],
[-1/10,19/120,-1/5,1/24],[3/20,-17/120,0,17/120],
[-11/40,17/40,1/20,-1/10],[-1/20,-7/24,3/20,1/60],
[3/10,-3/10,1/10,3/40],[-13/40,11/40,-1/8,-1/40],
[11/40,-17/120,3/40,1/15],[-1/10,29/120,-1/5,-1/24],
[-9/40,4/15,-1/10,-1/24],[1/8,-7/30,7/20,1/120],[
1/4,1/48,0,-1/48],[1/8,1/24,1/16,1/48],[-3/16,1/8,
1/16,1/16],[3/16,-1/48,-1/16,-1/24],[1/4,-7/48,-1/16,
-1/24],[1/16,11/48,1/8,1/48],[-3/16,1/24,1/16,1/48],
[0,0,0,0],[0,0,0,0],[-1/4,-1/48,0,1/48],[0,
1/6,1/16,1/48],[3/16,-7/24,-1/8,-1/12],[-1/16,-7/48,
-1/16,-1/24],[1/16,-1/12,-1/8,-1/24],[-5/16,7/48,1/8,
5/48],[1/20,1/40,1/40,0],[3/20,11/120,-1/40,-7/60],
[1/40,-19/120,-3/40,7/120],[-1/20,-1/40,-1/40,0],
[-1/10,-1/30,0,1/120],[1/20,-13/120,-1/20,1/120],
[-3/20,1/6,-3/40,13/120],[-2/15,-1/120,7/120,1/120
],[1/10,1/8,3/20,1/40],[1/20,-3/40,-1/40,-1/40],
[2/15,-3/20,-1/30,-1/40],[0,-17/60,3/40,13/120],
[-1/20,-1/20,1/40,-1/20],[-3/20,3/40,1/40,1/20],
[3/40,7/120,0,1/24],[1/8,-7/60,3/40,-7/120],[
1/8,-11/120,-3/40,-1/12],[1/20,1/30,3/20,1/60],[0,
0,0,0],[1/20,-1/4,1/40,-1/40],[-11/40,1/4,1/40,
-1/10],[7/20,-1/6,0,1/60],[0,0,0,0],[0,0,0,
0],[-9/40,13/60,-1/40,7/120],[1/40,-1/40,1/20,0],
[0,1/30,-1/20,-1/120],[3/20,-37/120,1/20,1/30],[
-1/8,1/120,-1/40,-19/120],[1/20,-11/120,-1/10,-1/30],
[0,-1/24,1/40,-1/120],[3/10,-1/15,1/40,17/120],
[-7/40,3/20,1/20,-3/20],[3/40,-1/40,0,1/20],[
7/40,-13/120,0,1/120],[-1/40,-7/120,-1/20,1/120],[
1/10,1/24,1/40,1/120],[1/8,-31/120,0,-7/60],[9/40,
-7/20,3/20,1/40],[-1/20,7/40,3/40,0],[9/40,-19/60,
1/20,-1/120],[0,-1/120,1/5,7/120],[-3/20,-1/30,1/10,
7/120],[-3/20,1/8,-1/40,-1/40],[1/10,0,-3/20,-1/20],
[-3/40,1/120,1/20,1/24],[1/40,-17/120,1/40,-7/120],
[1/10,-1/15,0,1/24],[-1/40,-1/8,-1/40,0],[-1/4,
2/5,-3/10,3/40],[-3/40,1/30,0,1/24],[-1/20,1/20,
-1/40,0],[3/8,-11/60,-1/40,13/120],[-1/4,11/30,0,
1/120],[9/40,-59/120,3/10,1/60],[-1/10,29/120,-1/20,
1/12],[1/20,-1/40,-1/5,-1/40],[0,-11/120,0,1/60],
[0,7/120,1/20,-1/30],[3/20,-1/30,-1/40,-1/60],
[3/16,-1/4,-3/16,-3/32],[3/32,-13/96,-3/32,-5/96],
[1/16,3/32,1/32,1/32],[0,-13/96,-3/32,-1/48],[0,
-1/6,-3/32,-5/96],[1/4,-7/96,-1/8,-1/12],[-3/32,
7/48,3/32,1/24],[-1/32,1/96,0,-1/96],[0,0,0,0],
[-5/32,25/96,3/16,1/12],[3/16,-5/48,-1/32,-1/48],
[-3/16,-1/32,0,1/32],[-7/32,1/6,3/32,5/96],[-1/32,
