_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
F := FreeGroup(2) >;
//Standard generators of L3(4) are a and b where a has order 2, b has
//order 4, ab has order 7 and abb has order 5.
//Standard generators of 12b.L3(4) are preimages A and B
//where A has order 2, B has order 4, AB has order 21 and ABB has order 5. 

_LR`AI := [[a,
      a*b^-1*a*b*a*b^-1*a*b*a*b*a*b^-1*a*b*a*b*a*b^-1*a*b*a*b^-1*(a*b)^7],
       //L34.2_1 = field x duality - order 2 - not same as in Online ATLAS.
            [ a, (b^-1*a)^3*(b*a)^3*b ],
       //L34.2_2 = field  - order 2 - not same as in Online ATLAS.
            [ a, b^-1]  ]
       //L34.2_3 = duality  - order 2
                  where a is (_LR`F).1 where b is (_LR`F).2;

//four constituents permuted transitively by automorphisms
_LR`G := 
/*
Original group: c9Group("12bl34p")
From DB /nb/reps/d84.12bL34.nfdeg4.i105.M
Schur index: 1
Character: ( 84, -84, 0, -84*zeta(12)_3 - 84, 84*zeta(12)_3, 0, -84*zeta(12)_4, 
84*zeta(12)_4, 0, 2*zeta(12)_4, 2, -2, -2*zeta(12)_4, -1, -1, -84*zeta(12)_3, 
84*zeta(12)_3 + 84, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0, 0, 2*zeta(12)_3, 
2*zeta(12)_4*zeta(12)_3, -2*zeta(12)_3, -2*zeta(12)_3 - 2, 
2*zeta(12)_4*zeta(12)_3 + 2*zeta(12)_4, -2*zeta(12)_4*zeta(12)_3, 2*zeta(12)_3 +
2, -2*zeta(12)_4*zeta(12)_3 - 2*zeta(12)_4, 0, 0, 0, 0, -zeta(12)_3, 
-zeta(12)_3, zeta(12)_3 + 1, zeta(12)_3 + 1, zeta(12)_4, zeta(12)_4, 
-zeta(12)_4, -zeta(12)_4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, zeta(12)_3, 
zeta(12)_3, -zeta(12)_3 - 1, -zeta(12)_3 - 1, 0, 0, 0, 0, -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*zeta(12)_3 - zeta(12)_4, zeta(12)_4*zeta(12)_3, 
-zeta(12)_4*zeta(12)_3, zeta(12)_4*zeta(12)_3, zeta(12)_4*zeta(12)_3 + 
zeta(12)_4, 0, 0, 0, 0, 0, 0, 0, 0 )
*/
MatrixGroup<84, K | [
    Matrix(SparseMatrix(K, 84, 84, [
    <1, 4, w>,  <2, 3, w^3 - w>,  <3, 2, -w>,  <4, 1, -w^3 + w>,  <5, 8, w>,  
    <6, 7, w^3 - w>,  <7, 6, -w>,  <8, 5, -w^3 + w>,  <9, 11, w^2 - 1>,  <10, 
