_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;

//eight constituents cycled by automorphisms
_LR`G := 
/*
Original group: c9Group("12bl34p")
From DB /nb/reps/d60.12bL34.nfdeg8.M
Schur index: 1
Character: ( 60, -60, 0, 60*zeta(84)_3, -60*zeta(84)_3 - 60, 0, -60*zeta(84)_4, 
60*zeta(84)_4, 0, 2, -2, -2*zeta(84)_4, 2*zeta(84)_4, 0, 0, -60*zeta(84)_3, 
60*zeta(84)_3 + 60, 0, 0, 0, -zeta(84)_7^4 - zeta(84)_7^2 - zeta(84)_7, 
zeta(84)_7^4 + zeta(84)_7^2 + zeta(84)_7 + 1, 0, 0, 0, 0, 
-60*zeta(84)_4*zeta(84)_3, 60*zeta(84)_4*zeta(84)_3 + 60*zeta(84)_4, 
60*zeta(84)_4*zeta(84)_3, -60*zeta(84)_4*zeta(84)_3 - 60*zeta(84)_4, 0, 0, 
-2*zeta(84)_4*zeta(84)_3 - 2*zeta(84)_4, 2*zeta(84)_3 + 2, 
2*zeta(84)_4*zeta(84)_3, 2*zeta(84)_3, -2*zeta(84)_3, -2*zeta(84)_4*zeta(84)_3, 
2*zeta(84)_4*zeta(84)_3 + 2*zeta(84)_4, -2*zeta(84)_3 - 2, 0, 0, zeta(84)_7^4 + 
zeta(84)_7^2 + zeta(84)_7, -zeta(84)_7^4 - zeta(84)_7^2 - zeta(84)_7 - 1, 0, 0, 
0, 0, 0, 0, 0, 0, zeta(84)_3*zeta(84)_7^4 + zeta(84)_3*zeta(84)_7^2 + 
zeta(84)_3*zeta(84)_7 + zeta(84)_7^4 + zeta(84)_7^2 + zeta(84)_7, 
zeta(84)_3*zeta(84)_7^4 + zeta(84)_3*zeta(84)_7^2 + zeta(84)_3*zeta(84)_7 + 
zeta(84)_3, -zeta(84)_3*zeta(84)_7^4 - zeta(84)_3*zeta(84)_7^2 - 
zeta(84)_3*zeta(84)_7 - zeta(84)_3 - zeta(84)_7^4 - zeta(84)_7^2 - zeta(84)_7 - 
1, -zeta(84)_3*zeta(84)_7^4 - zeta(84)_3*zeta(84)_7^2 - zeta(84)_3*zeta(84)_7, 
0, 0, 0, 0, zeta(84)_4*zeta(84)_7^4 + zeta(84)_4*zeta(84)_7^2 + 
zeta(84)_4*zeta(84)_7, zeta(84)_4*zeta(84)_7^4 + zeta(84)_4*zeta(84)_7^2 + 
zeta(84)_4*zeta(84)_7 + zeta(84)_4, -zeta(84)_4*zeta(84)_7^4 - 
zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7 - zeta(84)_4, 
-zeta(84)_4*zeta(84)_7^4 - zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7, 0, 
0, 0, 0, -zeta(84)_3*zeta(84)_7^4 - zeta(84)_3*zeta(84)_7^2 - 
zeta(84)_3*zeta(84)_7 - zeta(84)_7^4 - zeta(84)_7^2 - zeta(84)_7, 
zeta(84)_3*zeta(84)_7^4 + zeta(84)_3*zeta(84)_7^2 + zeta(84)_3*zeta(84)_7 + 
zeta(84)_3 + zeta(84)_7^4 + zeta(84)_7^2 + zeta(84)_7 + 1, 
zeta(84)_3*zeta(84)_7^4 + zeta(84)_3*zeta(84)_7^2 + zeta(84)_3*zeta(84)_7, 
-zeta(84)_3*zeta(84)_7^4 - zeta(84)_3*zeta(84)_7^2 - zeta(84)_3*zeta(84)_7 - 
zeta(84)_3, 0, 0, 0, 0, 0, 0, 0, 0, -zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - 
zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - zeta(84)_4*zeta(84)_3*zeta(84)_7 - 
zeta(84)_4*zeta(84)_3 - zeta(84)_4*zeta(84)_7^4 - zeta(84)_4*zeta(84)_7^2 - 
zeta(84)_4*zeta(84)_7 - zeta(84)_4, zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + 
zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + zeta(84)_4*zeta(84)_3*zeta(84)_7 + 