-1/48,0,1/48],[3/32,7/48,1/8,1/96],[1/10,3/10,3/20,
1/20],[-1/4,1/5,3/20,1/10],[-1/10,13/60,1/20,1/30],
[-3/20,11/60,3/20,1/15],[1/3,-1/4,-1/30,-1/20],[
-1/20,-1/60,1/10,1/15],[-1/10,-1/60,0,-1/30],[1/30,
1/20,-1/30,0],[-3/20,1/30,1/10,1/60],[13/60,-1/20,
1/30,-1/20],[-1/30,2/15,1/30,1/60],[1/20,-1/10,-3/20,
-1/20],[7/40,-3/10,1/4,1/20],[9/40,-4/15,7/40,-1/30],
[1/10,-1/30,-1/10,1/120],[-13/40,11/40,-1/8,-1/40],
[1/10,-5/24,-1/20,2/15],[-3/8,29/60,-7/40,-11/60],
[0,0,0,0],[3/20,-17/120,0,17/120],[-11/40,17/40,
1/20,-1/10],[0,-1/120,-13/40,1/12],[0,0,0,0],
[0,0,0,0],[-3/20,17/120,0,-17/120],[-1/20,-7/24,
3/20,1/60],[13/40,-13/60,3/20,-7/120],[11/40,-29/60,
11/40,1/12],[-1/20,1/10,1/20,9/40],[1/8,1/24,-3/20,
7/30],[-1/10,19/120,-1/5,1/24],[-1/10,1/15,0,7/120],
[1/40,-1/12,-3/40,1/30],[-3/40,1/10,-3/10,-1/20],
[-3/40,1/40,-1/10,-1/20],[1/8,-7/30,7/20,1/120],
[-1/10,7/24,0,-1/6],[-9/40,4/15,-1/10,-1/24],[
-3/40,-13/120,1/10,-7/60],[-1/40,1/10,-1/20,-7/40],
[-3/40,1/30,-1/40,7/60],[3/20,-37/120,3/40,-1/60],
[1/10,-49/120,11/40,2/15],[3/40,-1/5,1/4,-1/20],
[3/40,3/40,-7/40,9/40],[1/10,-31/120,7/20,1/30],
[-1/5,-1/120,3/40,-1/15],[1/40,1/12,-3/10,-1/30],
[3/40,-7/24,7/40,-1/120],[9/40,-29/120,3/20,-1/30],
[0,-23/120,1/20,-13/120],[-1/10,29/120,-1/5,-1/24
],[-1/40,17/120,0,-1/60],[0,17/120,-1/10,1/12],
[1/20,-4/15,3/20,-1/120],[-3/40,9/40,-1/40,-3/40],
[7/40,-31/120,3/40,-1/15],[3/10,-13/40,1/20,1/40],[
-3/40,13/60,-3/20,7/120],[-1/40,-1/12,0,5/24],[3/16,
-1/48,-1/16,-1/24],[1/16,11/48,1/8,1/48],[1/4,1/48,
0,-1/48],[-3/16,1/8,1/16,1/16],[-3/16,1/24,1/16,
1/48],[-1/16,-7/48,-1/16,-1/24],[-5/16,7/48,1/8,
5/48],[1/16,-1/12,-1/8,-1/24],[0,0,0,0],[-1/8,
-1/16,-1/16,0],[-1/4,-1/48,0,1/48],[0,0,0,0],
[1/8,1/24,1/16,1/48],[3/16,-7/24,-1/8,-1/12],[1/4,
-7/48,-1/16,-1/24],[1/8,-11/40,-3/40,-1/20],[1/8,1/24,
-1/40,-1/60],[3/8,-4/15,-1/10,-1/12],[11/40,-1/24,
-3/40,-1/30],[-1/8,-3/40,-1/5,-1/20],[7/40,-7/60,0,
-7/120],[1/10,-1/40,1/40,1/40],[1/20,-11/60,-3/40,
-1/60],[1/8,1/60,0,-1/24],[-3/20,-7/60,-1/8,1/60],
[3/40,-11/120,-1/10,-1/30],[-1/20,1/24,3/40,1/120],
[-1/5,7/40,-7/40,-3/40],[-1/20,1/12,-1/5,11/120],
[3/40,-1/3,9/40,-11/120],[1/8,-29/120,1/10,1/15],
[-1/20,4/15,3/40,-1/60],[3/40,-13/120,1/40,13/120],
