//Standard generators of L2(32) are a, b where a has order 2,
//b has order 3 and ab is in class 31A/B/C/D/E.
//Alternatively: a has order 2, b has order 3, ab has order 31
//and ababb has order 11.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
        _LR`AI:=[[a,b*a*b*a*b*a*b*a*b*a*b^-1*a*b^-1*a*b^-1*a*b^-1]]
             where a is (_LR`F).1 where b is (_LR`F).2;
//15 representations cycled by auto
_LR`G :=
/*
Original group: c9Group("l232p")
Recomputed by BB method
Schur index: 1
Character: ( 33, 1, 0, 0, 0, 0, 0, 0, zeta(31)_31^25 + zeta(31)_31^6, 
zeta(31)_31^19 + zeta(31)_31^12, zeta(31)_31^18 + zeta(31)_31^13, zeta(31)_31^24
+ zeta(31)_31^7, -zeta(31)_31^29 - zeta(31)_31^28 - zeta(31)_31^27 - 
zeta(31)_31^26 - zeta(31)_31^25 - zeta(31)_31^24 - zeta(31)_31^23 - 
zeta(31)_31^22 - zeta(31)_31^21 - zeta(31)_31^20 - zeta(31)_31^19 - 
zeta(31)_31^18 - zeta(31)_31^17 - zeta(31)_31^16 - zeta(31)_31^15 - 
zeta(31)_31^14 - zeta(31)_31^13 - zeta(31)_31^12 - zeta(31)_31^11 - 
zeta(31)_31^10 - zeta(31)_31^9 - zeta(31)_31^8 - zeta(31)_31^7 - zeta(31)_31^6 -
zeta(31)_31^5 - zeta(31)_31^4 - zeta(31)_31^3 - zeta(31)_31^2 - 1, 
zeta(31)_31^26 + zeta(31)_31^5, zeta(31)_31^20 + zeta(31)_31^11, zeta(31)_31^17 
+ zeta(31)_31^14, zeta(31)_31^23 + zeta(31)_31^8, zeta(31)_31^29 + 
zeta(31)_31^2, zeta(31)_31^27 + zeta(31)_31^4, zeta(31)_31^21 + zeta(31)_31^10, 
zeta(31)_31^16 + zeta(31)_31^15, zeta(31)_31^22 + zeta(31)_31^9, zeta(31)_31^28 
+ zeta(31)_31^3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 )
*/
MatrixGroup<33, 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]),
Matrix(K,33,33,
[[-5/16,1/2,167/16,-255/16,-635/16,489/8,685/16,-1391/16,3/16,
97/2,-309/16,-45/8,91/16,-23/16,1/8],[-5/16,17/16,41/16,
-209/16,217/16,207/8,-227/4,71/16,453/8,-603/16,-59/8,285/16,
-65/8,13/8,-1/8],[7/16,-1/2,-55/16,41/8,75/16,-149/16,21/16,
33/8,-11/4,11/16,-1/16,0,0,0,0],[-1/8,13/16,-1,-83/16,
49/8,91/16,-161/16,23/16,33/8,-11/4,11/16,-1/16,0,0,0],[
-1/8,-2,-7/16,75/8,51/16,-141/8,5/16,227/16,-91/16,-23/8,21/8,
-11/16,1/16,0,0],[-1/8,5/8,3/4,-173/16,5/4,447/16,-113/8,
-369/16,339/16,21/16,-33/4,4,-13/16,1/16,0],[1/4,5/4,-23/8,
-31/2,273/16,83/2,-827/16,-27,977/16,-277/16,-287/16,65/4,
-45/8,15/16,-1/16],[-3/16,-1/16,5/2,27/16,-199/16,-4,117/4,
-7,-215/8,77/4,55/16,-71/8,65/16,-13/16,1/16],[-5/16,-1/4,
53/16,103/16,-67/4,-139/8,163/4,77/16,-83/2,307/16,77/8,-49/4,
77/16,-7/8,1/16],[1/16,17/8,-21/8,-45/2,24,861/16,-623/8,
-407/16,1409/16,-561/16,-351/16,403/16,-155/16,7/4,-1/8],[0,