    12, 1>,  <11, 9, -w^2>,  <12, 10, 1>,  <13, 15, w^2 - 1>,  <14, 16, 1>,  
<15,13,-w^2>,<16,14,1>,<17,20,-1>,<18,19,-w^3+w>,<19,18,
w>,<20,17,-1>,<21,24,-1>,<22,23,-w^3+w>,<23,22,w>,<24,
21,-1>,<25,33,w^2>,<26,29,w^3>,<27,32,w^3-w>,<28,35,
-w^3>,<29,26,-w^3>,<30,36,w^2-1>,<31,34,-w>,<32,27,-w>,
<33,25,-w^2+1>,<34,31,w^3-w>,<35,28,w^3>,<36,30,-w^2>,
<37,45,w^2>,<38,41,w^3>,<39,44,w^3-w>,<40,47,-w^3>,<41,
38,-w^3>,<42,48,w^2-1>,<43,46,-w>,<44,39,-w>,<45,37,-w^2
+1>,<46,43,w^3-w>,<47,40,w^3>,<48,42,-w^2>,<49,57,w^2>,
<50,53,w^3>,<51,56,w^3-w>,<52,59,-w^3>,<53,50,-w^3>,<54,
60,w^2-1>,<55,58,-w>,<56,51,-w>,<57,49,-w^2+1>,<58,55,
w^3-w>,<59,52,w^3>,<60,54,-w^2>,<61,69,w^2>,<62,65,w^3>,
<63,68,w^3-w>,<64,71,-w^3>,<65,62,-w^3>,<66,72,w^2-1>,
<67,70,-w>,<68,63,-w>,<69,61,-w^2+1>,<70,67,w^3-w>,<71,
64,w^3>,<72,66,-w^2>,<73,81,w^2>,<74,77,w^3>,<75,80,w^3-
w>,<76,83,-w^3>,<77,74,-w^3>,<78,84,w^2-1>,<79,82,-w>,
<80,75,-w>,<81,73,-w^2+1>,<82,79,w^3-w>,<83,76,w^3>,<84,
78,-w^2>])),
Matrix(K,84,84,
[[-1/8,0,0,1/16],[-1/16,-1/8,1/16,0],[-1/16,-1/8,1/16,0
],[0,0,0,0],[0,0,1/48,0],[0,0,0,1/48],[0,0,0,1/48
],[0,0,0,0],[0,0,0,0],[-1/12,0,0,-1/24],[-1/24,
1/12,1/24,0],[0,-1/12,-1/24,1/12],[0,0,0,0],[0,0,0,
1/24],[1/24,0,-1/24,0],[0,0,1/24,0],[1/48,0,0,-1/24],
[-1/24,0,0,-1/48],[0,-1/48,1/24,1/48],[1/16,0,0,1/8],[
0,1/48,0,-1/48],[0,0,-1/48,0],[-1/48,0,1/48,0],[0,
1/16,0,-1/16],[1/16,1/8,-1/16,0],[-1/8,1/16,1/8,0],[0,
0,0,0],[1/16,1/8,-1/16,0],[0,-1/16,-1/8,1/16],[0,0,0,
0],[1/16,0,0,1/8],[0,-1/8,1/16,1/8],[0,0,0,0],[0,
-3/16,0,3/16],[0,0,0,-3/16],[0,0,3/16,0],[-1/16,1/16,
0,-1/16],[0,0,1/16,-1/16],[-1/16,0,1/16,0],[-1/16,1/16,
0,-1/16],[-1/16,0,0,1/16],[1/16,0,-1/16,0],[1/16,1/16,
-1/16,0],[1/16,0,0,1/16],[0,-1/16,0,1/16],[1/16,1/16,
0,1/16],[-1/16,-1/8,1/16,1/16],[1/8,0,-1/16,-1/16],[
1/16,1/16,-1/16,-1/16],[0,1/16,1/16,0],[1/16,0,-1/16,1/16
],[1/16,1/16,-1/16,-1/16],[0,-1/8,-1/16,0],[-1/16,0,
1/16,-1/16],[0,0,1/8,1/16],[-1/8,-1/16,1/8,1/16],[-1/16,
1/16,1/16,-1/16],[-1/16,-1/16,-1/16,1/8],[1/8,-1/16,-1/16,