[0,0,0,0],[-7/40,7/60,-3/20,-17/120],[3/8,-13/60,
-3/40,17/120],[-1/10,-11/120,1/4,-7/120],[0,0,0,
0],[0,0,0,0],[1/5,-3/20,-1/8,3/40],[-1/8,4/15,
-1/10,-11/120],[3/40,-1/5,-1/10,0],[-13/40,23/60,
1/40,-2/15],[0,1/20,-1/20,-1/20],[-3/40,-1/40,7/40,
-1/8],[1/8,-47/120,1/4,1/15],[3/40,1/40,-1/8,-3/40],
[-3/20,29/120,1/20,1/120],[-1/20,-1/5,13/40,3/40],
[3/40,-1/5,1/4,-3/40],[1/20,9/40,-9/40,-1/40],
[0,-1/40,-1/20,1/10],[7/40,-1/5,11/40,3/40],
[-1/8,43/120,-2/5,1/60],[-9/40,1/15,1/40,2/15],
[7/40,-1/15,3/20,-7/120],[-1/8,19/120,-1/5,1/60],
[-9/40,7/15,-3/20,-1/24],[7/40,1/40,-7/40,1/10],
[1/20,-1/60,1/10,-19/120],[-3/20,9/40,-1/5,1/40],[
1/40,1/120,0,17/120],[-3/20,1/6,1/20,-1/15],[-1/4,
53/120,-1/4,1/120],[-3/20,7/120,-1/8,1/60],[-11/40,
7/20,-1/10,1/20],[1/5,-13/40,1/4,-3/40],[3/20,-7/40,
-1/8,1/40],[-1/40,-1/15,9/40,-1/12],[0,23/120,-1/40,
1/120],[1/20,-23/120,0,1/60],[1/20,-1/10,-1/10,1/20
],[-3/40,1/10,-3/40,1/40],[1/20,1/20,1/20,-7/40],
[-1/8,41/120,1/40,-11/120],[-3/32,-3/32,-1/16,0],
[3/32,-3/16,-1/8,-1/16],[-1/8,-7/48,-3/32,-1/24],[
7/32,1/32,1/32,0],[1/8,11/96,1/32,1/96],[-3/16,5/32,
1/16,1/32],[1/4,-1/24,0,-5/96],[0,-1/24,1/32,1/96],
[0,0,0,0],[1/32,5/96,1/32,1/96],[5/32,1/8,3/32,
1/32],[1/32,-1/16,-1/16,-1/32],[-5/32,-5/96,-1/16,
-1/96],[-9/32,13/48,5/32,5/48],[0,-1/32,-1/32,0],
[9/40,-7/20,-9/40,-1/10],[23/40,-1/5,-1/8,-3/20],
[0,-11/30,-7/40,-1/30],[13/40,1/60,-1/40,-1/60],
[0,1/60,-1/40,1/120],[3/40,-1/120,-1/40,1/120],
[-1/4,7/24,1/20,13/120],[1/40,-2/15,-1/20,-1/24],
[-1/40,7/120,3/40,1/24],[-1/40,-1/15,-3/20,-1/120],
[7/20,-19/60,-1/8,-13/120],[0,-11/120,1/20,1/24],
[1/40,-1/60,-1/20,7/60],[-13/40,47/120,-1/8,-1/6],
[3/10,-11/30,3/10,-1/120],[7/40,-1/30,-3/20,1/30],
[-1/10,5/24,-3/40,-1/12],[1/20,-37/120,3/20,-1/60],
[0,0,0,0],[1/20,-5/24,1/40,7/120],[1/20,-1/120,
1/20,1/30],[-1/8,41/120,0,-11/120],[0,0,0,0],[
0,0,0,0],[3/40,-9/40,1/10,1/20],[1/20,-1/10,1/20,
0],[3/40,1/60,-1/20,1/30],[-1/8,-1/30,1/10,1/30],
[1/5,-7/120,3/40,1/120],[1/10,13/120,-1/4,11/120],
[-9/40,1/3,-1/40,11/120],[-1/20,1/15,-1/10,-1/15],[
-1/40,-7/120,-1/40,-11/120],[-9/40,1/15,-1/10,7/120],
[13/40,-9/40,-1/20,3/40],[3/40,-1/24,7/40,-7/120],
[3/40,-1/8,7/40,-1/20],[3/40,-5/24,1/20,1/30],
[0,1/12,-1/10,-7/120],[0,2/15,-3/20,-13/120],[
