_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/d48.12bL34.nfdeg8.i63.M
Schur index: 1
Character: ( 48, -48, 0, -48*zeta(60)_3 - 48, 48*zeta(60)_3, 0, 48*zeta(60)_4, 
-48*zeta(60)_4, 0, 0, 0, 0, 0, zeta(60)_5^3 + zeta(60)_5^2 + 1, -zeta(60)_5^3 - 
zeta(60)_5^2, 48*zeta(60)_3 + 48, -48*zeta(60)_3, 0, 0, 0, -1, -1, 0, 0, 
-zeta(60)_5^3 - zeta(60)_5^2 - 1, zeta(60)_5^3 + zeta(60)_5^2, 
48*zeta(60)_4*zeta(60)_3 + 48*zeta(60)_4, -48*zeta(60)_4*zeta(60)_3 - 
48*zeta(60)_4, -48*zeta(60)_4*zeta(60)_3, 48*zeta(60)_4*zeta(60)_3, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, zeta(60)_3*zeta(60)_5^3 + zeta(60)_3*zeta(60)_5^2 
+ zeta(60)_5^3 + zeta(60)_5^2, -zeta(60)_3*zeta(60)_5^3 - 
zeta(60)_3*zeta(60)_5^2, -zeta(60)_3*zeta(60)_5^3 - zeta(60)_3*zeta(60)_5^2 - 
zeta(60)_3 - zeta(60)_5^3 - zeta(60)_5^2 - 1, zeta(60)_3*zeta(60)_5^3 + 
zeta(60)_3*zeta(60)_5^2 + zeta(60)_3, zeta(60)_4*zeta(60)_5^3 + 
zeta(60)_4*zeta(60)_5^2, -zeta(60)_4*zeta(60)_5^3 - zeta(60)_4*zeta(60)_5^2, 
-zeta(60)_4*zeta(60)_5^3 - zeta(60)_4*zeta(60)_5^2 - zeta(60)_4, 
zeta(60)_4*zeta(60)_5^3 + zeta(60)_4*zeta(60)_5^2 + zeta(60)_4, -zeta(60)_3, 
-zeta(60)_3, zeta(60)_3 + 1, zeta(60)_3 + 1, 0, 0, 0, 0, zeta(60)_4, 
-zeta(60)_4, -zeta(60)_4, zeta(60)_4, -zeta(60)_3*zeta(60)_5^3 - 
zeta(60)_3*zeta(60)_5^2 - zeta(60)_3, zeta(60)_3*zeta(60)_5^3 + 
zeta(60)_3*zeta(60)_5^2, -zeta(60)_3*zeta(60)_5^3 - zeta(60)_3*zeta(60)_5^2 - 
zeta(60)_5^3 - zeta(60)_5^2, zeta(60)_3*zeta(60)_5^3 + zeta(60)_3*zeta(60)_5^2 +
zeta(60)_3 + zeta(60)_5^3 + zeta(60)_5^2 + 1, -zeta(60)_3 - 1, zeta(60)_3, 
zeta(60)_3, -zeta(60)_3 - 1, -zeta(60)_4*zeta(60)_3*zeta(60)_5^3 - 
zeta(60)_4*zeta(60)_3*zeta(60)_5^2 - zeta(60)_4*zeta(60)_5^3 - 
zeta(60)_4*zeta(60)_5^2, -zeta(60)_4*zeta(60)_3*zeta(60)_5^3 - 
zeta(60)_4*zeta(60)_3*zeta(60)_5^2 - zeta(60)_4*zeta(60)_3, 
-zeta(60)_4*zeta(60)_3*zeta(60)_5^3 - zeta(60)_4*zeta(60)_3*zeta(60)_5^2, 
zeta(60)_4*zeta(60)_3*zeta(60)_5^3 + zeta(60)_4*zeta(60)_3*zeta(60)_5^2 + 
zeta(60)_4*zeta(60)_5^3 + zeta(60)_4*zeta(60)_5^2, 
zeta(60)_4*zeta(60)_3*zeta(60)_5^3 + zeta(60)_4*zeta(60)_3*zeta(60)_5^2, 
-zeta(60)_4*zeta(60)_3*zeta(60)_5^3 - zeta(60)_4*zeta(60)_3*zeta(60)_5^2 - 
zeta(60)_4*zeta(60)_3 - zeta(60)_4*zeta(60)_5^3 - zeta(60)_4*zeta(60)_5^2 - 
zeta(60)_4, zeta(60)_4*zeta(60)_3*zeta(60)_5^3 + 
zeta(60)_4*zeta(60)_3*zeta(60)_5^2 + zeta(60)_4*zeta(60)_3, 
zeta(60)_4*zeta(60)_3*zeta(60)_5^3 + zeta(60)_4*zeta(60)_3*zeta(60)_5^2 + 
zeta(60)_4*zeta(60)_3 + zeta(60)_4*zeta(60)_5^3 + zeta(60)_4*zeta(60)_5^2 + 
zeta(60)_4, -zeta(60)_4*zeta(60)_3, zeta(60)_4*zeta(60)_3 + zeta(60)_4, 
