_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 the cover 12a.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, not fixed by any automorphism.
_LR`G :=
/*
Original group: c9Group("12al34p")
From DB /nb/reps/d48.12aL34.nfdeg8.i105.M
Schur index: 1
Character: ( 48, -48, 0, 48*zeta(60)_3, -48*zeta(60)_3 - 48, 0, 48*zeta(60)_4, 
-48*zeta(60)_4, 0, 0, 0, -zeta(60)_5^3 - zeta(60)_5^2, zeta(60)_5^3 + 
zeta(60)_5^2 + 1, -48*zeta(60)_3, 48*zeta(60)_3 + 48, 0, 0, 0, -1, -1, 0, 0, 
zeta(60)_5^3 + zeta(60)_5^2, -zeta(60)_5^3 - zeta(60)_5^2 - 1, 
48*zeta(60)_4*zeta(60)_3, 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, 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)_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)_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)_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)_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)_3, zeta(60)_3 + 1, -zeta(60)_3, 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)_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 - 1, zeta(60)_3, -zeta(60)_3 - 1, 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)_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)_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)_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)_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)_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*zeta(60)_3 - zeta(60)_4, 
zeta(60)_4*zeta(60)_3, -zeta(60)_4*zeta(60)_3 - zeta(60)_4 )
*/
MatrixGroup<48, K | [
DiagonalMatrix(K,[1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,
1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,
-1,1,1,-1,-1,-1,1,1,-1,1]),
Matrix(K,48,48,
[[1/32,13/48,-1/12,-1/4,1/24,1/12,-1/96,-1/48],[-1/96,9/32,
1/12,-5/12,-1/24,1/6,1/32,-5/96],[-7/192,9/64,13/12,-1/12,
-5/12,1/24,29/192,-1/192],[-13/96,0,-11/24,13/24,1/6,-5/24,
-5/96,1/12],[-5/96,-1/32,-1/24,1/3,1/24,-1/8,-1/96,5/96],[
-11/96,-11/32,19/24,5/4,-7/24,-11/24,3/32,5/32],[1/4,13/96,
-1/3,-5/24,1/8,1/12,-1/24,-1/32],[35/192,-41/192,-1/8,4/3,
1/24,-1/2,-1/192,35/192],[1/6,-5/32,1/8,-19/24,-1/12,7/24,
1/24,-11/96],[-17/64,39/64,-1/24,-11/24,1/24,1/6,-7/192,
-7/192],[-193/192,221/192,65/24,-79/24,-25/24,5/4,67/192,
-79/192],[53/96,-9/32,-35/12,47/12,9/8,-3/2,-13/32,53/96],[
-5/48,-1/16,-5/6,47/24,1/3,-3/4,-7/48,13/48],[-53/192,-41/64,
61/24,-11/12,-1,1/3,71/192,-31/192],[-3/64,-73/192,3/2,
-29/24,-7/12,11/24,43/192,-37/192],[7/8,-67/48,-43/24,14/3,
2/3,-43/24,-5/24,29/48],[15/32,-3/8,19/24,-65/24,-7/24,25/24,
13/96,-5/12],[25/192,19/192,-11/24,5/24,1/6,-1/12,-11/192,
7/192],[-31/96,61/48,-23/24,13/8,3/8,-5/8,-5/32,5/16],[