zeta(84)_4*zeta(84)_3 + zeta(84)_4*zeta(84)_7^4 + zeta(84)_4*zeta(84)_7^2 + 
zeta(84)_4*zeta(84)_7 + zeta(84)_4, zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + 
zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + zeta(84)_4*zeta(84)_3*zeta(84)_7 + 
zeta(84)_4*zeta(84)_3, -zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - 
zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - zeta(84)_4*zeta(84)_3*zeta(84)_7, 
zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + 
zeta(84)_4*zeta(84)_3*zeta(84)_7 + zeta(84)_4*zeta(84)_7^4 + 
zeta(84)_4*zeta(84)_7^2 + zeta(84)_4*zeta(84)_7, 
-zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - 
zeta(84)_4*zeta(84)_3*zeta(84)_7 - zeta(84)_4*zeta(84)_7^4 - 
zeta(84)_4*zeta(84)_7^2 - zeta(84)_4*zeta(84)_7, 
-zeta(84)_4*zeta(84)_3*zeta(84)_7^4 - zeta(84)_4*zeta(84)_3*zeta(84)_7^2 - 
zeta(84)_4*zeta(84)_3*zeta(84)_7 - zeta(84)_4*zeta(84)_3, 
zeta(84)_4*zeta(84)_3*zeta(84)_7^4 + zeta(84)_4*zeta(84)_3*zeta(84)_7^2 + 
zeta(84)_4*zeta(84)_3*zeta(84)_7 )
*/
MatrixGroup<60, K | [
Matrix(SparseMatrix(K,60,60,[
<1,3,1/40*(-w^7+5*w^5-5*w^3-12*w)>,<1,4,1/40*(-3*w^7-5*w^5+
5*w^3-16*w)>,<1,5,1/20*(3*w^6+5*w^4+15*w^2+16)>,<1,6,1>,<2,
2,1>,<2,4,1/40*(3*w^7+5*w^5-5*w^3+16*w)>,<2,5,1/20*(3*w^6+
5*w^4+15*w^2+36)>,<3,1,1/10*(-w^7-7*w)>,<3,4,1/20*(3*w^6+
5*w^4+15*w^2+16)>,<3,5,1/40*(w^7-5*w^5+5*w^3+12*w)>,<3,6,
1/10*(w^7+7*w)>,<4,5,1/10*(w^7+7*w)>,<5,4,1/40*(w^7-5*w^5+
5*w^3+12*w)>,<6,6,1>,<7,7,-1>,<8,12,1>,<9,10,1/20*(3*w^6+
5*w^4+15*w^2+36)>,<10,9,1/20*(-3*w^6-5*w^4-15*w^2-16)>,<11,
11,-1>,<12,8,1>,<13,17,1/20*(3*w^6+5*w^4+15*w^2+16)>,<13,
19,1/40*(w^7-5*w^5+5*w^3+12*w)>,<13,21,1>,<14,17,1/20*(3*w^6+
5*w^4+15*w^2+36)>,<14,19,1/40*(3*w^7+5*w^5-5*w^3+16*w)>,<15,
13,1/10*(-w^7-7*w)>,<15,15,-1>,<15,21,1/10*(-w^7-7*w)>,<16,13,
1/10*(-w^7-7*w)>,<16,14,1/10*(w^7+7*w)>,<16,15,1/20*(3*w^6+5*w^4
+15*w^2+16)>,<16,18,1>,<16,19,-1>,<16,20,1/40*(w^7-5*w^5+
5*w^3+12*w)>,<16,21,1/10*(-w^7-7*w)>,<17,14,1/20*(-3*w^6-5*w^4
-15*w^2-36)>,<17,17,1/20*(3*w^6+5*w^4+15*w^2+36)>,<17,19,
1/10*(w^7+7*w)>,<18,13,1/10*(w^7+7*w)>,<18,14,1/10*(-w^7-7*w)>,
<18,18,-1>,<18,19,1>,<18,21,1/10*(w^7+7*w)>,<19,14,1/10*(-w^7
-7*w)>,<19,17,1/40*(w^7-5*w^5+5*w^3+12*w)>,<19,19,1/20*(-3*w^6
-5*w^4-15*w^2-16)>,<20,13,1/20*(3*w^6+5*w^4+15*w^2+36)>,<20,
15,1/40*(-3*w^7-5*w^5+5*w^3-16*w)>,<20,16,1/10*(w^7+7*w)>,<20,
18,1/10*(w^7+7*w)>,<20,21,1/20*(3*w^6+5*w^4+15*w^2+36)>,<21,
13,1>,<21,17,1/20*(-3*w^6-5*w^4-15*w^2-16)>,<21,19,1/40*(-w^7+
5*w^5-5*w^3-12*w)>,<22,26,1/20*(3*w^6+5*w^4+15*w^2+16)>,<22,