-29/16,-1/2,11/2,21/8,-19/8,-121/16,-9/8,161/16,-47/16,-57/16,
43/16,-11/16,1/16,0],[-3/8,3/8,29/16,-3,-29/4,29/8,149/8,
-119/16,-21,255/16,67/16,-143/16,65/16,-13/16,1/16],[-5/16,
23/16,25/8,-55/4,1/16,571/16,-117/4,-379/16,707/16,-219/16,
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9,-385/16,9/16,251/16,-25/4,-45/16,21/8,-11/16,1/16,0],[0,
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],[-3/16,1/8,99/16,-13/8,-205/8,139/16,325/8,-47/2,-403/16,
199/8,1/8,-65/8,4,-13/16,1/16],[-5/16,-5/8,35/8,31/8,
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15/8,-1/4,-173/16,6,157/8,-35/2,-12,145/8,-9/4,-89/16,53/16,
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13/8,-1/8,0],[1/4,27/16,-133/16,-143/16,679/16,79/16,-311/4,
29,885/16,-181/4,-55/16,17,-129/16,13/8,-1/8],[0,-5/4,61/16,
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27/8,-3/4,1/16,0,0],[-1/8,-29/16,-29/16,49/4,101/16,-249/8,
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1/8],[-1/8,-7/16,-61/16,5,79/4,-73/4,-489/16,537/16,197/16,
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],[-1/8,-35/16,75/16,315/16,-227/8,-657/16,1079/16,31/2,
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253/16,-1135/16,527/16,131/8,-175/8,143/16,-27/16,1/8],[5/16,
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309/16,45/8,-91/16,23/16,-1/8],[-1/16,-3/16,19/4,-13/16,-16,
39/4,231/16,-125/8,1/16,99/16,-27/8,3/4,-1/16,0,0],[1/8,
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],[-3/16,-25/16,27/8,29/2,-109/4,-491/16,1169/16,17/16,-71,
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41/8,75/16,-149/16,21/16,33/8,-11/4,11/16,-1/16,0,0,0,0],[
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11/16,-1/16,0,0,0],[1/8,2,7/16,-75/8,-51/16,141/8,-5/16,
-227/16,91/16,23/8,-21/8,11/16,-1/16,0,0],[-1/8,5/8,3/4,
-173/16,5/4,447/16,-113/8,-369/16,339/16,21/16,-33/4,4,-13/16,
1/16,0],[1/4,5/4,-23/8,-31/2,273/16,83/2,-827/16,-27,977/16,
-277/16,-287/16,65/4,-45/8,15/16,-1/16],[-3/16,-1/16,5/2,
27/16,-199/16,-4,117/4,-7,-215/8,77/4,55/16,-71/8,65/16,
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77/16,-83/2,307/16,77/8,-49/4,77/16,-7/8,1/16],[1/16,17/8,
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403/16,-155/16,7/4,-1/8],[0,29/16,1/2,-11/2,-21/8,19/8,
121/16,9/8,-161/16,47/16,57/16,-43/16,11/16,-1/16,0],[-3/8,
3/8,29/16,-3,-29/4,29/8,149/8,-119/16,-21,255/16,67/16,