zeta(60)_4*zeta(60)_3, -zeta(60)_4*zeta(60)_3, -zeta(60)_4*zeta(60)_3 - 
zeta(60)_4, zeta(60)_4*zeta(60)_3, zeta(60)_4*zeta(60)_3 + zeta(60)_4, 
-zeta(60)_4*zeta(60)_3 - zeta(60)_4 )
*/

MatrixGroup<48,K | [
Matrix(SparseMatrix(K,48,48,[<1,1,1/4*(3*w^7 - 8*w^5 + 20*w^3
- w)>,<1,7,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<2,2,1>,
<2,3,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<3,3,-1>,<4,4,
-1>,<5,1,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<5,4,2>,<5,
5,1>,<5,6,1/8*(3*w^7 - w^6 - 8*w^5 + 24*w^3 - w - 5)>,<5,7,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<5,8,1/4*(3*w^7 - 8*w^5 +
24*w^3 - w)>,<6,6,-1>,<7,1,1/4*(-3*w^7 + 8*w^5 - 20*w^3 +
w - 4)>,<7,7,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<8,8,-1>,
<9,1,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<9,2,1/8*(3*w^7 -
w^6 - 8*w^5 + 24*w^3 - w - 5)>,<9,4,1/8*(-3*w^7 - w^6 + 8*w^5 -
24*w^3 + w - 5)>,<9,5,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<9,6,
1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<9,8,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w + 4)>,<9,9,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<9,11,
1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<9,12,1/8*(-3*w^7 - w^6 +
8*w^5 - 24*w^3 + w - 5)>,<10,1,1/4*(15*w^7 - 40*w^5 + 104*w^3 -
5*w)>,<10,2,1/8*(-9*w^7 + w^6 + 24*w^5 - 64*w^3 + 3*w + 13)>,
<10,3,1/8*(-9*w^7 - w^6 + 24*w^5 - 64*w^3 + 3*w - 13)>,<10,4,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<10,5,1/8*(-15*w^7 - w^6 +
40*w^5 - 104*w^3 + 5*w - 21)>,<10,6,-2>,<10,7,1/8*(15*w^7 -
w^6 - 40*w^5 + 104*w^3 - 5*w - 21)>,<10,8,1/4*(3*w^7 - 8*w^5 +
20*w^3 - w - 4)>,<10,9,1/8*(-15*w^7 + w^6 + 40*w^5 - 104*w^3 +
5*w + 21)>,<10,10,1>,<10,11,1/8*(-15*w^7 + w^6 + 40*w^5 -
104*w^3 + 5*w + 21)>,<10,12,1/8*(9*w^7 + w^6 - 24*w^5 + 64*w^3 -
3*w + 13)>,<11,1,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w + 4)>,<11,4,
1/8*(9*w^7 + w^6 - 24*w^5 + 64*w^3 - 3*w + 13)>,<11,6,1/8*(-9*w^7
- w^6 + 24*w^5 - 64*w^3 + 3*w - 13)>,<11,7,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w + 4)>,<11,8,1/8*(9*w^7 - w^6 - 24*w^5 + 64*w^3 - 3*w -
13)>,<11,11,1>,<12,1,1/4*(-9*w^7 + 24*w^5 - 64*w^3 + 3*w)>,
<12,2,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<12,3,1/4*(-3*w^7 +
8*w^5 - 20*w^3 + w + 4)>,<12,4,1/8*(9*w^7 + w^6 - 24*w^5 + 64*w^3 -
3*w + 13)>,<12,5,1/8*(9*w^7 + w^6 - 24*w^5 + 64*w^3 - 3*w + 13)>,
<12,7,1/8*(-9*w^7 + w^6 + 24*w^5 - 64*w^3 + 3*w + 13)>,<12,8,
1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<12,9,1/8*(9*w^7 - w^6 -