-19/192,11/192,1/12,-1/3,-1/24,1/8,1/192,-3/64],[-107/96,
47/32,13/6,-17/2,-5/6,13/4,25/96,-37/32],[-5/64,211/192,-5/8,
-31/24,1/4,1/2,-19/192,-25/192],[-45/32,67/48,5/6,-29/12,
-1/3,11/12,5/96,-13/48],[-31/48,5/24,1/8,-29/24,-1/24,11/24,
-1/48,-1/6],[19/24,101/96,-2,9/8,19/24,-5/12,-1/4,7/32],[
11/192,9/64,5/24,-2/3,-1/12,1/4,7/192,-17/192],[-145/192,
-65/192,15/4,-29/24,-35/24,11/24,33/64,-37/192],[23/96,-7/48,
5/12,5/24,-1/6,-1/12,7/96,1/48],[65/48,-119/96,-1/8,13/24,
1/24,-5/24,1/16,1/96],[17/48,13/96,13/24,-17/12,-5/24,13/24,
5/48,-19/96],[-31/192,-187/192,5/2,-11/4,-23/24,25/24,23/64,
-29/64],[7/192,-25/64,-1/6,-23/24,1/12,3/8,-5/192,-31/192],[
-5/192,7/192,1/6,-3/4,-1/12,7/24,7/192,-7/64],[25/192,1/64,
1,-3/2,-5/12,13/24,29/192,-41/192],[-7/96,-3/32,25/24,-7/6,
-3/8,11/24,13/96,-17/96],[3/32,-13/16,1/3,4/3,-1/8,-1/2,
5/96,7/48],[7/96,1/48,-5/12,-5/12,1/6,1/6,-5/96,-1/16],[
-1/96,55/96,1/24,-7/24,1/24,1/8,-1/96,-1/96],[1/64,115/192,
-5/4,-1/4,11/24,1/8,-11/64,-1/192],[17/96,29/96,-13/12,7/24,
11/24,-1/12,-5/32,5/96],[13/192,43/192,1/12,1/12,-1/24,-1/24,
1/192,7/192],[-29/64,5/192,1,-19/24,-3/8,7/24,7/64,-23/192],
[-23/192,41/192,1/6,-17/24,-1/24,7/24,5/192,-19/192],[1/6,
13/32,7/24,-13/8,-1/12,5/8,1/24,-7/32],[15/64,-5/192,-1/24,
13/12,0,-5/12,1/192,31/192],[1/96,-11/32,-13/24,23/24,1/6,
-3/8,-7/96,11/96],[13/64,-91/192,-7/24,17/8,1/8,-5/6,-5/192,
19/64],[35/192,-19/192,-3/8,37/24,1/6,-7/12,-3/64,41/192],[
19/96,47/96,-1/2,1/24,1/6,0,-5/96,1/32],[-13/48,-5/48,1/4,
53/24,-1/12,-5/6,1/48,5/16],[35/192,-13/192,-1/3,13/24,1/8,
-5/24,-3/64,5/64],[-5/32,1/48,-7/24,1,1/8,-3/8,-1/32,7/48],
[23/96,-15/32,-2/3,3/8,7/24,-1/6,-3/32,1/32],[-7/48,-1/12,
-1/12,7/8,1/24,-1/3,-1/48,1/8],[-1/12,0,7/24,-13/24,-1/6,
5/24,1/24,-1/12],[-17/192,-37/64,1/3,1/12,-1/6,-1/24,11/192,
-1/64],[9/16,-5/24,-49/24,14/3,19/24,-43/24,-13/48,2/3],[
27/64,-149/192,-53/24,65/12,5/6,-25/12,-59/192,143/192],[
127/192,-43/64,-17/8,53/12,5/6,-5/3,-53/192,115/192],[11/32,
-25/48,-13/12,19/8,5/12,-11/12,-5/32,5/16],[15/32,-13/16,3/8,
-3/4,-1/6,7/24,3/32,-7/48],[37/192,19/64,-17/6,71/24,13/12,
-9/8,-79/192,85/192],[-61/192,31/64,3/8,-31/24,-1/8,1/2,
7/192,-31/192],[-25/48,19/96,7/4,-23/6,-5/8,3/2,11/48,-53/96
],[11/32,25/96,-29/24,13/24,11/24,-5/24,-5/32,3/32],[
-161/192,-125/192,37/24,-5/8,-7/12,1/4,35/192,-25/192],[5/24,
-1/8,13/8,-13/24,-5/8,5/24,1/4,-1/12],[-35/192,-5/64,11/6,
-25/12,-17/24,19/24,49/192,-59/192],[11/32,5/16,-2,31/12,3/4,
-1,-9/32,19/48],[-97/192,69/64,7/8,-7/8,-1/3,1/3,19/192,
-13/192],[19/24,-71/96,-13/12,2/3,5/12,-1/4,-1/8,5/96],[
-1/8,83/96,-13/24,65/24,5/24,-25/24,-1/12,43/96],[-3/8,25/48,