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-571/16,117/4,379/16,-707/16,219/16,207/16,-13,39/8,-7/8,1/16
],[-3/16,-15/8,61/16,123/16,-245/16,-9,385/16,-9/16,-251/16,
25/4,45/16,-21/8,11/16,-1/16,0],[0,11/16,-35/8,-105/16,
435/16,73/16,-409/8,331/16,513/16,-453/16,5/8,129/16,-4,13/16,
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389/16,-93/4,-11/16,131/16,-4,13/16,-1/16],[3/16,-1/8,-99/16,
13/8,205/8,-139/16,-325/8,47/2,403/16,-199/8,-1/8,65/8,-4,
13/16,-1/16],[5/16,5/8,-35/8,-31/8,421/16,-41/16,-783/16,
443/16,113/4,-121/4,11/4,119/16,-63/16,13/16,-1/16],[1/16,
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27/16,-133/16,-143/16,679/16,79/16,-311/4,29,885/16,-181/4,
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1/8],[1/2,-5/8,-51/8,147/16,191/16,-541/16,197/16,535/16,
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49/16,25/8,-10,-8,247/16,57/8,-239/16,3/2,45/8,-53/16,3/4,
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1/16,0],[1/4,-7/16,-21/16,35/4,-7/2,-217/8,449/16,313/16,
-663/16,13,13,-13,39/8,-7/8,1/16],[-1/16,-31/16,-9/16,99/8,
17/16,-447/16,35/4,201/8,-299/16,-7/2,71/8,-65/16,13/16,-1/16,
0],[1/8,19/16,-41/16,-97/16,117/8,141/16,-531/16,25/4,57/2,
-317/16,-27/8,71/8,-65/16,13/16,-1/16],[-3/16,-25/16,49/16,
109/8,-20,-429/16,797/16,47/8,-373/8,353/16,143/16,-195/16,
77/16,-7/8,1/16],[1/16,1,-1/16,-35/8,35/16,77/16,-63/16,
-3/4,13/8,-9/16,1/16,0,0,0,0],[1/4,1/16,-2,-41/16,49/8,
63/16,-147/16,21/16,33/8,-11/4,11/16,-1/16,0,0,0],[-1/8,
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-11/16,1/16,0,0],[0,1/8,23/8,-75/16,-10,309/16,35/8,
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49/8,11/4,-445/16,31/8,713/16,-91/4,-429/16,407/16,1/16,-65/8,
4,-13/16,1/16],[-1/16,7/16,15/8,17/16,-189/16,-33/8,117/4,
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195/8,-273/16,-65/16,143/16,-65/16,13/16,-1/16],[-3/16,5/16,
15/8,-55/8,21/16,385/16,-25,-299/16,637/16,-199/16,-209/16,13,
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-21/16,425/16,-233/16,-25/4,153/16,-33/8,13/16,-1/16,0],[
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363/16,3/4,-131/16,4,-13/16,1/16],[-1/16,15/16,-37/16,-53/16,
141/8,-3/8,-573/16,275/16,407/16,-187/8,-11/16,131/16,-4,13/16,
-1/16],[1/16,7/8,-67/16,-47/8,95/4,57/16,-45,37/2,473/16,
-209/8,0,65/8,-4,13/16,-1/16],[3/16,5/8,-1/8,-3/2,-91/16,
-3/16,321/16,-91/16,-91/4,33/2,33/8,-143/16,65/16,-13/16,1/16
],[1/16,7/8,1/8,-159/16,121/16,28,-547/16,-139/8,703/16,
-243/16,-99/8,207/16,-39/8,7/8,-1/16],[-1/16,3/8,-3/2,-97/16,