-1/16],[1/16,-1/16,1/16,1/8],[-1/16,0,1/16,0],[0,-1/16,
0,0],[-1/8,0,1/16,0],[-1/16,0,1/16,0],[0,3/16,0,-1/8
],[1/8,0,-1/16,0],[-1/8,0,-1/16,0],[1/16,0,-3/16,0],[
0,-1/8,0,1/16],[0,0,0,-1/16],[0,1/16,0,0],[-1/16,0,
0,0],[1/8,0,-1/16,0],[0,1/16,0,1/16],[1/16,0,0,0],[
1/8,0,-1/16,0],[0,-1/16,0,-1/16],[-1/16,0,0,0],[-1/16,
0,1/8,0],[-1/8,0,1/16,0],[0,1/16,0,0],[0,-1/16,0,0
],[0,1/16,0,-1/16],[-1/16,0,1/16,0],[-1/8,1/16,1/8,0],
[-1/16,0,0,-1/8],[0,0,0,0],[1/16,0,0,1/8],[1/48,0,
0,0],[0,-1/48,0,1/48],[0,0,0,0],[0,1/48,0,-1/48],[
-1/24,1/12,1/24,0],[-1/12,-1/24,1/12,0],[-1/24,0,0,1/12
],[0,0,0,0],[1/24,0,-1/24,0],[0,1/24,0,0],[1/24,0,
0,0],[0,0,0,0],[-1/48,0,0,1/24],[-1/8,0,0,1/16],[
0,1/48,-1/24,-1/48],[-1/48,0,0,1/24],[0,-1/48,0,1/48],[
0,0,1/16,0],[1/48,0,-1/48,0],[0,-1/48,0,1/48],[0,1/8,
-1/16,-1/8],[0,0,0,-3/16],[0,-1/8,1/16,1/8],[0,0,0,0
],[0,0,0,0],[1/16,0,0,1/8],[0,-1/8,1/16,1/8],[-3/16,
0,0,0],[0,-3/16,0,3/16],[0,0,0,0],[0,-1/16,-1/8,1/16
],[-1/16,0,0,-1/8],[-1/16,0,0,-1/16],[-1/16,-1/8,1/16,
1/16],[1/16,0,-1/16,1/16],[1/16,0,0,0],[0,0,0,1/16],
[1/16,1/16,-1/16,0],[1/16,0,-1/16,1/16],[-1/16,1/16,1/8,
0],[1/16,1/16,0,1/16],[0,-1/16,0,1/16],[-1/16,0,0,1/16
],[0,-1/16,1/16,0],[1/8,1/16,-1/8,-1/16],[1/8,-1/16,
-1/16,-1/16],[0,0,1/16,1/16],[-1/16,1/16,0,-1/16],[0,0,
1/16,-1/16],[0,0,1/8,1/16],[0,0,1/16,1/16],[-1/8,-1/16,
1/16,-1/16],[-1/16,-1/16,-1/16,1/8],[-1/16,1/16,1/16,-1/16
],[0,-1/8,-1/16,0],[-1/16,-1/16,0,0],[-1/16,0,3/16,0],
[0,1/16,0,0],[0,0,-1/16,0],[1/16,0,1/16,0],[0,-1/16,
0,1/8],[-1/8,0,-1/16,0],[0,0,-1/16,0],[1/16,0,-1/16,0
],[0,0,0,-1/16],[0,-1/8,0,1/16],[0,3/16,0,-1/8],[
1/16,0,0,0],[1/8,0,-1/16,0],[0,1/16,0,-1/16],[-1/16,
0,1/8,0],[0,0,-1/16,0],[0,1/16,0,-1/16],[-1/16,0,1/8,
0],[-1/16,0,1/8,0],[0,0,-1/16,0],[0,-1/16,0,0],[0,
1/16,0,0],[0,-1/16,0,-1/16],[-1/16,0,-1/16,0],[1/8,0,
0,-1/16],[0,0,0,0],[-1/16,0,0,-1/8],[1/16,0,0,1/8],
[0,0,-1/48,0],[0,0,0,0],[0,-1/48,0,1/48],[0,1/48,0,
-1/48],[1/24,0,0,-1/12],[0,0,0,0],[-1/24,0,0,1/12],[
0,1/12,1/24,-1/12],[-1/24,0,0,0],[0,0,0,0],[1/24,0,