24*w^5 + 64*w^3 - 3*w - 13)>,<12,11,1/8*(9*w^7 - w^6 - 24*w^5 +
64*w^3 - 3*w - 13)>,<12,12,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,
<13,13,1>,<14,14,1>,<15,15,1>,<15,18,1>,<15,20,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w + 4)>,<15,21,1/4*(-3*w^7 +
8*w^5 - 20*w^3 + w - 4)>,<15,22,1/4*(-3*w^7 + 8*w^5 - 20*w^3 +
w)>,<15,24,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<16,13,1>,
<16,14,1>,<16,16,-1>,<16,21,-1>,<17,13,-1>,<17,14,
-1>,<17,15,-1>,<17,17,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,
<17,23,-1>,<17,24,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<18,13,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<18,14,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w)>,<18,17,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w + 4)>,<18,
21,1>,<18,22,1>,<18,24,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,
<19,13,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<19,14,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w)>,<19,15,-1>,<19,17,-1>,<19,18,-1>,
<19,19,-1>,<19,22,-1>,<19,23,-1>,<19,24,1/2*(-3*w^7 +
8*w^5 - 20*w^3 + w - 2)>,<20,15,-1>,<20,17,-1>,<20,18,-1>,
<20,20,-1>,<20,21,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<20,22,
-1>,<20,23,-1>,<20,24,1/2*(-3*w^7 + 8*w^5 - 20*w^3 + w - 2)>,
<21,21,1>,<22,13,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<22,14,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<22,17,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w + 4)>,<22,18,1>,<22,21,-1>,<22,24,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w + 4)>,<23,15,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w -
4)>,<23,17,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<23,18,-1>,
<23,20,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<23,21,1/4*(3*w^7
- 8*w^5 + 20*w^3 - w + 4)>,<23,22,1/4*(3*w^7 - 8*w^5 + 20*w^3 -
w)>,<23,23,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<23,24,-2>,<24,
13,1>,<24,14,1>,<24,15,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,
<24,17,1>,<24,23,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<25,
21,1>,<25,22,1>,<25,27,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,
<26,13,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<26,14,1/4*(-3*w^7 +
8*w^5 - 20*w^3 + w)>,<26,15,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,
<26,17,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w + 4)>,<26,18,1>,<26,
21,-1>,<26,24,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<26,28,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<27,13,-1>,<27,14,-1>,