31/24,-29/24,-1/2,11/24,1/6,-7/48],[25/192,-43/64,-13/6,3/8,
5/6,-1/8,-59/192,1/64],[83/192,-53/64,-19/24,47/12,7/24,-3/2,
-17/192,101/192],[59/96,-27/32,-7/8,9/4,1/3,-7/8,-3/32,9/32
],[-83/96,61/96,15/8,-65/24,-17/24,25/24,7/32,-35/96],[
-13/96,-33/32,17/12,31/24,-13/24,-1/2,19/96,13/96],[-1/192,
61/64,-3/4,1/3,7/24,-1/8,-7/64,19/192],[-139/192,-45/64,25/8,
31/24,-29/24,-1/2,27/64,29/192],[77/192,-23/192,-3/2,41/24,
5/8,-5/8,-13/64,15/64],[-17/192,41/64,1/6,-9/8,-1/24,11/24,
1/64,-25/192],[35/96,-7/96,-5/12,-11/24,5/24,1/6,-5/96,-7/96
],[23/96,-35/96,-1/6,7/8,1/12,-1/3,-1/96,3/32],[1/6,-2/3,
-1/12,2,1/12,-3/4,0,1/4],[-1/48,-37/96,1/8,3/8,-1/24,-1/8,
1/48,1/32],[23/192,-59/192,7/12,-1/6,-7/24,1/24,19/192,-7/192
],[-7/32,-1/24,7/8,7/24,-1/3,-1/8,11/96,1/24],[3/64,
-55/192,1/3,7/12,-1/8,-5/24,13/192,13/192],[-41/192,-37/192,
-11/24,11/12,5/24,-1/3,-13/192,23/192],[-41/192,-59/192,17/24,
1/2,-7/24,-1/6,19/192,3/64],[-3/32,1/32,3/8,-11/12,-1/8,3/8,
1/32,-13/96],[35/192,13/64,-1/2,-7/24,1/6,1/8,-3/64,-5/192],
[1/6,1/4,-1/8,-1,1/24,3/8,0,-1/8],[-31/192,-3/64,7/8,-3/4,
-1/3,1/4,7/64,-7/64],[-5/64,11/64,-17/24,-31/24,1/4,1/2,
-19/192,-35/192],[41/96,-13/96,-25/24,-1/3,3/8,1/8,-11/96,
-5/96],[-35/192,13/192,1/3,-13/24,-1/8,5/24,3/64,-5/64],[
7/32,-7/96,-1/24,-1,1/24,3/8,1/96,-5/32],[-1/96,5/24,-25/24,
-1/12,3/8,1/24,-13/96,0],[-33/64,-85/192,11/8,5/12,-13/24,
-1/6,11/64,7/192],[23/192,11/192,-1/4,-13/24,1/12,5/24,
-5/192,-17/192],[1/4,-11/48,5/24,-3/8,-1/12,1/8,1/24,-1/16],
[0,-13/32,-7/24,13/24,1/12,-5/24,-1/24,5/96],[11/16,-47/96,
-5/8,-1/4,7/24,1/8,-1/16,-7/96],[-127/192,43/64,17/8,-53/12,
-5/6,5/3,53/192,-115/192],[-41/192,77/192,15/8,-10/3,-3/4,
5/4,17/64,-29/64],[41/96,-9/32,-5/3,47/24,2/3,-3/4,-23/96,
25/96],[-29/24,11/16,19/8,-43/12,-11/12,11/8,7/24,-23/48],[
-37/192,125/192,13/12,-55/24,-5/12,7/8,31/192,-55/192],[
-47/192,19/192,13/8,-19/8,-5/8,11/12,15/64,-65/192],[5/24,
1/6,-11/12,1/4,3/8,-1/12,-1/8,1/24],[-1/2,7/24,13/8,-71/24,
-5/8,9/8,5/24,-5/12],[27/64,-217/192,-7/8,47/24,1/3,-3/4,
-19/192,43/192],[11/12,-41/24,-71/24,139/24,9/8,-53/24,-3/8,
3/4],[-43/192,223/192,1,-23/4,-3/8,53/24,25/192,-149/192],[
-35/96,-23/48,4/3,-23/12,-1/2,3/4,17/96,-5/16],[-161/192,
-125/192,37/24,-5/8,-7/12,1/4,35/192,-25/192],[-115/96,65/96,
13/6,-47/12,-5/6,3/2,25/96,-17/32],[-11/32,-25/96,29/24,
-13/24,-11/24,5/24,5/32,-3/32],[29/64,-191/192,0,17/12,0,
-13/24,1/64,29/192],[13/96,5/24,-9/8,3/4,5/12,-7/24,-5/32,
1/8],[-121/192,91/64,-13/12,-71/24,5/12,9/8,-37/192,-67/192],
[209/192,25/64,-11/8,2/3,13/24,-1/4,-9/64,23/192],[145/192,
-89/192,-11/6,17/12,17/24,-13/24,-43/192,35/192],[25/192,