28,1/40*(w^7-5*w^5+5*w^3+12*w)>,<22,30,1>,<23,26,1/20*(3*w^6+
5*w^4+15*w^2+36)>,<23,28,1/40*(3*w^7+5*w^5-5*w^3+16*w)>,<24,
22,1/10*(-w^7-7*w)>,<24,24,-1>,<24,30,1/10*(-w^7-7*w)>,<25,22,
1/10*(-w^7-7*w)>,<25,23,1/10*(w^7+7*w)>,<25,24,1/20*(3*w^6+5*w^4
+15*w^2+16)>,<25,27,1>,<25,28,-1>,<25,29,1/40*(w^7-5*w^5+
5*w^3+12*w)>,<25,30,1/10*(-w^7-7*w)>,<26,23,1/20*(-3*w^6-5*w^4
-15*w^2-36)>,<26,26,1/20*(3*w^6+5*w^4+15*w^2+36)>,<26,28,
1/10*(w^7+7*w)>,<27,22,1/10*(w^7+7*w)>,<27,23,1/10*(-w^7-7*w)>,
<27,27,-1>,<27,28,1>,<27,30,1/10*(w^7+7*w)>,<28,23,1/10*(-w^7
-7*w)>,<28,26,1/40*(w^7-5*w^5+5*w^3+12*w)>,<28,28,1/20*(-3*w^6
-5*w^4-15*w^2-16)>,<29,22,1/20*(3*w^6+5*w^4+15*w^2+36)>,<29,
24,1/40*(-3*w^7-5*w^5+5*w^3-16*w)>,<29,25,1/10*(w^7+7*w)>,<29,
27,1/10*(w^7+7*w)>,<29,30,1/20*(3*w^6+5*w^4+15*w^2+36)>,<30,
22,1>,<30,26,1/20*(-3*w^6-5*w^4-15*w^2-16)>,<30,28,1/40*(-w^7+
5*w^5-5*w^3-12*w)>,<31,31,1>,<32,42,1/20*(3*w^6+5*w^4+15*w^2
+16)>,<33,39,1/40*(-3*w^7-5*w^5+5*w^3-16*w)>,<34,38,
1/40*(-3*w^7-5*w^5+5*w^3-16*w)>,<35,43,1/40*(-3*w^7-5*w^5+
5*w^3-16*w)>,<36,36,-1>,<37,37,1>,<38,34,1/40*(3*w^7+5*w^5-
5*w^3+16*w)>,<39,33,1/40*(3*w^7+5*w^5-5*w^3+16*w)>,<40,45,
1/40*(-w^7+5*w^5-5*w^3-12*w)>,<41,44,1/10*(-w^7-7*w)>,<42,32,
1/20*(-3*w^6-5*w^4-15*w^2-36)>,<43,35,1/40*(3*w^7+5*w^5-5*w^3
+16*w)>,<44,41,1/40*(-w^7+5*w^5-5*w^3-12*w)>,<45,40,
1/10*(-w^7-7*w)>,<46,46,1>,<47,57,1/20*(3*w^6+5*w^4+15*w^2+
16)>,<48,54,1/40*(-3*w^7-5*w^5+5*w^3-16*w)>,<49,53,
1/40*(-3*w^7-5*w^5+5*w^3-16*w)>,<50,58,1/40*(-3*w^7-5*w^5+
5*w^3-16*w)>,<51,51,-1>,<52,52,1>,<53,49,1/40*(3*w^7+5*w^5-
5*w^3+16*w)>,<54,48,1/40*(3*w^7+5*w^5-5*w^3+16*w)>,<55,60,
1/40*(-w^7+5*w^5-5*w^3-12*w)>,<56,59,1/10*(-w^7-7*w)>,<57,47,
1/20*(-3*w^6-5*w^4-15*w^2-36)>,<58,50,1/40*(3*w^7+5*w^5-5*w^3
+16*w)>,<59,56,1/40*(-w^7+5*w^5-5*w^3-12*w)>,<60,55,
1/10*(-w^7-7*w)>])),
Matrix(K,60,60,
[[31/150,17/50,1/15,1/10,1/30,1/15,1/50,1/50],[4/75,12/25,
-1/60,1/5,1/60,2/15,1/100,1/25],[3/25,-3/100,1/15,1/80,
-1/30,-1/80,-1/150,-13/1200],[-26/75,-2/25,-1/30,1/48,-1/30,
1/80,-1/25,17/1200],[-11/75,11/150,-13/120,0,-11/120,1/30,
-29/600,1/50],[-8/25,-7/50,-3/40,1/80,-1/40,-1/80,-7/200,
-3/400],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,
0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,
0,0],[0,0,0,0,0,0,0,0],[6/25,-7/200,3/20,1/160,1/20,
-1/160,1/50,1/800],[0,0,0,0,0,0,0,0],[-1/50,-3/50,1/80,
1/40,-1/80,1/40,1/400,-1/200],[13/100,1/25,1/40,1/40,1/40,
-1/40,3/200,-1/200],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,
0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[1/5,
-13/200,1/16,3/80,-1/80,1/80,1/80,-3/400],[4/25,11/100,-1/40,