<27,17,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<27,18,1/4*(-3*w^7
+ 8*w^5 - 20*w^3 + w)>,<27,24,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w +
4)>,<27,25,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<28,15,-1>,<28,
18,-1>,<28,20,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<28,21,
1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<28,24,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w - 4)>,<28,26,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<29,
29,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<29,30,1/4*(3*w^7 - 8*w^5 +
20*w^3 - w - 4)>,<30,29,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,
<30,30,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<31,30,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w + 4)>,<31,31,-1>,<31,47,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w - 4)>,<32,32,-1>,<32,36,1/4*(-3*w^7 + 8*w^5 - 20*w^3
+ w - 4)>,<32,38,-2>,<32,41,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w +
4)>,<33,30,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w + 4)>,<33,33,-1>,
<33,44,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<33,47,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w - 4)>,<34,29,1/2*(-3*w^7 + 8*w^5 - 20*w^3 +
w)>,<34,34,1>,<34,37,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,
<35,30,1/2*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<35,35,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w)>,<35,39,-2>,<35,42,1/4*(-3*w^7 + 8*w^5 -
20*w^3 + w + 4)>,<35,43,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,
<36,36,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<36,38,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w + 4)>,<36,41,1/4*(-3*w^7 + 8*w^5 - 20*w^3 +
w - 4)>,<37,29,2>,<37,30,1/2*(3*w^7 - 8*w^5 + 20*w^3 - w)>,
<37,37,-1>,<38,38,1>,<39,29,1/4*(-3*w^7 + 8*w^5 - 20*w^3 +
w + 4)>,<39,35,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w - 4)>,<39,39,
1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,<39,42,1/4*(3*w^7 - 8*w^5 +
20*w^3 - w + 4)>,<40,29,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,
<40,40,-1>,<40,45,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<41,
36,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<41,38,1/4*(3*w^7 -
8*w^5 + 20*w^3 - w + 4)>,<41,41,1/4*(-3*w^7 + 8*w^5 - 20*w^3 + w)>,
<42,30,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<42,39,1/4*(-3*w^7 +
8*w^5 - 20*w^3 + w - 4)>,<42,42,1>,<42,43,1/4*(3*w^7 - 8*w^5 +
20*w^3 - w - 4)>,<43,30,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,
<43,35,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<43,39,1/4*(-3*w^7