0,0],[0,0,-1/24,0],[1/48,-1/24,-1/48,0],[-1/24,-1/48,
1/24,0],[-1/8,0,0,1/16],[1/48,-1/24,-1/48,0],[0,0,0,
-1/48],[-1/48,0,0,0],[0,0,1/16,0],[0,0,0,-1/48],[
3/16,0,-3/16,0],[0,0,0,0],[0,0,-3/16,0],[1/16,0,0,
1/8],[0,3/16,0,0],[1/16,0,0,1/8],[0,0,0,0],[0,1/8,
-1/16,-1/8],[0,1/16,1/8,-1/16],[-1/8,1/16,1/8,0],[0,0,
0,0],[0,-1/8,1/16,1/8],[-1/16,-1/16,-1/16,1/16],[0,
-1/16,0,0],[-1/8,0,1/16,1/16],[1/16,1/16,-1/16,0],[0,
1/16,-1/16,-1/8],[0,1/16,-1/16,0],[0,0,1/16,0],[-1/16,
0,1/16,-1/16],[1/16,0,0,-1/16],[0,0,1/16,-1/16],[0,
1/16,0,0],[1/16,0,0,1/16],[1/16,1/8,-1/8,-1/16],[-1/16,
1/16,0,0],[-1/16,1/16,-1/16,-1/8],[0,0,1/8,1/16],[
-1/16,1/8,1/8,-1/16],[1/16,1/16,0,0],[0,1/16,-1/16,0],[
0,0,-1/16,-1/16],[0,1/8,1/16,0],[0,1/16,1/16,0],[1/16,
-1/16,0,0],[-1/8,-1/16,1/8,1/16],[0,0,1/16,0],[0,
-1/16,0,-1/16],[1/16,0,0,0],[-1/8,0,-1/16,0],[0,-1/16,
0,1/16],[-1/16,0,0,0],[-1/16,0,1/8,0],[0,0,1/16,0],
[0,-3/16,0,1/8],[0,-1/16,0,0],[0,1/16,0,1/16],[1/16,
0,-3/16,0],[1/16,0,0,0],[0,0,0,1/16],[1/16,0,-1/16,0
],[-1/16,0,1/8,0],[0,0,0,1/16],[1/16,0,1/16,0],[
1/16,0,-1/16,0],[1/16,0,-1/8,0],[0,1/16,0,1/16],[0,
1/16,0,1/16],[0,0,0,-1/16],[-1/8,0,1/16,0],[0,0,0,0
],[1/16,1/8,-1/16,0],[0,-1/8,1/16,1/8],[1/16,0,0,1/8],
[0,0,0,0],[0,0,0,-1/48],[0,1/48,0,0],[0,1/48,0,
-1/48],[0,-1/12,-1/24,1/12],[-1/12,-1/24,1/12,0],[0,0,
0,0],[0,1/12,1/24,-1/12],[0,0,1/24,0],[0,1/24,0,0],
[0,0,0,0],[0,0,-1/24,0],[0,-1/8,1/16,1/8],[0,1/48,
-1/24,-1/48],[-1/24,-1/48,1/24,0],[0,1/24,1/48,-1/24],[
0,1/16,0,0],[1/48,0,-1/48,0],[-1/48,0,0,0],[0,1/48,
0,0],[0,0,0,0],[1/8,-1/16,-1/8,0],[0,-1/8,1/16,1/8],
[0,0,3/16,0],[-1/8,0,0,1/16],[-3/16,0,0,0],[3/16,0,
0,0],[0,0,0,0],[0,1/16,1/8,-1/16],[1/8,0,0,-1/16],[
1/8,0,0,-1/16],[0,0,0,0],[0,0,-1/16,0],[0,-1/16,
-1/16,1/16],[1/16,0,0,1/16],[1/8,0,-1/16,-1/16],[-1/16,
1/16,1/16,-1/16],[-1/16,1/16,1/8,0],[1/16,-1/16,-1/8,0],
[0,0,-1/16,0],[1/16,-1/16,0,0],[1/16,-1/16,-1/16,0],[
1/16,-1/16,-1/16,1/16],[1/16,0,-1/16,0],[0,-1/16,1/16,0
],[1/16,0,-1/16,-1/8],[-1/8,-1/16,1/8,1/16],[1/16,-1/16,