13/160,-1/40,3/160,1/200,9/800],[0,0,0,0,0,0,0,0],[
1/20,-7/100,1/40,-1/80,1/40,-3/80,1/40,-9/400],[13/100,0,
1/16,-3/80,3/80,-1/80,1/400,1/80],[0,0,0,0,0,0,0,0],[
0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,
0,0,0],[4/25,1/10,3/80,9/160,1/80,-1/160,7/400,1/160],[0,
0,0,0,0,0,0,0],[-1/20,1/20,-1/12,1/96,0,-1/96,1/60,
-1/160],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
11/30,-1/15,1/8,1/48,1/24,-1/48,7/120,-1/80],[0,0,0,0,0,
0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
-1/20,11/120,-5/48,1/16,-1/16,1/48,-1/240,1/240],[0,0,0,0,
0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
-1/3,23/60,-1/12,1/16,-1/12,5/48,-1/12,11/240],[-13/30,-7/40,
-1/16,-17/96,-1/48,-7/96,-7/240,-17/480],[-13/60,-7/60,-1/8,
-1/96,-1/8,1/96,-1/40,-13/480],[0,0,0,0,0,0,0,0],[1/5,
1/15,0,1/16,0,1/48,1/60,1/80],[0,0,0,0,0,0,0,0],[0,
0,0,0,0,0,0,0],[-3/10,7/60,-1/8,-1/48,-1/24,1/48,-1/40,
-1/240],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,
0,0,0,0,0,0,0],[1/5,-1/12,1/12,0,0,0,1/60,0],[0,0,
0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0
],[2/5,-3/20,5/24,-1/12,1/8,-1/12,3/40,-1/30],[1/10,1/12,
-1/24,1/12,-1/24,0,1/120,0],[4/15,-7/60,1/8,-1/16,1/24,
-1/48,1/120,1/240],[-1/5,-37/150,-1/15,-1/16,-1/30,-3/80,
-1/30,-1/400],[41/150,-13/150,7/60,-3/80,1/12,-7/240,11/300,
1/400],[0,23/100,-1/60,-1/80,-1/60,1/80,1/60,13/1200],[
31/150,-17/100,-1/15,-1/12,1/30,-1/20,1/50,-2/75],[-31/150,
1/15,0,9/80,0,1/48,1/75,1/80],[12/25,19/75,11/60,1/16,7/60,
3/80,17/300,9/400],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,
0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,
0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[1/100,3/200,0,1/80,
-1/20,3/80,-1/50,3/400],[0,0,0,0,0,0,0,0],[-1/20,7/50,
-9/80,13/160,-3/80,3/160,-1/80,1/800],[-9/50,-21/200,-1/80,
-1/10,1/80,-1/20,-1/400,-3/200],[0,0,0,0,0,0,0,0],[0,
0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,
0,0],[9/100,-13/200,3/16,-1/20,1/16,0,3/400,1/200],[-3/20,
1/100,-1/20,1/80,0,-1/80,0,-3/400],[0,0,0,0,0,0,0,0],[
-1/25,0,1/40,-7/160,1/40,-1/160,1/200,1/160],[1/10,-1/40,
1/20,1/40,0,1/40,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,
0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
7/100,-1/40,-1/80,3/40,-3/80,1/40,-1/400,0],[0,0,0,0,0,0,
0,0],[-1/6,-5/24,-1/48,-7/96,-1/16,-1/96,-1/48,-1/32],[0,
0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[1/12,13/120,
-1/48,1/24,1/48,1/24,-1/48,1/30],[0,0,0,0,0,0,0,0],[0,
0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[-1/4,1/15,-1/24,
-1/32,-1/24,1/32,-1/24,1/480],[0,0,0,0,0,0,0,0],[0,0,