-43/64,-13/6,3/8,5/6,-1/8,-59/192,1/64],[181/192,-91/64,-7/8,
5/8,1/3,-1/4,-5/64,1/64],[3/8,-25/48,-31/24,29/24,1/2,
-11/24,-1/6,7/48],[-17/64,-43/192,7/24,1/6,-1/12,-1/12,1/192,
1/192],[1/192,61/192,-7/12,-29/24,5/24,11/24,-19/192,-31/192
],[41/192,-17/192,-17/24,1,7/24,-5/12,-19/192,9/64],[5/64,
23/192,-13/12,1/24,3/8,-1/24,-29/192,1/64],[-1/48,-49/96,
5/24,15/8,-1/24,-17/24,1/48,23/96],[0,-2/3,5/12,1/4,-1/6,
-1/12,1/12,0],[-1/96,-3/8,-5/24,1/8,1/24,-1/24,-1/96,0],[
-1/12,-3/16,13/12,-19/12,-11/24,7/12,1/6,-11/48],[13/192,
103/192,1/12,-7/6,-1/24,11/24,1/192,-29/192],[-13/192,25/64,
1/3,23/24,-1/12,-3/8,7/192,31/192],[1/32,-5/16,1/4,1/24,
-1/8,0,1/32,-1/48],[15/64,-61/192,-1/24,3/2,0,-7/12,1/192,
13/64],[31/96,25/96,-11/24,-17/12,1/6,13/24,-5/96,-19/96],[
31/192,5/64,0,7/24,-1/24,-1/8,1/64,11/192],[19/96,1/4,13/24,
-1,-5/24,3/8,7/96,-1/8],[-35/192,55/192,3/8,-7/24,-1/6,1/12,
3/64,-5/192],[-7/96,-17/32,2/3,1/24,-5/24,0,3/32,-1/32],[
-31/192,21/64,-7/24,1/4,1/8,-1/12,-11/192,11/192],[1/24,1/6,
0,7/24,1/24,-1/12,0,1/24],[-11/48,-1/6,7/12,7/8,-5/24,-1/3,
1/16,1/8],[-13/192,77/192,-1/12,1/12,0,-1/24,-1/192,3/64],[
-31/192,29/192,5/8,1/24,-5/24,0,13/192,1/192],[1/24,-5/24,
-7/24,1/12,1/8,-1/24,-1/24,0],[-1/32,-11/48,1/8,1/2,-1/24,
-5/24,1/96,1/16],[-17/48,1/48,2,-59/24,-19/24,11/12,13/48,
-17/48],[23/64,9/64,-29/12,13/8,11/12,-5/8,-21/64,47/192],[
9/64,-85/192,-1/12,43/24,0,-17/24,-1/192,47/192],[-13/32,
-13/24,25/24,5/3,-5/12,-5/8,13/96,5/24],[3/32,17/48,-4/3,
11/12,13/24,-1/3,-19/96,7/48],[-9/64,-13/64,1/24,25/24,-1/24,
-5/12,1/192,29/192],[11/192,-7/64,-7/8,0,1/3,0,-25/192,
-1/192],[5/32,-5/24,5/12,-5/24,-1/6,1/12,7/96,-1/24],[
19/32,-1,-17/24,71/24,7/24,-9/8,-7/96,3/8],[43/64,-67/192,
-37/24,11/24,7/12,-1/6,-35/192,3/64],[-59/48,155/96,-19/24,
-17/8,7/24,19/24,-3/16,-7/32],[13/64,21/64,7/6,-19/6,-11/24,
29/24,35/192,-85/192],[-13/16,55/48,5/12,-7/4,-1/6,2/3,1/48,
-3/16],[1/64,-91/192,-7/8,47/24,1/3,-3/4,-25/192,49/192],[
-1/24,1/2,-2,3/2,3/4,-7/12,-7/24,1/4],[5/12,-169/96,1/8,
97/24,-1/24,-37/24,1/24,47/96],[-27/64,175/192,-1/3,-13/24,
1/8,5/24,-13/192,-5/192],[3/8,1,-1,-2/3,3/8,1/4,-1/8,-1/24
],[-1/192,-109/192,15/8,-35/8,-17/24,5/3,17/64,-43/64],[
143/192,-97/192,-5/12,19/6,1/6,-29/24,-5/192,83/192],[79/192,
-91/64,3/4,1/3,-7/24,-1/8,9/64,-5/192],[-13/64,77/192,-7/24,
-19/8,1/8,11/12,-11/192,-21/64],[-67/192,5/64,17/8,-95/24,
-5/6,3/2,19/64,-109/192],[-1/4,-13/96,-13/8,17/12,5/8,-13/24,
-1/4,19/96],[-11/192,19/192,0,-23/24,0,3/8,1/192,-25/192],[
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-13/64],[53/192,-211/192,5/24,-13/4,-1/12,5/4,3/64,-103/192],