1/16,1/8],[-1/16,0,1/16,1/16],[-1/8,-1/16,1/16,-1/16],[
1/8,1/16,-1/16,1/16],[0,-1/16,1/16,0],[1/16,1/16,0,-1/16
],[1/16,1/8,0,-1/8],[1/16,0,-1/16,-1/16],[-1/16,0,1/16,
-1/16],[1/16,0,-1/8,0],[0,1/8,0,1/16],[1/16,0,-3/16,0
],[-1/16,0,0,0],[0,0,0,-1/16],[1/16,0,-1/16,0],[
-1/16,0,1/16,0],[1/16,0,-1/8,0],[0,-1/16,0,1/16],[0,
-1/16,0,3/16],[0,0,0,1/16],[1/8,0,-1/16,0],[-1/16,0,
1/16,0],[0,1/16,0,-1/8],[-1/8,0,1/16,0],[-1/16,0,1/16,
0],[0,-1/16,0,1/8],[0,0,-1/16,0],[0,0,1/16,0],[
-1/16,0,1/16,0],[0,1/8,0,-1/16],[0,1/8,0,-1/16],[0,
1/16,0,-1/8],[-1/16,0,0,0],[0,-5/16,0,0],[0,0,-5/16,
0],[0,0,-5/16,0],[0,0,0,0],[1/16,0,0,-1/24],[1/24,
1/16,-1/24,0],[1/24,1/16,-1/24,0],[0,0,0,0],[0,0,0,0
],[-1/12,-1/12,1/12,0],[0,1/12,1/12,-1/12],[-1/12,0,0,
1/12],[0,0,0,0],[-1/24,-1/8,1/24,0],[0,1/24,1/8,-1/24
],[-1/8,0,0,1/24],[23/48,-1/24,-23/48,0],[-1/24,-23/48,
1/24,0],[1/24,0,0,23/48],[-5/16,5/8,5/16,0],[-1/6,0,0,
3/16],[3/16,0,0,1/6],[0,1/6,-3/16,-1/6],[0,0,0,5/16],
[-1/8,0,-3/16,0],[0,3/16,0,-5/16],[0,3/4,0,-3/4],[
-1/8,0,-3/16,0],[0,-1/8,0,5/16],[0,-3/4,0,3/4],[5/16,
0,-3/16,0],[3/16,0,1/8,0],[3/4,0,0,0],[1/8,0,0,3/16
],[-1/8,-3/16,1/8,0],[3/16,0,0,-1/8],[1/16,1/8,-1/16,
1/16],[-3/16,1/16,1/8,0],[-1/4,-3/8,-3/16,-1/4],[1/16,
1/8,-1/16,1/16],[-3/16,1/16,-3/16,0],[1/4,3/8,3/16,1/4],
[0,3/16,-1/16,3/16],[1/16,-3/16,-1/16,3/8],[1/4,-1/4,
-5/8,-3/16],[3/16,-1/8,-3/16,1/16],[0,1/16,3/16,-1/8],[
-1/16,-3/16,1/8,0],[1/8,-1/8,-5/16,-1/16],[3/16,5/16,-1/8,
-3/16],[1/4,3/16,3/16,-5/8],[1/8,-1/8,-5/16,-1/16],[3/16,
0,-1/8,1/8],[-1/4,-3/16,-3/16,5/8],[1/8,-3/16,-1/8,1/8],
[1/8,-1/8,0,-1/16],[5/8,1/4,-7/16,3/16],[1/4,3/16,-1/16,
1/16],[-3/16,-1/4,1/4,3/16],[1/4,-1/16,-3/16,-3/16],[
-1/8,1/8,-1/16,0],[-1/8,1/16,1/8,-3/16],[5/16,1/8,-1/8,
3/8],[-1/8,1/8,-1/16,0],[-1/8,1/16,1/8,-3/16],[-5/16,
-1/8,1/8,-3/8],[-3/16,1/8,1/8,-1/8],[-1/8,1/8,-1/16,0],[
-3/8,5/16,1/2,-1/8],[-1/8,1/16,0,-1/8],[1/8,1/16,-1/8,
1/16],[-1/16,0,-1/16,1/8],[-1/16,0,0,-1/8],[1/8,0,0,
-1/16],[3/16,3/8,-3/16,0],[-1/16,0,0,-1/8],[1/8,0,0,