0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[7/20,-5/24,11/48,
-1/24,5/48,-1/24,7/240,0],[1/30,31/120,-5/48,7/96,1/48,1/96,
-1/240,7/480],[-1/12,19/60,-1/24,3/32,-1/24,7/96,-1/24,7/160
],[0,0,0,0,0,0,0,0],[1/15,-1/30,1/24,-1/16,1/24,-1/48,
-1/120,1/240],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],
[7/30,-1/3,1/6,-5/48,1/12,-1/16,1/30,-1/48],[0,0,0,0,0,
0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
7/30,-1/60,1/12,-1/24,1/12,-1/24,1/30,-1/120],[0,0,0,0,0,
0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
-19/30,1/30,-1/6,-1/48,-1/12,1/48,-1/15,-1/240],[0,-4/15,
1/12,-1/16,0,-1/48,0,-7/240],[1/6,-2/15,1/8,-1/24,1/24,
-1/24,1/24,-1/40],[-1/5,9/50,-1/12,0,1/60,0,-1/60,1/150],[
-7/25,39/100,-1/60,11/80,-1/60,1/16,-7/300,49/1200],[-13/150,
-1/25,1/120,3/80,-1/120,-1/240,3/200,7/400],[13/150,1/25,
-1/120,-3/80,1/120,1/240,-3/200,-7/400],[-3/10,11/100,-1/20,
7/80,-1/20,1/80,-1/20,7/400],[3/25,1/5,1/20,0,-1/20,0,
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-17/1600],[-1/80,47/800,1/20,3/64,0,9/320,-1/80,17/1600],[
0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,
0,0,0],[-3/400,77/800,-3/160,31/640,3/160,9/640,7/800,
-1/3200],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
1/80,-47/800,-1/20,-3/64,0,-9/320,1/80,-17/1600],[0,0,0,0,
0,0,0,0],[19/60,-1/24,7/48,-5/96,1/48,-1/32,1/80,-1/96],[
0,0,0,0,0,0,0,0],[7/120,-13/120,-5/96,-5/192,1/96,-1/64,
-1/480,-17/960],[-1/30,-17/120,-1/12,-1/96,0,1/96,-1/60,
-3/160],[5/24,23/240,1/16,1/96,1/48,1/32,1/48,1/160],[
17/60,-1/80,5/96,-1/96,1/32,1/96,13/480,-1/160],[7/60,
-11/120,-1/96,-7/192,1/96,-1/192,1/160,-19/960],[-19/60,1/24,
-7/48,5/96,-1/48,1/32,-1/80,1/96],[0,0,0,0,0,0,0,0],[
17/60,-1/80,5/96,-1/96,1/32,1/96,13/480,-1/160],[-9/40,
-23/240,-5/48,-1/64,-1/48,-5/192,-7/240,-11/960],[-3/20,
11/120,1/24,1/16,1/24,1/48,1/120,1/240],[-3/10,1/60,-1/24,
1/32,-1/24,-1/32,-1/40,-1/480],[-11/30,-1/30,-3/16,1/48,
-1/16,-1/48,-3/80,1/240],[0,0,0,0,0,0,0,0],[3/20,7/30,
1/24,1/16,1/24,1/48,-1/120,1/80],[0,0,0,0,0,0,0,0],[
-7/60,-1/12,-5/96,-5/96,-1/32,-1/32,-13/480,-1/96],[-1/10,
-43/120,-1/24,-11/96,1/24,-5/96,-1/120,-11/480],[1/60,-29/240,
-1/24,-13/192,0,-1/64,1/120,-13/960],[3/40,-1/40,1/48,-1/48,
1/48,-1/48,-1/240,-1/80],[-1/30,-7/48,-1/48,-1/32,1/48,-1/96,
1/240,-1/96],[-3/20,-7/30,-1/24,-1/16,-1/24,-1/48,1/120,-1/80
],[0,0,0,0,0,0,0,0],[3/40,-1/40,1/48,-1/48,1/48,-1/48,
-1/240,-1/80],[-23/120,-7/120,-7/96,-1/32,-5/96,-1/96,-11/480,
1/480],[7/30,-1/60,5/48,1/16,1/16,1/48,13/240,1/80],[-2/15,
19/60,1/24,17/96,-1/24,7/96,-1/40,7/160],[-3/10,-1/20,-1/16,