+ 8*w^5 - 20*w^3 + w - 4)>,<43,42,1/4*(-3*w^7 + 8*w^5 - 20*w^3 +
w + 4)>,<43,43,-1>,<44,44,1>,<45,29,1/4*(3*w^7 - 8*w^5 +
20*w^3 - w + 4)>,<45,30,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w + 4)>,<45,
45,1>,<46,29,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<46,30,
-2>,<46,45,1/2*(3*w^7 - 8*w^5 + 20*w^3 - w)>,<46,46,-1>,<46,
48,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<47,29,1/4*(-3*w^7 +
8*w^5 - 20*w^3 + w - 4)>,<47,30,1/4*(-3*w^7 + 8*w^5 - 20*w^3 +
w - 4)>,<47,47,1>,<48,29,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w -
4)>,<48,30,1/4*(3*w^7 - 8*w^5 + 20*w^3 - w - 4)>,<48,48,1>
])),Matrix(K,48,48,
[[17/16,11/32,-61/80,-49/80,3/10,21/80,-3/40,-13/160],
[27/160,-15/32,1/10,3/8,-1/40,-1/8,-1/160,1/32],[
-9/32,29/64,-23/80,-99/80,3/20,41/80,-11/160,-51/320],
[-27/64,-11/80,7/16,77/40,-1/16,-61/80,1/64,1/4],
[-77/160,-17/320,31/40,119/40,-9/40,-23/20,11/160,
139/320],[-109/320,-13/80,29/80,5/16,1/20,-3/16,-1/64,
3/80],[151/320,17/80,-1/5,1,1/20,-3/8,-1/64,13/80],
[-29/320,19/320,-1/40,-1/4,1/10,1/8,-9/320,-9/320],
[29/160,-81/160,9/40,3/80,-7/80,-1/40,7/160,-3/160],
[-1/160,3/160,1/10,-13/40,-3/20,7/40,7/160,-1/32],
[-1/80,-109/160,1/5,9/80,-9/80,-3/40,1/40,-3/160],
[3/20,-1/64,-5/16,-33/80,1/4,7/80,-7/80,-17/320],[
25/24,43/40,-79/15,-35/6,59/30,23/10,-71/120,-91/120],
[443/240,35/16,-104/15,-103/10,38/15,4,-37/48,-109/80],
[17/60,7/240,-17/5,-42/5,17/15,19/6,-9/20,-19/16],
[-7/20,-25/48,37/30,14/3,-1/2,-11/6,1/12,151/240],
[319/240,19/15,-14/5,-23/5,16/15,28/15,-23/80,-3/5],
[61/240,69/80,26/15,13/15,-11/15,-3/10,13/48,43/240],
[17/240,341/240,8/3,13/6,-16/15,-13/15,17/48,97/240],
[-13/12,-893/240,-2,2/3,17/30,-13/30,-7/20,-17/240],
[-817/240,-3,239/30,73/6,-89/30,-47/10,211/240,47/30
],[-151/120,1/5,3,5/6,-17/15,-3/10,3/8,2/15],[
-59/60,3/10,137/30,-11/30,-26/15,1/10,31/60,-1/15],
[3/10,81/80,59/30,-31/30,-7/10,2/5,4/15,-17/240],
[17/20,101/80,-43/30,-191/30,3/5,12/5,-11/60,-41/48],
[-41/60,13/240,44/15,31/15,-17/15,-5/6,23/60,73/240],
[1/3,187/120,-13/30,2/3,2/15,-4/15,-1/30,23/120],
[7/20,25/48,-37/30,-14/3,1/2,11/6,-1/12,-151/240],[
41/192,-87/64,-7/6,65/12,5/12,-17/8,-35/192,143/192],
[-27/32,37/48,23/12,-23/24,-3/4,11/24,19/96,-7/48],
[-119/192,-13/64,-9/8,15/8,11/24,-3/4,-9/64,15/64],
[13/24,-13/12,-11/24,31/8,1/6,-35/24,-1/12,1/2],
[7/32,-205/192,-5/4,95/24,5/8,-19/12,-5/32,103/192],
[-73/96,7/8,7/24,5/24,-1/6,-1/8,7/96,1/12],[-109/192,
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[37/192,-23/48,-9/8,37/48,19/48,-7/24,-9/64,1/12],