3/40,19/120,-3/20,1/6],[-3/20,-1/15,-1/40,-1/30],
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[-1/20,23/240,0,-1/48],[-1/80,-19/240,-1/20,-7/120],
[-1/24,-5/48,-1/30,1/240],[-13/80,31/240,3/40,1/48],
[3/40,1/80,-7/40,0],[1/80,-7/40,21/80,-1/16],[3/10,
-37/120,13/80,17/240],[-9/40,37/120,-21/80,-17/240],
[1/4,-19/60,0,5/48],[-9/80,9/40,-17/80,-1/80],
[1/16,17/120,-13/80,23/240],[-3/40,-1/40,0,1/40],
[1/16,-1/12,1/10,1/120],[-11/80,7/40,1/10,1/20],
[-1/80,3/40,-1/10,0],[-3/40,0,0,0],[0,0,0,0],
[-1/80,11/120,-3/80,1/12],[-1/8,1/20,-11/80,1/10],
[1/10,1/12,-1/16,1/60],[-21/80,7/30,-7/80,-1/12],
[1/16,-1/8,3/16,-3/40],[-1/20,1/60,1/16,-23/120],
[3/16,-7/24,3/20,-23/240],[13/80,-11/60,3/40,7/48],
[-3/80,3/40,-3/40,1/80],[1/20,-3/40,1/5,-1/16],
[7/80,-47/240,-1/8,-13/240],[-7/40,29/120,-3/40,
-1/240],[1/40,-17/80,3/20,-1/8],[1/16,-43/240,3/40,
-7/120],[3/80,3/80,0,7/40],[1/5,-5/48,1/16,1/240],
[1/20,-23/240,3/40,1/120],[-1/5,97/240,-3/20,-1/60],
[-3/20,7/48,-1/40,7/240],[0,1/48,-11/80,13/240],[
-9/40,79/240,-1/16,-37/240],[7/80,-1/80,1/16,11/80],
[13/80,-17/80,3/80,3/80],[-11/80,13/48,-3/16,-17/240],
[-13/80,43/240,1/8,17/240],[1/80,-13/240,-1/16,1/60],
[-7/40,1/5,-9/80,1/80],[1/40,-37/240,1/40,-1/48],
[1/20,1/48,1/40,1/240],[-1/80,-19/240,1/8,-1/30],
[1/80,-17/240,1/16,1/120],[-1/40,-1/80,1/16,1/20],
[1/10,23/240,-1/80,-7/120],[-7/80,19/80,-1/8,1/80],
[-13/80,23/240,-1/80,1/24],[-1/40,-11/80,1/80,0],
[-5/64,1/192,0,-1/192],[3/16,-9/64,-5/64,-5/64],
[1/8,1/192,0,-1/192],[-3/64,-1/96,0,1/96],[5/32,
11/192,1/16,-1/96],[-9/32,9/32,5/32,7/64],[-5/64,
-5/96,1/64,1/192],[-5/64,23/192,5/64,5/96],[0,0,0,
0],[-1/8,1/32,-1/64,1/64],[13/64,0,-1/16,-3/64],
[7/64,-61/192,-5/32,-7/96],[3/32,-9/64,-5/64,-1/32],
[-1/32,19/96,5/64,1/48],[-5/64,-1/192,-5/64,1/192],
[-13/40,7/48,3/40,19/240],[1/4,-1/240,0,-1/48],
[7/40,-3/20,-1/8,-1/16],[-1/10,-49/240,-3/40,-1/48],
[-29/240,11/120,1/30,1/30],[-1/16,-17/240,1/16,-1/60],
[-13/80,1/10,3/80,1/80],[-19/240,3/80,-1/120,-1/80],
[-9/80,17/240,-3/80,-1/30],[-31/240,-7/240,-1/30,7/240
],[-1/48,1/15,1/30,1/120],[-1/80,1/12,1/80,7/240],
[3/80,7/240,3/80,-19/240],[3/16,-19/120,1/16,1/30],
[-1/80,1/8,-3/80,-3/40],[9/40,-77/240,9/80,13/120],
[-19/80,27/80,-3/80,3/80],[1/16,17/240,-1/16,13/240],