0,-5/48,0,-11/240,1/60],[0,0,0,0,0,0,0,0],[0,0,0,0,
0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[
0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[13/150,-3/50,
1/120,-1/15,-1/120,-1/30,1/600,-1/75],[1/25,1/50,0,1/80,
1/30,1/48,1/50,7/1200],[-4/75,-1/300,-1/20,-1/48,-1/20,-1/80,
-1/100,1/400],[-7/150,3/100,-1/40,1/60,-1/120,1/60,1/600,
1/150],[-4/75,-13/300,-1/120,-1/240,1/120,1/240,-1/600,-1/1200
],[1/75,-1/60,1/20,1/120,1/60,-1/120,-1/100,-1/120],[-1/50,
7/400,1/32,7/320,7/160,1/320,17/800,-1/1600],[-1/20,51/800,
-9/160,17/640,-3/32,7/640,-1/32,17/3200],[7/100,1/200,3/64,
1/40,9/320,0,11/1600,-1/100],[0,0,0,0,0,0,0,0],[
-13/100,-31/800,-3/80,3/640,1/80,1/128,-1/400,3/3200],[
-23/400,49/400,-17/320,3/160,-7/320,1/160,-1/1600,9/800],[
11/100,1/50,3/40,23/160,1/40,9/160,1/200,3/800],[7/100,-1/80,
1/20,-7/640,0,-1/640,-3/200,1/640],[31/200,9/400,21/160,
1/160,11/160,-1/160,17/800,-1/800],[3/40,-1/50,3/40,-1/64,
1/40,-3/320,0,-1/1600],[-31/400,7/800,-5/64,3/640,1/320,
-11/640,23/1600,-21/3200],[2/25,-13/800,13/320,-1/64,3/320,
-3/320,9/1600,-3/1600],[0,0,0,0,0,0,0,0],[7/400,-13/800,
7/320,1/128,1/320,3/640,-1/1600,-11/3200],[-39/400,-3/50,
-3/320,-31/640,3/320,-9/640,-3/1600,-11/3200],[3/100,21/200,
-3/80,1/40,-1/80,-1/40,1/400,-1/100],[-3/50,7/400,-5/64,
3/128,-3/64,9/640,-13/1600,3/3200],[1/25,1/400,3/160,-1/320,
-3/160,1/320,-9/800,7/1600],[1/15,-1/20,1/48,-1/48,1/48,1/48,
1/80,-1/240],[-9/40,23/240,-1/12,1/64,-1/24,5/192,-1/120,
11/960],[1/3,7/60,5/24,-1/48,1/8,1/48,1/24,-1/240],[-1/20,
7/60,-1/48,0,-1/48,0,-1/240,1/60],[-5/24,-41/240,-1/16,
-1/24,-1/48,0,-1/48,-1/80],[17/120,-49/240,0,-11/96,0,-5/96,
1/120,-3/160],[1/40,3/80,1/48,1/64,1/16,5/192,1/80,1/320],[
-17/120,49/240,0,11/96,0,5/96,-1/120,3/160],[-9/40,23/240,
-1/12,1/64,-1/24,5/192,-1/120,11/960],[3/10,1/24,1/8,0,1/24,
0,1/40,0],[1/15,-1/20,1/48,-1/48,1/48,1/48,1/80,-1/240],[
1/40,3/80,1/48,1/64,1/16,5/192,1/80,1/320],[0,0,0,0,0,0,
0,0],[0,0,0,0,0,0,0,0],[31/120,-13/120,13/96,-5/192,
7/96,-1/64,17/480,-17/960],[1/10,-1/120,0,-1/96,0,1/96,
1/120,1/160],[1/120,1/15,1/32,1/48,1/96,1/48,7/480,1/80],[
1/15,-7/60,-1/24,-1/48,1/24,1/48,-1/120,-3/80],[0,-1/120,
1/24,-1/48,0,-1/48,0,-1/240],[-1/10,-7/80,-1/24,1/192,0,
-1/192,-1/120,-7/960],[1/20,-13/80,0,-5/64,0,-3/64,-1/60,
-23/960],[1/24,-7/40,-1/32,-7/96,1/32,-1/96,1/96,-7/480],[
-1/20,13/80,0,5/64,0,3/64,1/60,23/960],[1/120,1/15,1/32,
1/48,1/96,1/48,7/480,1/80],[1/20,1/20,1/16,1/48,1/48,1/48,
1/240,1/240],[1/10,-1/120,0,-1/96,0,1/96,1/120,1/160],[
1/24,-7/40,-1/32,-7/96,1/32,-1/96,1/96,-7/480],[0,0,0,0,0,
