//Standard generators of U3(9) are a and b where a has order 2,
//b has order 6 and ab has order 15.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
   _LR`AI:=[[a, b*a*b^-1*a*b^-1*a*b^3*a*b^-1*a*b^-2*a*b^-2], //order 4
            [a, b^-1]] //order 2
                  where a is (_LR`F).1 where b is (_LR`F).2;
//second automorphism is square of first - must handle that somehow!
//4 constituents
_LR`G :=
/*
Original group: c9Group("u39p")
From DB /nb/reps/d73.U39.ni730.M
Schur index: 1
Character: ( 73, 9, -8, 1, 1, -9*zeta(5)_5^3 - zeta(5)_5^2 - zeta(5)_5 - 1, 
zeta(5)_5^3 - 8*zeta(5)_5, -8*zeta(5)_5^2 + zeta(5)_5, 8*zeta(5)_5^3 + 
9*zeta(5)_5^2 + 8*zeta(5)_5 + 8, zeta(5)_5^3 + zeta(5)_5^2 + 1, -zeta(5)_5^3 - 
zeta(5)_5^2, 0, 1, 1, -8*zeta(5)_5^3 - 7*zeta(5)_5^2 - 8*zeta(5)_5 - 8, 
8*zeta(5)_5^2 + zeta(5)_5, 7*zeta(5)_5^3 - zeta(5)_5^2 - zeta(5)_5 - 1, 
zeta(5)_5^3 + 8*zeta(5)_5, -zeta(5)_5^2, -zeta(5)_5, zeta(5)_5^3 + zeta(5)_5^2 +
zeta(5)_5 + 1, -zeta(5)_5^3, -zeta(5)_5^3 - zeta(5)_5^2 - 2*zeta(5)_5 - 2, 
-zeta(5)_5^3 + zeta(5)_5^2 - 1, zeta(5)_5^3 - zeta(5)_5^2 - 1, zeta(5)_5^3 + 
zeta(5)_5^2 + 2*zeta(5)_5, zeta(5)_5^3 + zeta(5)_5^2 + 2, -zeta(5)_5^3 - 
zeta(5)_5^2 + 1, zeta(5)_5^3 + zeta(5)_5, zeta(5)_5^2 + zeta(5)_5, -zeta(5)_5^3 
- zeta(5)_5 - 1, -zeta(5)_5^2 - zeta(5)_5 - 1, -1, -1, -1, -1, zeta(5)_5, 
zeta(5)_5^3, zeta(5)_5^2, -zeta(5)_5^3 - zeta(5)_5^2 - zeta(5)_5 - 1, 
-2*zeta(5)_5^3 - zeta(5)_5^2 - zeta(5)_5 - 1, zeta(5)_5^3 - zeta(5)_5, 
zeta(5)_5^3 + 2*zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2 + zeta(5)_5, 
zeta(5)_5^3, -zeta(5)_5^3 - zeta(5)_5^2 - zeta(5)_5 - 1, zeta(5)_5, zeta(5)_5^2,
zeta(5)_5^3, zeta(5)_5^2, -zeta(5)_5^3 - zeta(5)_5^2 - zeta(5)_5 - 1, zeta(5)_5,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
zeta(5)_5^3 + zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5^3, 
-zeta(5)_5, zeta(5)_5^3 + zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5,
zeta(5)_5^3 + zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^2, -zeta(5)_5^3, 
-zeta(5)_5, zeta(5)_5^3 + zeta(5)_5^2 + zeta(5)_5 + 1, -zeta(5)_5^3, -zeta(5)_5,
-zeta(5)_5^3, -zeta(5)_5^2 )
*/

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

return _LR;