[-77/192,295/192,25/12,-107/24,-19/24,41/24,55/192,-109/192],[
1/8,-79/48,-7/4,-37/24,2/3,7/12,-1/4,-5/16],[9/32,89/96,
-11/24,-55/24,1/6,7/8,-5/96,-9/32],[7/64,-313/192,17/12,
43/12,-13/24,-11/8,41/192,83/192],[7/48,3/16,-19/24,-5/2,
7/24,23/24,-5/48,-17/48],[-77/64,97/192,35/12,55/24,-9/8,
-7/8,23/64,23/64],[-73/192,-21/64,37/24,17/12,-13/24,-7/12,
35/192,37/192],[-71/192,-71/192,7/8,9/8,-7/24,-5/12,7/64,
29/192],[-11/64,41/192,-5/24,-1/4,1/24,1/12,-5/192,-1/64],[
-13/96,43/96,1/6,-7/8,-1/12,1/3,1/32,-3/32],[-7/24,13/32,
13/24,1/12,-1/6,-1/24,1/24,1/32],[35/192,79/192,-7/8,-7/8,
3/8,1/3,-25/192,-7/64],[67/192,1/64,1/6,11/8,-1/12,-13/24,
7/192,13/64],[1/6,15/32,-5/8,-7/4,1/4,17/24,-1/12,-23/96],[
35/96,5/96,-9/8,-31/24,3/8,13/24,-13/96,-19/96],[55/192,
47/64,-17/24,-23/12,5/24,3/4,-13/192,-47/192],[1/16,-1/96,
11/24,-1/3,-1/6,1/8,1/16,-5/96],[1/192,-77/192,5/24,5/12,
-1/12,-1/6,5/192,7/192],[13/64,-23/192,-1/3,-7/24,1/12,1/8,
-5/192,-11/192],[-19/192,-11/192,11/12,3/8,-3/8,-1/8,25/192,
3/64],[5/192,-83/192,-1/2,-7/24,5/24,1/8,-5/64,-5/64],[
-49/192,11/64,1,1/12,-3/8,-1/24,9/64,5/192],[35/96,5/96,
1/24,-25/24,0,3/8,1/32,-5/32],[-47/192,-41/192,7/24,1/6,
-1/8,-1/12,5/192,1/64],[-5/96,-5/12,-1/2,5/4,1/4,-1/2,-3/32,
1/6],[17/32,55/96,-7/24,-2,1/24,19/24,-1/96,-25/96],[
-37/64,-5/64,5/6,1/8,-7/24,-1/24,13/192,5/192],[11/192,3/64,
-5/6,-1/6,3/8,1/24,-25/192,-1/64],[-3/16,29/96,7/24,13/24,
-1/12,-5/24,1/48,3/32],[1/32,5/24,-1/24,-1/12,1/24,1/24,
-1/96,0],[-23/96,59/96,65/24,-35/12,-25/24,9/8,37/96,-37/96
],[37/192,-65/192,-1/8,11/24,1/24,-1/6,1/192,11/192],[
125/192,-27/64,-17/6,103/24,13/12,-13/8,-71/192,115/192],[
17/96,13/96,13/24,7/24,-5/24,-1/8,3/32,5/96],[-3/8,25/32,
-25/24,-29/24,3/8,11/24,-1/6,-13/96],[-25/192,109/192,-37/24,
29/12,7/12,-11/12,-15/64,73/192],[-7/64,-79/192,0,29/24,0,
-11/24,-1/192,29/192],[-5/96,-1/32,-7/24,23/24,1/8,-3/8,
-5/96,13/96],[9/32,-11/48,-3/4,13/12,7/24,-5/12,-3/32,7/48],
[-13/192,-1/64,13/12,-5/2,-5/12,23/24,31/192,-71/192],[25/96,
3/8,-1/3,-29/12,1/8,11/12,-1/32,-1/3],[-115/192,-153/64,
13/24,19/8,-5/24,-11/12,3/64,41/192],[-5/16,5/12,9/8,23/24,
-5/12,-3/8,7/48,1/6],[13/192,67/64,55/24,7/4,-7/8,-2/3,
65/192,61/192],[7/96,27/32,19/24,-17/12,-7/24,13/24,11/96,
-5/32],[-15/32,-1/4,17/24,1/12,-1/4,-1/24,7/96,0],[-29/64,
181/192,1/3,-55/24,-1/8,7/8,5/192,-55/192],[73/96,-15/16,
-11/8,13/8,13/24,-5/8,-5/32,3/16],[223/192,31/64,-5/4,1,
11/24,-3/8,-7/64,11/64],[17/64,-1/64,-79/24,-47/24,5/4,3/4,
-89/192,-55/192],[-103/192,-7/64,3/2,13/24,-7/12,-5/24,37/192,
5/64],[-161/192,-131/192,65/24,89/24,-25/24,-17/12,67/192,
97/192],[25/192,-17/192,5/12,11/6,-1/6,-17/24,13/192,17/64],