0,0,0],[0,0,0,0,0,0,0,0],[1/6,-1/60,5/96,0,1/32,0,
1/96,-1/120],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,
0,0,0],[0,0,0,0,0,0,0,0],[1/25,1/50,0,1/80,1/30,
1/48,1/50,7/1200],[-1/150,-2/15,-1/20,-3/40,-1/60,-1/40,
-1/300,-1/120],[-1/150,-2/15,-1/20,-3/40,-1/60,-1/40,-1/300,
-1/120],[-4/75,-13/300,-1/120,-1/240,1/120,1/240,-1/600,
-1/1200],[1/25,1/50,0,1/80,1/30,1/48,1/50,7/1200],[4/75,
13/300,1/120,1/240,-1/120,-1/240,1/600,1/1200],[-1/8,-3/200,
-27/320,-31/320,-13/320,-9/320,-3/320,13/1600],[29/400,-51/400,
1/16,-21/320,3/80,-11/320,1/200,-37/1600],[-17/200,-7/200,
-13/160,-11/640,-11/160,3/640,-29/800,9/3200],[9/50,7/160,
19/160,1/160,1/32,-1/160,7/800,0],[3/80,9/200,1/40,7/160,
1/40,1/32,1/80,3/800],[1/40,21/400,19/160,31/640,1/32,9/640,
-1/160,19/3200],[1/20,-21/800,-1/20,-3/80,-1/40,-1/80,0,
-3/800],[9/100,23/200,1/20,7/160,1/20,1/160,1/50,-9/800],[
-1/16,-9/400,-3/80,-1/20,-1/80,0,0,3/400],[-19/200,-29/800,
-7/320,1/320,-1/320,7/320,-11/1600,11/1600],[13/80,-7/800,
11/160,13/640,1/160,11/640,1/160,21/3200],[-1/10,3/200,
-31/320,17/640,-9/320,7/640,1/320,-11/3200],[-1/400,11/800,
-1/40,0,-1/40,0,-3/400,3/800],[9/400,-3/800,3/80,-3/640,
1/80,-1/128,1/200,-11/3200],[-1/200,-3/400,-13/320,11/640,
-11/320,-3/640,-9/1600,-17/3200],[-9/400,13/800,-1/160,-1/160,
1/160,1/160,1/800,1/200],[1/10,-11/100,9/80,-3/40,3/80,-1/40,
1/80,-1/200],[-17/400,-1/800,0,13/640,0,11/640,-1/400,13/3200
],[-1/30,-1/8,-7/96,-7/192,-1/96,-1/192,-1/160,1/192],[5/24,
41/240,1/16,1/24,1/48,0,1/48,1/80],[1/40,3/80,1/48,1/64,
1/16,5/192,1/80,1/320],[-1/6,1/30,0,1/32,0,1/96,0,1/160],
[9/40,-23/240,1/12,-1/64,1/24,-5/192,1/120,-11/960],[1/15,
-1/20,1/48,-1/48,1/48,1/48,1/80,-1/240],[-17/120,49/240,0,
11/96,0,5/96,-1/120,3/160],[-1/15,13/60,1/24,1/48,-1/24,
-1/48,1/120,1/240],[0,0,0,0,0,0,0,0],[1/20,-7/60,1/48,
0,1/48,0,1/240,-1/60],[-17/120,49/240,0,11/96,0,5/96,
-1/120,3/160],[-1/6,1/30,0,1/32,0,1/96,0,1/160],[11/120,
7/80,7/96,5/64,1/96,1/192,7/480,7/960],[0,0,0,0,0,0,0,0
],[-5/24,-41/240,-1/16,-1/24,-1/48,0,-1/48,-1/80],[-1/5,
-11/80,-5/48,-5/96,-1/16,-1/32,-3/80,-1/160],[1/10,7/80,1/24,
-1/192,0,1/192,1/120,7/960],[1/24,-7/40,-1/32,-7/96,1/32,
-1/96,1/96,-7/480],[-1/12,1/60,-1/24,0,0,0,0,1/120],[
-1/120,-1/15,-1/32,-1/48,-1/96,-1/48,-7/480,-1/80],[1/10,
-1/120,0,-1/96,0,1/96,1/120,1/160],[-1/20,13/80,0,5/64,0,
3/64,1/60,23/960],[8/15,7/60,7/24,-1/48,1/24,1/48,7/120,
-1/240],[0,0,0,0,0,0,0,0],[0,1/120,-1/24,1/48,0,1/48,
0,1/240],[-1/20,13/80,0,5/64,0,3/64,1/60,23/960],[-1/12,
1/60,-1/24,0,0,0,0,1/120],[0,7/60,1/24,7/192,0,1/192,0,