-1/16],[-3/16,-3/8,3/16,0],[-1/16,-1/8,1/16,0],[-1/16,0,
0,-1/8],[0,3/16,3/8,-3/16],[0,-1/16,1/8,1/16],[-1/8,0,
0,-1/16],[0,1/8,1/16,-1/8],[0,-5/16,0,5/16],[5/16,0,
-5/16,0],[0,0,0,0],[-5/16,0,5/16,0],[1/16,-1/24,-1/16,
0],[1/24,0,0,1/16],[0,0,0,0],[-1/24,0,0,-1/16],[0,
1/12,1/12,-1/12],[0,-1/12,1/12,1/12],[-1/12,1/12,1/12,0],
[0,0,0,0],[0,1/24,1/8,-1/24],[0,-1/8,1/24,1/8],[-1/8,
1/24,1/8,0],[0,0,0,0],[-23/48,1/24,23/48,0],[-5/8,
-5/16,5/8,0],[-1/24,0,0,-23/48],[-23/48,1/24,23/48,0],[
1/6,0,0,-3/16],[-5/16,0,0,0],[0,-1/6,3/16,1/6],[1/6,
0,0,-3/16],[-3/16,0,-1/8,0],[-1/8,-3/16,1/8,0],[5/16,
0,-1/8,0],[0,-3/4,0,0],[3/4,0,-3/4,0],[5/16,0,-3/16,
0],[5/16,0,-1/8,0],[-3/16,1/8,3/16,0],[1/8,0,0,3/16],
[3/4,0,0,0],[0,-1/8,0,5/16],[-3/16,0,5/16,0],[-1/16,
3/16,1/16,-3/8],[0,1/16,3/16,-1/8],[0,-3/16,1/16,1/8],[
-3/16,-1/4,7/16,5/8],[-3/8,-7/16,-1/4,1/4],[0,3/16,-1/16,
3/16],[0,-3/16,1/16,1/8],[-1/16,3/16,-1/16,-3/16],[3/16,
-1/8,-3/16,1/16],[1/4,-1/4,-5/8,-3/16],[-3/16,1/16,-3/16,0
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0,1/8,1/16,-1/16],[-1/16,1/16,0,1/8],[0,1/16,0,0],[
-5/16,1/16,-1/16,0],[0,-1/8,1/16,1/16],[-3/16,1/8,3/16,
-1/16],[-1/8,0,1/8,1/8],[3/16,1/16,-1/8,-1/16],[-1/16,0,
1/16,-1/4],[0,0,-1/16,0],[0,3/16,-1/8,-1/16],[-1/4,1/8,
1/8,0],[-1/16,1/8,1/16,-3/8],[-1/16,3/16,0,-1/16],[1/16,
0,-1/8,-1/8],[1/16,1/16,1/8,-1/16],[-1/8,3/16,3/16,-3/16
],[0,3/16,1/8,-3/16],[-1/16,-5/16,1/8,-1/16],[-3/16,3/16,
3/16,0],[-1/8,1/8,1/8,-1/16],[1/8,0,-1/8,3/16],[1/16,
-1/16,1/16,1/16],[1/16,1/16,-1/8,0],[1/16,-1/16,1/16,1/16
],[0,1/16,1/16,-1/16],[3/16,-1/16,-1/16,0],[-7/16,1/16,
1/4,-1/8],[1/16,-1/16,-1/8,3/16],[-1/16,-1/16,1/8,3/16],[
1/16,1/4,-1/4,0],[-1/16,-1/16,-1/16,1/16],[1/8,-5/16,1/8,
0],[0,0,1/8,1/16],[-3/16,3/16,1/16,-1/16],[-1/16,1/16,
1/4,-3/16],[-3/16,1/8,5/16,-1/8],[-1/8,0,-1/8,1/16],[
-1/8,3/16,1/8,-1/16],[1/8,-3/16,-1/8,1/16],[-3/16,0,1/8,
-1/4],[-1/16,-1/8,1/16,-1/16],[-1/16,1/16,0,-3/16],[
-1/16,-1/8,1/16,1/8],[0,0,-1/16,1/4],[3/16,0,-1/16,-1/8