[1/32,-37/96,-1/3,-5/24,1/8,1/12,-5/96,-5/96],[29/192,
37/192,5/24,-7/8,-1/8,1/3,3/64,-23/192],[-41/192,17/64,-1/24,
-13/8,0,7/12,-5/192,-41/192],[17/64,-11/64,-1/8,5/12,1/24,
-1/6,-1/192,11/192],[19/192,-23/192,-5/12,13/8,1/8,-5/8,
-3/64,15/64],[-7/48,-5/96,1/2,-1/24,-1/6,0,1/16,-1/96],[
-1/4,1/24,-1/6,1/24,1/24,0,-1/24,0],[23/96,-13/48,-2/3,9/8,
1/3,-5/12,-3/32,7/48],[-41/96,1/12,1/8,7/24,-1/24,-1/8,
-1/96,1/24],[-53/192,29/192,5/12,7/12,-1/8,-5/24,7/192,17/192
],[49/192,29/64,-1/4,-7/24,1/12,1/8,-1/64,-5/192],[-3/32,
-5/16,-1/12,-1/24,1/24,0,-1/96,-1/48],[49/192,-9/64,-25/24,
-1/2,5/12,1/6,-9/64,-5/64],[5/32,9/32,-11/24,-2/3,1/6,7/24,
-5/96,-3/32],[25/192,35/64,1/6,-3/8,-1/24,1/8,5/192,-1/64],
[-1/48,-25/96,-5/24,-1/2,1/24,5/24,-1/48,-3/32],[55/192,
145/192,-7/24,-37/24,1/12,7/12,-5/192,-35/192],[-15/64,
103/192,7/8,5/24,-1/3,-1/12,23/192,11/192],[-61/192,-85/192,
1/3,25/24,-1/8,-3/8,7/192,23/192],[-15/64,-11/192,7/24,-5/24,
-1/8,1/12,7/192,-7/192],[-5/32,11/96,1/4,17/24,-1/8,-1/4,
1/96,11/96],[9/32,5/12,-1/6,5/12,1/12,-1/6,-1/96,1/12],[
-1/6,-29/96,1/24,-1/4,-1/24,1/8,0,-5/96],[3/32,11/96,11/24,
1/12,-1/8,-1/24,5/96,1/32],[11/192,-71/192,-17/24,5/8,5/24,
-1/4,-17/192,13/192],[-7/32,61/96,1/3,-11/24,-1/8,1/6,1/32,
-1/32],[-7/32,-7/16,7/24,49/24,-1/8,-19/24,1/32,13/48],[
-19/32,37/48,-5/12,-31/24,1/6,1/2,-3/32,-7/48],[-43/192,
55/192,-1/4,17/12,1/12,-13/24,-7/192,43/192],[11/64,11/64,
-5/6,29/24,7/24,-11/24,-19/192,37/192],[-11/24,5/16,19/24,
-27/8,-7/24,31/24,1/12,-23/48],[-1/48,-33/32,15/8,19/24,
-17/24,-7/24,13/48,5/96],[11/192,-83/192,-23/24,4/3,3/8,-1/2,
-25/192,11/64],[125/192,-145/192,-23/12,23/6,3/4,-35/24,
-47/192,33/64],[-125/192,-31/64,13/8,-79/24,-5/8,5/4,13/64,
-97/192],[-79/192,-23/192,-1/4,-25/12,1/12,19/24,-11/192,
-59/192],[11/32,7/24,-1/3,-29/12,1/8,11/12,-1/32,-1/3],[
53/96,-115/96,-53/24,27/8,5/6,-31/24,-9/32,41/96],[125/192,
-173/192,-13/12,97/24,5/12,-37/24,-23/192,103/192],[9/8,-7/24,
-15/8,11/6,17/24,-17/24,-5/24,1/4],[-5/192,69/64,-7/24,17/6,
1/8,-13/12,-3/64,91/192],[-31/48,125/96,-11/24,-65/24,1/6,
25/24,-5/48,-31/96],[37/48,-67/48,-13/6,19/8,5/6,-11/12,
-13/48,13/48],[35/64,-49/192,-7/8,-3/2,1/3,7/12,-19/192,
-15/64],[11/64,65/192,11/12,29/24,-3/8,-11/24,29/192,37/192],
[-47/64,217/192,-7/24,-17/6,1/8,13/12,-17/192,-67/192],[
-59/96,137/96,7/12,-53/24,-5/24,5/6,5/96,-23/96],[-47/96,
71/48,7/12,-5/12,-5/24,1/6,5/96,1/48],[-119/96,11/96,97/24,
-23/24,-37/24,3/8,49/96,-13/96],[47/192,-71/192,-1/4,0,1/8,
-1/24,-5/192,-1/64],[-55/192,23/192,3/8,-25/24,-1/8,5/12,
5/192,-29/192],[-1/16,1/6,-1/24,-1/8,0,1/24,-1/48,0],[