[23/192,1,-13/24,-25/16,11/48,5/8,-17/192,-3/16],[
-49/192,-5/96,43/24,89/48,-31/48,-17/24,47/192,25/96],
[23/192,5/24,-5/4,-7/16,23/48,5/24,-11/64,-1/16],[
-123/320,-191/160,9/40,169/40,-7/80,-127/80,1/64,87/160],
[-15/64,-61/320,-11/40,9/10,1/10,-7/20,-23/320,39/320],
[1/5,-31/320,43/80,13/20,-11/40,-9/40,7/80,29/320],
[-71/320,133/320,-17/80,-33/16,1/10,3/4,-7/320,-83/320
],[77/320,67/64,-131/80,-169/40,49/80,127/80,-71/320,
-177/320],[11/320,27/320,-1/80,-19/40,1/20,3/20,-1/64,
-9/320],[-69/160,-9/10,-5/16,139/80,1/8,-51/80,-11/160,
1/5],[9/320,-9/64,1/8,-15/16,-1/16,3/8,1/320,-9/64],
[37/160,119/320,-13/20,-83/80,9/40,2/5,-11/160,-41/320
],[1/16,-3/80,-1/16,23/80,0,-7/80,0,1/80],[9/160,
121/320,29/80,-71/80,-11/80,29/80,9/160,-7/64],[-41/320,
-29/80,37/80,131/80,-13/80,-27/40,19/320,1/4],[-3/10,
199/240,46/15,-1/10,-1,1/15,11/30,1/80],[-169/240,
35/24,241/60,-91/60,-22/15,7/12,127/240,-17/120],[
-43/40,83/48,79/30,-16/5,-9/10,19/15,31/120,-31/80],
[31/80,17/240,-21/20,-3/4,2/5,17/60,-9/80,-9/80],[
-13/40,107/240,221/60,-131/60,-3/2,47/60,67/120,-13/48],
[-37/240,-51/80,19/12,-1/12,-2/3,1/20,59/240,-1/48],
[-1/240,-14/15,11/20,21/20,-4/15,-29/60,1/16,1/10],[
-131/240,301/120,109/60,-47/20,-19/30,13/12,61/240,-9/40],
[22/15,223/240,-61/12,-37/20,5/3,37/60,-7/12,-3/16],[
-1/120,-31/240,-73/60,-101/60,11/30,7/12,-23/120,-59/240],
[-29/240,209/240,-59/60,-81/20,4/15,89/60,-29/240,-41/80
],[-9/20,-71/48,37/20,43/60,-3/5,-13/60,1/5,1/240],
[-31/60,17/80,97/60,19/60,-17/30,-3/20,1/6,7/240],[
7/24,31/80,-17/12,-83/60,17/30,11/20,-23/120,-47/240],
[13/240,1/120,-1/12,53/60,1/15,-19/60,-11/240,13/120],
[11/30,109/120,-7/12,-139/60,4/15,53/60,-1/12,-7/24],
[-23/96,53/96,1/8,-61/24,1/24,23/24,-1/32,-31/96],
[19/96,-1/4,-31/16,-59/48,19/24,7/16,-9/32,-1/6],
[-77/192,-69/64,-11/24,31/12,5/24,-1,-25/192,61/192],
[-67/192,173/192,1/3,-17/4,-1/12,5/3,1/192,-37/64],[
-31/192,-53/96,-7/48,133/48,1/24,-49/48,-7/192,35/96],
[11/48,133/192,25/48,-29/16,-5/24,31/48,1/12,-13/64],
[55/192,11/24,-9/16,41/48,5/24,-17/48,-3/64,1/6],[
-49/192,121/192,-5/8,-11/6,7/24,17/24,-7/64,-43/192],
[-29/192,-17/32,-11/48,59/48,1/12,-7/16,-5/192,13/96],
[3/64,-89/192,-7/24,5/12,1/8,-1/6,-11/192,11/192],
[13/64,131/192,-7/12,-43/24,1/4,2/3,-13/192,-41/192],
[-31/192,71/192,0,7/24,1/24,-1/12,-1/64,11/192],
[-1/8,59/96,-35/48,-25/16,1/4,31/48,-5/48,-7/32],
[-53/96,-13/16,37/24,49/24,-7/12,-3/4,19/96,11/48],[
-1/4,31/96,-3/4,-25/24,1/4,5/12,-1/8,-13/96],[-49/192,
-77/192,35/24,67/24,-7/12,-25/24,43/192,71/192],[13/96,
5/6,29/48,-127/48,-5/24,49/48,7/96,-1/3],[-23/96,