[-11/40,1/20,0,-1/20],[1/8,-13/48,1/10,-13/240],
[-3/40,37/240,1/10,17/240],[-1/5,73/240,-1/10,1/48],
[-1/5,3/40,0,-3/40],[3/5,-1/5,0,1/5],[-11/80,2/15,
1/20,5/48],[3/80,-67/240,1/20,-1/30],[-11/80,67/240,
0,1/120],[-9/80,3/20,-1/10,-3/80],[17/80,-11/60,9/40,
-1/240],[-3/80,7/80,-1/20,-1/20],[-1/8,1/24,7/80,1/48
],[3/20,-7/120,3/80,17/240],[3/20,-1/12,-1/80,11/240
],[1/8,-7/80,11/80,1/40],[1/80,-1/24,-1/40,1/60],
[-1/20,-23/240,-1/16,-11/120],[-17/80,1/8,9/80,-7/80],
[-19/80,47/240,1/16,-1/120],[1/80,17/240,-9/80,17/120],
[3/20,-1/5,0,-7/80],[9/80,-1/40,1/80,1/16],[-1/16,
-1/30,-7/80,-7/240],[-3/16,11/48,0,1/48],[1/8,-1/15,
0,19/240],[0,1/120,1/20,-11/240],[-1/8,9/80,7/40,
1/20],[1/10,-59/240,-1/20,1/120],[1/40,49/240,-9/40,
-1/60],[-1/80,-1/120,1/40,1/30],[-1/40,1/30,-9/80,
-1/30],[-5/16,1/3,-1/16,7/60],[1/16,-3/16,0,-1/16],
[1/16,-1/48,0,1/48],[13/80,-79/240,3/16,-2/15],[3/20,
-19/120,1/16,1/12],[-1/40,-1/240,9/80,1/240],[-7/40,
17/48,-1/16,-1/240],[3/80,-1/30,-1/40,-1/24],[-3/10,
3/8,-1/80,1/20],[1/8,-27/80,1/80,-7/80],[1/64,0,0,
0],[1/32,0,0,-1/64],[9/64,1/192,0,-1/192],[3/32,
-1/192,0,1/192],[5/64,1/48,3/64,-1/192],[-5/32,9/64,
5/64,1/16],[-5/64,-7/192,-1/64,1/192],[-1/16,7/48,
5/64,1/24],[-1/4,0,0,0],[-7/64,1/96,1/64,1/48],
[3/32,1/96,-3/64,-5/192],[3/64,-11/64,-5/64,-1/32],
[1/8,-9/64,-5/64,-3/64],[1/64,5/192,0,-1/96],[0,
1/64,-1/32,0],[1/80,-53/240,-13/80,-13/240],[31/80,
-11/240,-1/80,-7/240],[3/40,-19/120,-3/16,-19/240],
[3/16,-29/240,-3/80,-7/240],[-1/48,1/30,1/48,1/240],
[1/20,-1/60,1/20,-17/240],[-11/80,5/48,1/80,-1/60],
[1/120,-7/80,-1/12,-1/40],[-1/40,11/120,-1/10,-13/240
],[1/120,-17/80,-11/60,-1/20],[-11/240,13/120,-1/240,
7/240],[-3/80,31/240,-1/80,1/30],[-1/40,1/20,3/80,
-1/10],[17/80,-37/240,-1/20,7/240],[-7/80,11/80,1/40,
-13/80],[7/80,-7/30,9/80,1/30],[-1/20,13/120,-3/80,
1/60],[0,11/120,-1/16,1/30],[-3/20,-1/40,0,1/40],[
-1/80,7/240,1/16,1/48],[-21/80,5/16,3/80,3/80],[9/80,
-7/240,-3/80,-23/240],[3/40,1/40,0,-1/40],[0,0,0,0
],[11/80,-1/8,1/10,1/20],[1/10,-59/240,11/80,-1/240],
[3/40,37/240,-9/80,23/240],[-9/80,17/120,-3/20,1/120],
[7/80,-7/60,9/40,-1/12],[-3/20,9/80,-1/16,-9/80],
[7/40,-37/80,11/40,1/16],[1/40,7/240,-1/10,11/240],
[-3/40,19/80,-1/8,-1/16],[13/80,-7/40,3/16,3/40],[