-9/64,41/64,3/8,-1/12,-1/8,0,3/64,7/192],[13/96,-7/16,17/24,
1/4,-5/24,-1/8,3/32,1/48],[19/64,59/192,7/24,-3/2,-1/8,7/12,
13/192,-41/192],[-1/16,-43/48,1/3,53/24,-1/6,-5/6,1/16,13/48
],[5/24,1/4,-1/12,-21/8,1/24,1,0,-3/8],[-1/24,5/96,5/8,
3/8,-7/24,-1/8,1/12,5/96],[25/192,35/64,-11/24,-7/24,5/24,
1/12,-11/192,-1/64],[-7/192,1/64,1/8,13/24,-1/24,-1/4,5/192,
5/64],[-3/32,-23/32,-3/4,9/8,5/24,-5/12,-3/32,11/96],[
-1/96,9/32,1/6,-3/2,-1/8,7/12,1/32,-7/32],[-49/96,-55/96,
5/6,47/24,-7/24,-3/4,7/96,25/96],[1/4,1/4,-5/8,-23/12,1/4,
17/24,-1/12,-1/4],[-83/192,-23/192,17/12,5/3,-13/24,-5/8,
11/64,15/64],[11/96,1/32,1/8,17/24,-1/24,-7/24,1/32,11/96],
[9/64,29/192,13/24,9/8,-5/24,-5/12,5/64,11/64],[83/192,
25/192,-7/24,-3/4,1/8,1/4,-1/192,-19/192],[-5/8,-2/3,25/24,
9/4,-3/8,-7/8,1/8,7/24],[-5/192,-9/64,-1/24,-11/24,0,1/6,
-1/192,-5/64],[59/192,37/192,7/24,-5/24,-1/8,1/12,5/64,-7/192
],[7/96,-47/96,-11/8,-13/24,1/2,5/24,-17/96,-11/96],[
-97/192,5/64,41/24,3/2,-5/8,-7/12,43/192,43/192],[1/8,5/32,
-7/24,-1/12,1/8,1/24,-1/24,-1/96],[25/48,-7/24,-7/4,13/4,
2/3,-5/4,-11/48,11/24],[1/4,25/96,11/8,-49/24,-1/2,19/24,
5/24,-9/32],[-37/96,5/32,-3/4,11/24,7/24,-1/6,-13/96,7/96],
[-3/16,-47/96,31/24,-29/24,-1/2,11/24,3/16,-19/96],[7/24,
1/96,4/3,-1/4,-1/2,1/12,5/24,-1/32],[25/96,-19/96,1/4,-13/6,
-1/12,5/6,5/96,-31/96],[-17/32,11/96,11/8,-1,-13/24,3/8,
17/96,-13/96],[5/96,-71/96,1/3,21/8,-1/8,-1,5/96,11/32],[
-1/4,-29/96,-3/4,21/8,7/24,-1,-1/8,35/96],[-29/32,-21/32,1,
-47/24,-3/8,3/4,3/32,-31/96],[-19/48,17/24,-1/2,7/8,5/24,
-1/3,-5/48,1/6],[3/4,43/48,-1/2,-73/24,5/24,7/6,-1/24,-19/48
],[-1/2,11/24,-3/8,1,1/8,-3/8,-1/12,1/6],[1/6,127/96,-7/8,
-25/8,1/3,29/24,-1/8,-37/96],[-13/48,-13/96,13/24,17/12,
-5/24,-13/24,1/16,19/96],[-13/192,-19/192,-29/24,2/3,11/24,
-1/4,-11/64,17/192],[-27/64,-23/64,13/12,-11/4,-5/12,25/24,
9/64,-27/64],[73/96,-23/48,-5/3,-13/12,5/8,5/12,-19/96,-3/16
],[-131/192,5/192,55/24,-47/24,-7/8,3/4,19/64,-55/192],[
91/192,169/192,1/3,1/8,-1/8,-1/24,5/64,13/192],[-67/192,
65/192,31/24,-37/12,-1/2,7/6,11/64,-83/192],[31/96,13/32,5/8,
-5/3,-1/4,5/8,11/96,-7/32],[-103/192,-19/192,1/6,-5/3,-1/24,
5/8,-1/64,-47/192],[-7/48,23/32,-1/24,1/8,-1/24,-1/24,-1/48,
5/96],[-13/96,5/24,5/12,-31/24,-1/8,1/2,1/32,-1/6],[
-31/192,-79/192,7/24,3/2,-1/8,-7/12,5/192,37/192],[5/192,
-3/64,-5/24,1/3,1/12,-1/6,-7/192,11/192],[5/24,25/96,-5/12,
2/3,1/8,-1/4,-1/24,3/32],[13/96,1/8,-1/3,5/24,1/12,-1/12,
-1/32,1/24],[-35/192,7/64,1/6,7/12,-1/12,-5/24,1/192,17/192
],[1/6,7/32,3/4,-1/24,-1/3,0,1/8,1/96],[-1/12,-61/96,-1/2,
5/4,1/4,-1/2,-1/12,5/32],[-1/24,-3/32,-3/8,1/3,1/6,-1/8,
-1/24,1/32],[97/192,5/64,-9/8,-4/3,11/24,1/2,-9/64,-37/192],