-29/48,71/48,23/16,-7/12,-29/48,19/96,3/16],[-15/32,
-91/64,11/48,103/48,-1/8,-13/16,1/96,43/192],[-1/96,
11/96,13/16,-5/48,-7/24,1/48,3/32,-1/96],[-187/320,
-207/320,-19/16,-289/80,7/16,111/80,-63/320,-179/320],
[9/160,1/80,-19/20,-69/80,29/80,13/40,-21/160,-1/8],
[-17/80,-93/320,119/80,11/4,-23/40,-17/16,1/5,123/320],
[109/160,59/64,1/8,-41/40,-1/16,33/80,11/160,-33/320],
[71/64,181/160,-1/20,-21/16,1/80,1/2,19/320,-21/160
],[-1/160,-11/320,3/10,0,-11/80,0,9/160,1/320],[
29/80,-23/320,-29/20,-83/20,11/20,8/5,-3/16,-39/64],[
-43/320,-29/320,27/40,47/80,-21/80,-9/40,29/320,27/320],
[59/320,17/320,-11/16,11/16,1/4,-1/4,-29/320,33/320],
[-33/160,-31/160,7/80,51/80,1/40,-19/80,-3/160,13/160],
[1/320,-33/320,-3/16,29/20,1/16,-11/20,-11/320,67/320
],[-27/80,-3/64,3/16,1/20,-1/8,-1/80,1/40,1/320],[
-97/240,-29/240,38/15,19/30,-16/15,-1/3,83/240,23/240],
[-19/40,43/60,77/30,-33/20,-21/20,17/30,41/120,-1/5],
[-17/48,41/60,8/3,-47/10,-29/30,26/15,79/240,-13/20],
[59/240,-1/8,5/6,79/60,-19/60,-1/2,7/48,23/120],[
-5/12,-379/240,33/10,239/60,-17/12,-47/30,1/2,25/48],
[71/240,-29/240,37/30,1/4,-19/60,-1/30,47/240,1/80],
[-1/120,-101/120,-1/6,37/12,1/60,-7/6,1/120,49/120],
[-7/60,277/240,-1/5,-287/60,17/60,28/15,-1/10,-31/48],
[-39/80,-7/8,-5/6,187/60,3/20,-6/5,-29/240,53/120],
[-1/8,-7/40,1/15,-107/60,-3/20,3/5,-1/120,-31/120],[
-13/240,-1/80,41/30,-17/60,-31/60,1/10,43/240,-11/240],
[43/80,-9/8,-11/15,-17/60,7/20,1/10,-23/240,-13/120],
[29/240,23/120,4/15,-121/60,-7/60,23/30,13/240,-7/24],
[7/30,-13/80,-11/15,7/12,17/60,-1/5,-1/12,17/240],
[1/120,101/120,1/6,-37/12,-1/60,7/6,-1/120,-49/120],
[1/240,61/120,9/10,-61/60,-17/60,13/30,11/80,-17/120],
[1/64,55/192,-1/4,3/4,1/8,-7/24,-3/64,9/64],[1/24,
-65/96,1/8,53/48,-1/48,-11/24,1/16,13/96],[13/192,
-89/192,-1/3,17/12,1/12,-13/24,-7/192,35/192],[-5/48,
-91/96,2/3,5/12,-7/24,-1/6,5/48,1/96],[-1/16,43/192,
1/8,-13/16,-1/16,1/3,0,-7/64],[-37/192,103/192,1/4,
-13/48,-1/48,1/12,1/64,-1/192],[-11/192,5/16,-7/24,
-15/16,7/48,3/8,-11/192,-1/8],[-5/192,-13/64,5/24,0,
-1/24,0,7/192,-1/64],[55/192,-85/192,-1/2,-49/48,7/48,
5/12,-3/64,-37/192],[17/96,-3/8,5/24,7/8,-1/24,-3/8,
5/96,1/8],[-23/192,21/64,7/8,0,-7/24,0,7/64,1/64],
[-1/24,1/3,5/12,-35/24,-1/6,7/12,1/24,-5/24],[-13/32,
-1/64,2/3,-31/48,-5/16,1/4,7/96,-19/192],[1/64,-45/64,
-1/2,19/12,1/8,-5/8,-3/64,37/192],[7/192,149/192,13/24,
-7/4,-1/6,2/3,11/192,-13/64],[1/8,1/8,-5/12,-7/12,1/8,
1/4,-1/24,-1/12],[-1/6,25/64,13/12,-1/16,-17/48,0,7/48,
1/64],[-1/16,-157/192,3/4,33/16,-5/16,-5/6,1/8,17/64],
[13/96,-5/192,-25/24,-5/48,17/48,1/12,-13/96,-5/192],
[3/32,-5/192,13/24,31/48,-3/16,-7/24,7/96,19/192],[