-11/80,1/24,-1/80,-7/240],[-7/80,11/60,-9/80,-7/120],
[-1/80,-43/240,17/80,-13/120],[0,-17/120,1/10,-11/240
],[-1/20,0,-1/20,7/80],[-1/40,1/20,-1/16,1/80],
[-3/80,13/80,9/80,1/10],[-3/16,19/80,-3/16,1/40],
[-1/20,23/240,-1/20,-1/12],[3/20,-1/10,9/80,9/80],
[-3/20,1/6,-1/80,-31/240],[-7/80,7/240,3/20,7/120],
[1/16,-17/80,-1/40,1/20],[1/80,59/240,-1/5,-1/30],
[-13/80,1/20,-1/80,-3/80],[-1/40,5/48,-17/80,1/120
],[-11/80,-1/48,0,29/240],[1/40,-7/80,7/40,0],[
7/40,-41/240,1/10,7/120],[1/40,13/120,1/8,-29/240],
[1/8,-29/80,23/80,1/10],[-7/80,-1/15,1/4,1/240],
[1/16,19/120,-1/8,1/240],[17/80,-2/15,7/80,23/240],
[-7/40,21/80,-3/16,0],[-3/80,-1/120,-7/40,11/240],
[-5/64,-1/96,3/64,5/192],[3/32,-7/48,-5/64,-11/192],
[1/8,5/192,-1/32,-1/96],[13/64,-1/64,-1/64,-1/64],
[-1/64,5/192,3/64,-1/96],[-11/64,11/96,5/64,7/96],
[-7/32,-1/24,-1/64,1/96],[-1/16,25/192,7/64,1/24],
[0,0,0,0],[-15/64,29/192,3/32,13/192],[1/4,-25/192,
-1/8,-17/192],[1/8,-13/96,-1/16,-7/192],[5/64,1/32,0,
-1/64],[-1/16,1/192,-3/64,-1/192],[-1/64,1/64,-1/32,
0],[-7/20,1/15,3/80,1/12],[1/5,1/40,-1/80,0],[
3/10,-31/240,-1/10,-23/240],[3/40,-47/120,-3/16,-1/12],
[-43/240,7/240,-1/48,1/120],[-1/10,-1/12,1/80,1/48],
[-3/40,1/10,1/10,1/80],[-47/240,3/80,1/30,0],[-1/10,
-19/120,-1/16,-13/240],[-29/240,-29/240,-11/120,1/120],
[-31/240,23/240,5/48,1/24],[1/10,2/15,1/40,-1/48],
[3/20,-29/240,11/80,-1/24],[1/8,-53/240,1/5,1/30],[
-1/40,13/240,3/40,-13/60],[1/16,-61/240,3/20,13/240],
[-1/10,49/240,-7/80,-1/15],[-3/20,61/240,-23/80,7/120
],[-3/40,-1/40,0,1/40],[0,1/15,7/80,1/30],[-1/20,
19/120,-1/80,1/15],[-1/40,-1/20,-3/80,1/40],[-3/40,
0,0,0],[0,0,0,0],[13/80,-29/120,1/16,13/240],
[-7/80,-1/120,-1/20,1/48],[1/16,-1/40,1/10,-1/80],
[-21/80,37/120,-13/80,-29/240],[19/80,-13/60,27/80,7/240
],[-3/16,11/40,1/20,-1/80],[1/80,-19/80,7/80,1/80],
[3/16,-7/48,7/80,29/240],[1/80,1/240,-1/80,-7/240],
[1/80,-1/16,1/8,-3/80],[-17/80,67/240,-11/80,-11/120],
[1/80,-1/16,1/40,-1/16],[1/10,-5/24,7/40,-49/240],[
-1/20,-1/30,1/16,-7/240],[-1/20,11/120,-9/80,29/240],
[1/20,11/240,1/20,-23/240],[1/8,-3/20,1/20,11/80],
[-1/5,4/15,-1/8,11/240],[7/80,-7/240,1/20,-1/30],[
1/8,1/240,-1/10,29/240],[-1/40,-47/240,11/40,-7/240],[
0,17/240,7/80,7/240],[11/40,-83/240,1/16,7/48],[-1/8,