],[-1/16,-1/8,3/16,-1/8],[1/4,-3/16,0,1/16],[1/16,-1/8,
3/16,1/16],[-1/16,0,3/16,-1/8],[1/16,1/16,1/16,-1/16],[
-1/16,-3/16,-1/16,5/16],[0,-3/16,1/8,1/8],[0,-1/8,0,3/16
],[0,1/16,-1/8,-1/16],[1/4,1/16,-5/16,1/8],[1/16,0,-1/8,
0],[1/8,1/16,-3/16,1/16],[1/48,0,-1/48,0],[-1/48,1/48,
0,0],[0,1/48,-1/24,1/48],[1/16,-1/48,-1/48,0],[1/48,
1/48,-1/16,1/12],[0,-1/48,-1/16,1/16],[1/24,7/48,1/16,
-1/16],[-1/8,3/16,-1/48,-7/48],[1/16,1/48,-1/48,0],[
-1/12,5/48,1/48,-1/16],[0,1/48,-1/48,1/48],[1/24,-1/48,
-1/48,1/16],[3/16,-1/12,-13/48,1/16],[-1/48,1/16,1/12,-1/24
],[1/12,-1/12,1/48,1/48],[1/48,-1/8,1/16,1/16],[1/24,
-1/24,-1/48,5/48],[-1/48,-1/48,-1/12,1/16],[1/8,1/16,-5/48,
-1/24],[0,1/24,-5/48,1/48],[-1/16,3/16,-1/16,-3/16],[
-1/8,1/16,1/16,1/8],[1/16,0,-3/8,1/16],[1/8,1/16,-1/16,0
],[1/16,-1/16,-1/8,1/16],[-1/16,0,0,1/16],[-1/8,1/8,
1/16,-1/8],[-1/4,1/16,1/8,0],[-1/8,0,-1/4,1/8],[1/16,
1/8,1/16,0],[0,0,-1/16,0],[1/16,-1/16,1/8,1/16],[-3/16,
0,0,-1/8],[-1/16,1/4,0,-1/4],[-1/8,1/16,3/16,0],[1/8,
0,-3/8,1/16],[0,-3/16,3/16,1/16],[0,0,0,-1/16],[-1/8,
-1/8,1/8,-1/8],[1/8,1/8,0,0],[-3/16,1/8,1/16,0],[1/16,
1/16,-1/16,-3/16],[-1/8,-1/16,1/8,1/8],[3/16,-1/16,-1/16,
1/16],[3/16,1/16,-1/8,-1/8],[-1/8,1/16,0,1/16],[-1/4,
1/8,-3/16,-1/16],[-1/16,1/8,1/16,-1/16],[-1/8,1/8,-1/16,
-1/16],[-3/16,1/8,3/16,-1/8],[-1/16,1/8,1/16,-1/16],[
-3/8,1/8,5/16,-1/16],[1/16,-1/8,-1/16,1/16],[3/16,0,0,
3/16],[0,-3/16,1/16,1/16],[1/16,1/16,-1/16,0],[-1/16,
1/16,3/16,-1/16],[-1/8,0,1/4,-5/16],[1/8,-1/16,0,-1/8],[
1/8,1/8,-1/8,3/16],[1/4,-1/8,0,-1/16],[-1/16,0,1/16,1/8
],[1/8,-1/4,1/16,3/16],[1/4,-1/4,-1/4,3/16],[-3/16,1/8,
1/16,-3/16],[-1/16,-1/8,1/16,1/16],[-1/16,1/8,-1/8,-1/8],
[0,-1/4,1/16,1/8],[3/16,0,-1/16,0],[1/16,-1/4,-1/16,1/4
],[1/16,-5/16,-1/8,1/8],[-1/8,1/4,1/16,-1/16],[1/16,-1/8,
-3/16,1/8],[1/8,3/16,-1/8,-1/16],[1/8,0,-3/16,1/4],[
-1/8,0,-1/16,1/16],[1/8,-1/8,1/8,-1/16],[-1/8,0,1/8,1/16
],[-1/16,-1/16,0,-1/16],[0,1/8,-1/8,1/16]])
]> where w := K.1 where K := ext<K|Polynomial(K, [1, 0, -1, 0, 1])> where K is 
RationalField();

return _LR;