-263/320,-509/320,17/20,379/80,-27/80,-73/40,5/64,39/64],
[-11/320,-33/320,33/80,51/80,-3/20,-19/80,13/320,27/320],
[83/320,173/320,3/20,-43/40,-1/10,17/40,3/64,-47/320],[
129/320,231/320,-121/80,-41/16,11/20,15/16,-63/320,-101/320
],[209/320,247/320,-11/4,-301/80,17/16,57/40,-119/320,
-161/320],[3/80,1/8,-1/40,-33/80,-7/80,3/20,0,-3/80],[
-151/320,-287/320,-11/16,17/16,1/4,-7/16,-39/320,37/320],
[-29/320,97/320,41/80,-2/5,-19/80,13/80,23/320,-3/64],
[47/320,-43/320,3/20,-11/40,-1/10,1/10,11/320,-3/64],
[-13/320,-37/320,11/40,11/16,-3/80,-1/4,11/320,27/320],
[7/160,7/20,13/20,-47/80,-23/80,9/40,17/160,-1/16],
[-13/160,-3/16,5/8,111/80,-5/16,-11/20,13/160,1/5],[
59/80,407/240,-14/5,-173/30,6/5,67/30,-33/80,-181/240],
[47/240,67/40,-43/15,-68/15,17/15,17/10,-109/240,-67/120
],[-8/15,-1/40,-11/5,-11/5,29/30,9/10,-2/5,-13/40],[
-3/8,-169/240,1/6,3/10,-1/10,-1/6,-1/120,1/80],[11/120,
143/80,-8/5,-33/5,2/3,12/5,-11/40,-69/80],[-89/240,
29/60,13/30,-53/15,-7/30,4/3,11/240,-29/60],[41/240,
1/2,6/5,-41/30,-7/15,1/2,3/16,-1/6],[-11/30,-181/240,
-7/3,7/5,5/6,-7/15,-1/3,13/80],[-47/240,-191/120,7/15,
4,-7/30,-47/30,13/240,19/40],[-8/15,-133/240,4/15,-2/15,
-1/30,1/30,-1/30,-17/240],[-101/240,-39/40,-14/15,4/15,
11/30,-1/10,-41/240,-1/120],[-3/80,2/3,5/6,-73/15,
-3/10,28/15,7/48,-2/3],[13/40,109/240,-3/5,-53/30,
3/10,2/3,-3/40,-11/48],[23/120,-59/80,-1/3,23/30,1/15,
-3/10,-1/120,19/240],[-3/16,-1/12,-1/3,4/15,1/5,-1/30,
-17/240,1/60],[17/48,-7/60,-53/30,-1,23/30,13/30,-11/48,
-3/20],[3/32,5/96,-5/12,-9/8,1/8,11/24,-7/96,-5/32],
[-17/96,7/24,-1/2,-9/8,1/6,5/12,-3/32,-1/8],[0,-49/48,
17/24,35/12,-1/4,-13/12,1/12,17/48],[-5/16,1/48,-1/12,
1/2,0,-1/6,-1/48,1/16],[25/192,-13/192,1/3,5/8,-1/6,
-5/24,13/192,5/64],[39/64,97/192,-5/8,-23/24,1/4,1/3,
-5/64,-19/192],[9/32,17/48,-3/4,-3/2,1/4,13/24,-3/32,
-3/16],[1/12,5/24,-7/8,11/24,1/3,-1/6,-1/8,1/12],
[-83/192,-37/192,1/12,29/24,-1/24,-11/24,1/192,31/192],
[1/24,-17/96,-7/24,1/4,1/24,-1/12,-1/24,1/32],[1/24,
7/12,1/6,-5/6,-1/12,1/3,1/24,-1/12],[1/24,11/32,-1/8,
-1/4,1/24,1/8,0,-1/32],[-1/24,-13/24,1/6,41/24,-1/24,
-2/3,1/24,5/24],[-1/192,-39/64,17/24,23/12,-5/24,-3/4,
19/192,47/192],[15/64,49/64,-3/4,-5/8,1/4,1/4,-5/64,
-3/64],[7/64,-11/192,-1/24,1/12,0,-1/24,1/192,1/192
],[13/192,19/64,-29/24,1/24,11/24,0,-31/192,5/192],
[-5/64,107/192,17/24,-13/12,-1/4,5/12,13/192,-25/192],
[-11/96,-23/32,1/6,9/4,-1/12,-7/8,1/96,9/32],[13/192,
41/192,-1/2,-1,5/24,5/12,-5/64,-9/64]])
]> where w := K.1 where K := ext<K|Polynomial(K,[1,0,-3,0,8,0,
-3,0,1])> where K is RationalField();

return _LR;