67/8,57/4,-141/8,-77/8,137/8,-17/8,-89/16,53/16,-3/4,1/16,0],
[1/4,23/16,-11/2,-43/4,393/16,77/4,-395/8,-13/8,351/8,-171/8,
-9,195/16,-77/16,7/8,-1/16],[-1/16,-7/16,13/16,21/16,-65/16,
-7/8,49/8,-35/16,-5/2,35/16,-5/8,1/16,0,0,0],[0,-5/16,
-27/16,-11/16,139/16,-35/16,-105/8,21/2,45/16,-55/8,55/16,-3/4,
1/16,0,0],[1/8,-9/8,-5/16,153/16,-71/16,-347/16,289/16,
111/8,-159/8,45/16,11/2,-53/16,3/4,-1/16,0],[1/4,3/4,-9/2,
-89/16,295/16,217/16,-629/16,-49/16,159/4,-149/8,-155/16,49/4,
-77/16,7/8,-1/16],[-5/16,-1/16,17/4,-29/16,-107/8,39/4,
203/16,-59/4,-1/16,99/16,-27/8,3/4,-1/16,0,0],[0,-11/16,
-31/16,13/2,29/16,-71/4,71/8,243/16,-63/4,1/16,99/16,-27/8,
3/4,-1/16,0],[1/8,-11/8,-3/16,223/16,-77/8,-525/16,305/8,
145/8,-729/16,63/4,197/16,-207/16,39/8,-7/8,1/16],[3/16,
-15/8,-21/8,83/4,-27/8,-773/16,30,575/16,-631/16,15/16,221/16,
-117/16,25/16,-1/8,0],[-1/16,-1,-19/8,19,-171/16,-947/16,
1215/16,573/16,-853/8,341/8,241/8,-559/16,221/16,-41/16,3/16],
[1/4,-7/16,-21/16,35/4,-7/2,-217/8,449/16,313/16,-663/16,13,
13,-13,39/8,-7/8,1/16],[-1/16,-31/16,-9/16,99/8,17/16,
-447/16,35/4,201/8,-299/16,-7/2,71/8,-65/16,13/16,-1/16,0],[
1/8,19/16,-41/16,-97/16,117/8,141/16,-531/16,25/4,57/2,-317/16,
-27/8,71/8,-65/16,13/16,-1/16],[-3/16,-25/16,49/16,109/8,-20,
-429/16,797/16,47/8,-373/8,353/16,143/16,-195/16,77/16,-7/8,
1/16],[-1/16,-1,1/16,35/8,-35/16,-77/16,63/16,3/4,-13/8,
9/16,-1/16,0,0,0,0],[-1/4,-1/16,2,41/16,-49/8,-63/16,
147/16,-21/16,-33/8,11/4,-11/16,1/16,0,0,0],[1/8,1/8,-3/16,
-15/8,-41/16,49/8,63/16,-147/16,21/16,33/8,-11/4,11/16,-1/16,
0,0],[0,1/8,23/8,-75/16,-10,309/16,35/8,-411/16,207/16,
109/16,-77/8,33/8,-13/16,1/16,0],[-1/8,-5/8,49/8,11/4,
-445/16,31/8,713/16,-91/4,-429/16,407/16,1/16,-65/8,4,-13/16,
1/16],[1/16,-7/16,-15/8,-17/16,189/16,33/8,-117/4,7,215/8,
-77/4,-55/16,71/8,-65/16,13/16,-1/16],[1/16,5/4,-23/16,
-169/16,55/4,183/8,-325/8,-115/16,85/2,-309/16,-77/8,49/4,
-77/16,7/8,-1/16],[-5/16,9/8,7/2,-15/2,-57/8,247/16,21/8,
-213/16,65/16,55/16,-43/16,11/16,-1/16,0,0],[0,-13/16,-9/8,
31/4,15/4,-93/4,77/16,195/8,-273/16,-65/16,143/16,-65/16,13/16,
-1/16,0],[-1/4,3/8,27/16,3/8,-67/8,-25/8,185/8,-77/16,
-195/8,273/16,65/16,-143/16,65/16,-13/16,1/16],[3/16,-5/16,
-15/8,55/8,-21/16,-385/16,25,299/16,-637/16,199/16,209/16,-13,
39/8,-7/8,1/16],[-1/16,7/8,27/16,-115/16,-115/16,89/4,21/16,
-425/16,233/16,25/4,-153/16,33/8,-13/16,1/16,0],[3/8,-11/16,
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341/16,363/16,-363/16,-3/4,131/16,-4,13/16,-1/16],[1/16,