[7/64,1/192,-3/8,0,1/12,0,-7/192,-1/64],[-15/64,-113/192,
5/24,13/12,-1/24,-5/12,-1/192,9/64],[-1/64,-67/192,5/12,
17/24,-1/8,-7/24,3/64,17/192],[-11/192,47/192,-5/24,-7/6,
1/12,5/12,-7/192,-29/192],[-41/96,-17/48,1/2,0,-1/6,0,1/32,
-1/48],[37/96,7/48,-5/4,-5/12,11/24,1/6,-5/32,-1/16],[
-7/48,5/96,13/24,-5/8,-1/6,5/24,1/16,-7/96],[-1/192,37/192,
5/12,1/2,-1/6,-5/24,11/192,17/192],[25/48,5/8,-23/24,-37/24,
1/3,5/8,-5/48,-5/24],[1/32,-61/96,-1/3,-11/24,1/6,1/6,-5/96,
-3/32],[-53/192,13/192,7/6,9/8,-11/24,-11/24,31/192,11/64],[
-7/48,5/48,1/2,-5/24,-5/24,1/12,1/16,-1/48],[-1/64,-5/192,
1/24,5/6,1/24,-1/3,1/192,23/192],[41/96,11/32,-19/8,19/24,
11/12,-7/24,-31/96,13/96],[-1/8,25/24,1/3,-13/4,-1/8,5/4,
1/24,-5/12],[13/24,-27/32,-7/12,37/12,5/24,-7/6,-1/24,13/32
],[95/192,7/64,1/4,-7/12,-1/12,5/24,11/192,-5/64],[91/192,
-89/64,11/12,7/24,-3/8,-1/8,31/192,-7/192],[-1/96,-3/32,-5/4,
25/8,1/2,-7/6,-17/96,43/96],[-43/96,119/96,5/24,-17/12,-1/12,
13/24,1/96,-13/96],[83/192,-37/64,-1/8,13/4,1/24,-5/4,-1/192,
85/192],[-53/192,23/192,19/8,-47/24,-11/12,3/4,21/64,-53/192
],[-185/192,-41/192,5/3,16/3,-5/8,-49/24,35/192,49/64],[
9/64,-95/192,-5/8,125/24,1/4,-2,-17/192,47/64],[-43/96,-7/24,
13/24,1/8,-5/24,-1/24,5/96,0],[11/96,1/12,13/12,-7/4,-5/12,
2/3,5/32,-1/4],[-17/192,1/192,1,-23/6,-3/8,35/24,9/64,
-107/192],[-17/48,-15/32,0,-13/6,0,5/6,-1/48,-11/32],[
293/192,7/192,-9/8,-5/24,5/12,1/12,-5/64,-5/192],[3/8,-37/32,
-11/24,17/4,1/6,-13/8,-1/24,53/96],[-25/24,-7/8,15/8,1/3,
-17/24,-1/8,5/24,0],[-39/32,29/96,23/24,-1/3,-3/8,1/8,7/96,
-1/32],[15/32,-7/24,-43/24,1/12,17/24,-1/24,-23/96,0],[
29/64,11/192,-5/4,5/2,11/24,-23/24,-29/192,71/192],[89/64,
-67/192,-41/12,15/8,31/24,-17/24,-27/64,49/192],[51/64,
-43/192,-59/24,-11/24,11/12,1/6,-59/192,-5/64],[-11/192,
277/192,0,29/24,0,-11/24,1/192,49/192],[-13/48,7/16,-5/24,
-9/8,1/12,11/24,-1/16,-7/48],[55/192,35/192,-3/8,11/24,1/8,
-1/6,-5/192,5/64],[1/48,0,-1/6,1/24,1/12,0,-1/48,0],[1/6,
-1/8,-7/8,3/8,1/3,-1/8,-1/8,1/24],[-25/192,11/64,-5/12,
-5/12,1/8,5/24,-13/192,-11/192],[-7/24,11/96,-7/8,-25/24,3/8,
3/8,-1/6,-13/96],[0,55/96,0,-9/4,0,5/6,0,-29/96],[-25/64,
-29/192,-3/4,35/24,1/3,-13/24,-31/192,13/64],[-11/96,7/32,
3/8,7/24,-1/8,-1/8,5/96,5/96],[-11/96,-25/48,5/24,1/3,-1/24,
-1/8,1/96,1/48],[9/64,17/64,-1/12,-17/24,1/24,7/24,-1/192,
-17/192],[17/192,19/64,3/4,1/12,-1/4,-1/24,7/64,5/192],[
1/16,5/48,-1/8,11/12,1/8,-3/8,-1/48,7/48],[5/12,17/24,1/4,
-1/6,-1/8,1/12,1/12,0],[-23/192,-19/192,7/24,43/24,-1/8,
-2/3,5/192,49/192],[97/192,25/64,-3/4,-1,7/24,3/8,-11/192,
-25/192]])
]> 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;