23/80,-17/80,-1/16],[-11/80,19/240,-9/80,1/120],[-1/80,
1/24,-11/80,-1/15],[-3/40,11/80,-1/8,1/8],[-7/80,1/80,
0,1/40],[1/16,-7/240,-1/20,1/15],[1/10,-17/120,3/16,
-17/240],[11/80,-7/60,7/80,1/15],[-1/16,-1/30,3/40,
1/12],[1/16,1/60,-1/40,-1/24],[7/80,1/16,3/80,1/20],
[-21/80,7/24,-3/80,7/120],[-1/80,1/10,-1/20,-3/40],
[11/64,-9/64,-5/64,-1/16],[1/32,-1/64,1/32,-1/64],
[7/64,1/192,0,1/96],[-1/32,13/96,5/64,5/96],[3/16,
1/96,1/32,-5/192],[-15/64,23/192,1/32,13/192],[-3/32,
-1/64,-3/64,0],[-5/64,7/48,5/64,1/24],[0,0,0,0],
[-5/32,35/192,3/32,5/96],[5/64,-1/64,-3/64,-1/64],[
-3/32,-17/96,-5/64,-5/192],[13/64,-5/48,-1/16,-5/96],[
-5/64,1/32,0,-1/64],[-3/32,1/192,1/64,5/192],[-17/20,
7/60,7/80,7/48],[1/10,29/120,13/80,23/240],[41/80,
-47/240,-13/80,-17/120],[11/40,-41/60,-5/16,-43/240],
[-1/240,7/120,1/60,1/240],[-3/80,-7/60,7/80,-1/48],
[1/80,-1/24,1/40,-7/120],[-7/48,1/15,-1/240,-1/60],
[-9/80,13/120,-1/80,-11/240],[-59/240,-1/30,-1/240,
7/120],[-1/240,1/8,1/24,1/80],[-1/80,7/30,0,1/60],
[-3/20,3/16,-1/40,-9/80],[1/20,-17/240,1/16,-1/24],
[1/40,3/80,1/80,-1/40],[1/5,-21/40,27/80,1/8],[3/40,
1/240,1/40,-19/240],[3/40,-13/240,-1/40,31/240],[0,
0,0,0],[7/40,-7/40,13/80,3/80],[-3/10,19/40,-1/80,
-3/80],[1/10,-1/5,7/80,1/16],[0,0,0,0],[0,0,0,
0],[1/10,-1/16,-1/80,9/80],[0,-59/240,3/40,1/120],
[-1/10,47/240,-1/40,1/60],[-7/40,7/80,3/80,-3/80],
[1/5,-61/240,27/80,-7/48],[-1/40,23/240,-3/40,-1/12],
[7/40,-1/3,1/10,-7/240],[7/40,-11/120,3/20,5/48],
[0,3/40,-3/40,-3/80],[1/8,-1/60,3/80,1/15],[1/80,
-1/20,-3/40,1/16],[-3/20,3/20,-1/80,-1/10],[-7/80,
1/12,1/40,-13/120],[-3/80,-13/120,13/80,-7/240],[
-11/80,31/120,-1/80,43/240],[1/80,19/80,-1/16,-3/40],
[-3/80,1/30,-1/40,-1/120],[9/80,-2/15,1/40,13/120],
[-1/80,-1/8,1/16,1/40],[1/16,-11/80,1/16,1/40],
[-3/80,-1/48,1/80,1/30],[1/80,-1/48,1/8,-13/240],
[1/16,-7/48,1/8,17/240],[11/80,13/240,-1/8,1/48],[
-11/80,7/120,1/40,-11/240],[-7/80,13/240,-9/80,-13/240],
[-7/40,13/240,-1/16,13/120],[-1/16,3/20,-1/80,1/40],
[7/80,-1/60,-9/80,1/60],[3/80,-7/120,7/80,-19/240],
[7/80,-11/80,1/16,1/16],[-3/16,1/16,3/20,-1/20],
[3/80,11/48,-7/40,1/12],[-9/80,1/6,-1/40,11/240],
[-9/80,7/48,-1/80,7/240],[3/16,-73/240,1/10,-7/120],
[-1/64,0,0,1/64],[7/64,7/192,1/64,-1/48],[1/64,
7/48,5/64,1/24],[1/4,-7/48,-5/64,-11/192],[-1/64,