11/960],[0,0,0,0,0,0,0,0],[-1/10,-7/80,-1/24,1/192,0,
-1/192,-1/120,-7/960],[-13/30,7/30,-3/20,7/120,-11/60,1/120,
-1/20,7/120],[-3/25,-17/300,-13/120,-7/120,-11/120,-1/24,
-7/200,1/200],[-34/75,27/100,-1/12,3/20,-1/60,7/60,-1/100,
3/50],[-4/75,-149/300,-1/8,-13/80,1/40,-17/240,-11/600,-21/400
],[1/10,7/60,11/40,13/120,7/120,-1/120,1/120,-1/120],[7/10,
-1/30,9/40,-1/15,13/120,-1/30,7/120,-1/30],[0,0,0,0,0,0,
0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,
0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0
],[13/100,87/800,13/160,5/128,-1/160,-1/640,-3/800,9/3200],[
-13/100,-87/800,-13/160,-5/128,1/160,1/640,3/800,-9/3200],[0,
0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,
0,0],[-53/400,-9/400,-27/320,-3/160,-13/320,3/160,-11/1600,
11/800],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0],[0,
0,0,0,0,0,0,0],[9/400,3/160,-13/320,-1/640,-11/320,-7/640,
3/1600,-1/128],[-9/400,-3/160,13/320,1/640,11/320,7/640,
-3/1600,1/128],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0
],[0,0,0,0,0,0,0,0],[3/400,21/200,-13/320,47/640,-3/320,
5/128,11/1600,43/3200],[0,0,0,0,0,0,0,0],[0,0,0,0,0,
0,0,0],[0,0,0,0,0,0,0,0],[7/120,-13/120,-5/96,-5/192,
1/96,-1/64,-1/480,-17/960],[-1/20,-13/60,-1/8,-1/24,-1/24,
-1/24,-1/40,-1/40],[0,0,0,0,0,0,0,0],[0,0,0,0,0,0,
0,0],[-1/30,1/40,-1/16,-1/16,-1/48,-1/48,1/240,1/80],[
-11/120,-3/16,-7/96,-3/64,-1/96,-7/192,-7/480,-5/192],[-17/60,
1/80,-5/96,1/96,-1/32,-1/96,-13/480,1/160],[-7/60,11/120,
1/96,7/192,-1/96,1/192,-1/160,19/960],[1/20,13/60,1/8,1/24,
1/24,1/24,1/40,1/40],[-7/60,11/120,1/96,7/192,-1/96,1/192,
-1/160,19/960],[0,0,0,0,0,0,0,0],[-7/120,13/120,5/96,
5/192,-1/96,1/64,1/480,17/960],[-1/20,-13/60,-1/8,-1/24,
-1/24,-1/24,-1/40,-1/40],[-1/30,1/40,-1/16,-1/16,-1/48,-1/48,
1/240,1/80],[19/60,-1/24,7/48,-5/96,1/48,-1/32,1/80,-1/96],
[-7/60,-1/12,-5/96,-5/96,-1/32,-1/32,-13/480,-1/96],[-17/60,
-1/4,-1/24,-5/48,-1/24,-1/16,-7/120,-1/48],[0,0,0,0,0,0,
0,0],[0,0,0,0,0,0,0,0],[-7/30,1/20,-1/12,-7/96,-1/12,
-1/96,-1/30,-1/160],[-1/20,-1/40,1/48,7/192,1/48,1/192,
-1/240,1/320],[-3/40,1/40,-1/48,1/48,-1/48,1/48,1/240,1/80],
[1/30,7/48,1/48,1/32,-1/48,1/96,-1/240,1/96],[17/60,1/4,
1/24,5/48,1/24,1/16,7/120,1/48],[1/30,7/48,1/48,1/32,-1/48,
1/96,-1/240,1/96],[0,0,0,0,0,0,0,0],[7/60,1/12,5/96,
5/96,1/32,1/32,13/480,1/96],[-17/60,-1/4,-1/24,-5/48,-1/24,
-1/16,-7/120,-1/48],[-7/30,1/20,-1/12,-7/96,-1/12,-1/96,
-1/30,-1/160],[3/20,7/30,1/24,1/16,1/24,1/48,-1/120,1/80]])
]> where w := K.1 where K := ext<K|Polynomial(K, [16, 0, 12, 0, 5, 0, 3, 0, 1])>
where K is RationalField();

return _LR;