1/96,3/32,1/48],[-5/32,1/8,7/64,1/16],[1/32,-3/64,
-1/32,-1/64],[-13/64,9/64,5/64,3/64],[0,0,0,0],
[-1/8,-1/64,1/64,1/32],[5/32,-13/96,-1/8,-13/192],
[-3/64,-1/6,-5/64,-7/192],[3/64,-31/192,-1/8,-1/24
],[0,5/192,0,-1/96],[-1/64,7/192,-1/16,-1/192],
[3/80,7/60,3/80,1/30],[3/80,-1/24,-3/80,-1/120],
[1/20,-1/15,-1/80,-1/120],[-21/80,11/60,13/80,11/120
],[-1/24,13/60,31/240,17/240],[1/80,-31/240,-3/80,
-11/240],[-1/8,1/240,1/40,-1/240],[-29/240,-1/12,
1/120,-7/240],[-1/80,13/240,-3/80,-7/240],[-1/48,
-7/120,-1/60,1/48],[2/15,-13/60,-11/240,-11/240],[
3/40,-1/48,-1/40,-1/240],[-9/80,3/16,-1/40,-13/80],
[1/8,-11/80,1/16,1/80],[-3/40,7/48,-3/80,-23/240],
[3/80,-13/80,1/20,3/40],[1/16,-3/80,-1/40,-1/80],
[7/80,3/80,1/20,7/80],[-3/20,-1/40,0,1/40],[-1/80,
1/6,3/80,-1/24],[-9/80,1/8,1/16,3/20],[3/80,-1/30,
-1/16,-1/60],[3/40,1/40,0,-1/40],[0,0,0,0],
[-1/10,1/20,1/40,9/80],[-7/80,7/120,3/80,13/240],
[3/80,-3/40,1/16,1/80],[-1/8,23/120,-3/40,-13/240],
[9/40,-7/40,1/5,-3/80],[-9/80,1/10,1/80,-11/80],
[3/40,-21/80,3/16,0],[0,31/240,11/80,13/120],[
9/40,-19/80,-9/80,-1/40],[11/80,-17/80,7/40,1/10],
[-3/20,1/40,1/80,-3/80],[-3/16,49/240,-1/10,-1/60],
[1/40,-17/240,1/20,-19/240],[3/80,-1/16,9/80,-1/16],
[-9/80,11/80,-9/80,1/16],[13/40,-3/10,9/80,1/20],[
1/10,-23/240,1/8,-19/240],[-9/40,71/240,-11/40,5/48],
[-1/16,7/60,-7/40,-7/240],[-1/40,-1/120,-3/80,1/120],
[-3/20,11/120,1/16,-11/120],[1/80,-1/6,7/40,1/24],
[1/16,1/30,-1/10,1/24],[-9/80,7/24,-9/40,-11/120],
[-1/8,1/60,1/80,-7/240],[-3/20,29/240,-1/4,-7/120],
[-1/8,5/48,-1/16,23/240],[-3/80,7/120,1/20,-17/240],
[3/80,-9/40,9/40,3/80],[1/80,-31/240,3/16,-11/240],
[-3/40,13/80,-1/20,-1/40],[7/80,-37/240,17/80,1/24],
[-3/80,53/240,-9/80,-13/120],[1/10,0,1/16,-1/80],
[0,-31/240,7/40,11/120],[7/80,-19/80,3/16,-1/40],
[-1/16,-1/48,-3/64,1/192],[-1/16,-1/96,3/64,1/96],
[9/64,-1/96,1/32,-1/192],[11/64,1/32,1/64,0],[1/32,
37/192,1/8,5/192],[-3/64,25/192,1/16,1/24],[-1/64,
-35/192,-3/32,-7/192],[3/32,1/192,0,-1/48],[0,0,0,
0],[-1/4,1/192,1/64,5/192],[0,1/64,-3/64,-1/32],
[1/64,-11/64,-5/64,-1/64],[7/64,-23/192,-7/64,-5/96],
[-7/64,1/6,5/64,7/192],[-1/64,-1/96,-1/32,1/96]])
]> where w := K.1 where K := ext<K|Polynomial(K,[3,-4,2,1,1])>
where K is RationalField();

return _LR;