-15/16,37/16,53/16,-141/8,3/8,573/16,-275/16,-407/16,187/8,
11/16,-131/16,4,-13/16,1/16],[1/16,7/8,-67/16,-47/8,95/4,
57/16,-45,37/2,473/16,-209/8,0,65/8,-4,13/16,-1/16],[3/16,
5/8,-1/8,-3/2,-91/16,-3/16,321/16,-91/16,-91/4,33/2,33/8,
-143/16,65/16,-13/16,1/16],[-1/16,-7/8,-1/8,159/16,-121/16,
-28,547/16,139/8,-703/16,243/16,99/8,-207/16,39/8,-7/8,1/16],
[1/16,-3/8,3/2,97/16,-67/8,-57/4,141/8,77/8,-137/8,17/8,
89/16,-53/16,3/4,-1/16,0],[1/4,23/16,-11/2,-43/4,393/16,
77/4,-395/8,-13/8,351/8,-171/8,-9,195/16,-77/16,7/8,-1/16],[
1/16,7/16,-13/16,-21/16,65/16,7/8,-49/8,35/16,5/2,-35/16,5/8,
-1/16,0,0,0],[0,5/16,27/16,11/16,-139/16,35/16,105/8,-21/2,
-45/16,55/8,-55/16,3/4,-1/16,0,0],[-1/8,9/8,5/16,-153/16,
71/16,347/16,-289/16,-111/8,159/8,-45/16,-11/2,53/16,-3/4,1/16,
0],[-1/4,-3/4,9/2,89/16,-295/16,-217/16,629/16,49/16,-159/4,
149/8,155/16,-49/4,77/16,-7/8,1/16],[5/16,1/16,-17/4,29/16,
107/8,-39/4,-203/16,59/4,1/16,-99/16,27/8,-3/4,1/16,0,0],[
3/16,-19/16,-23/4,117/16,571/16,-235/8,-273/4,64,339/8,-493/8,
101/16,149/8,-169/16,37/16,-3/16],[1/16,15/16,17/16,-177/16,
-51/8,265/8,51/16,-637/16,159/16,19,-167/16,-25/16,5/2,-11/16,
1/16],[-1/8,11/8,3/16,-223/16,77/8,525/16,-305/8,-145/8,
729/16,-63/4,-197/16,207/16,-39/8,7/8,-1/16],[-1/16,-7/16,
-1/2,-7/8,9/4,137/16,-121/16,-177/16,13,5/8,-25/4,27/8,-3/4,
1/16,0],[1/4,-7/16,-21/16,35/4,-7/2,-217/8,449/16,313/16,
-663/16,13,13,-13,39/8,-7/8,1/16],[-1/16,-31/16,-9/16,99/8,
17/16,-447/16,35/4,201/8,-299/16,-7/2,71/8,-65/16,13/16,-1/16,
0],[1/8,19/16,-41/16,-97/16,117/8,141/16,-531/16,25/4,57/2,
-317/16,-27/8,71/8,-65/16,13/16,-1/16],[3/16,25/16,-49/16,
-109/8,20,429/16,-797/16,-47/8,373/8,-353/16,-143/16,195/16,
-77/16,7/8,-1/16],[-1/16,-1,1/16,35/8,-35/16,-77/16,63/16,
3/4,-13/8,9/16,-1/16,0,0,0,0],[-1/4,-1/16,2,41/16,-49/8,
-63/16,147/16,-21/16,-33/8,11/4,-11/16,1/16,0,0,0],[-1/8,
-1/8,3/16,15/8,41/16,-49/8,-63/16,147/16,-21/16,-33/8,11/4,
-11/16,1/16,0,0],[0,1/8,23/8,-75/16,-10,309/16,35/8,
-411/16,207/16,109/16,-77/8,33/8,-13/16,1/16,0],[1/8,5/8,
-49/8,-11/4,445/16,-31/8,-713/16,91/4,429/16,-407/16,-1/16,
65/8,-4,13/16,-1/16],[1/16,-7/16,-15/8,-17/16,189/16,33/8,
-117/4,7,215/8,-77/4,-55/16,71/8,-65/16,13/16,-1/16],[-1/16,
-5/4,23/16,169/16,-55/4,-183/8,325/8,115/16,-85/2,309/16,77/8,
-49/4,77/16,-7/8,1/16],[5/16,-9/8,-7/2,15/2,57/8,-247/16,
-21/8,213/16,-65/16,-55/16,43/16,-11/16,1/16,0,0],[0,-13/16,
-9/8,31/4,15/4,-93/4,77/16,195/8,-273/16,-65/16,143/16,-65/16,
13/16,-1/16,0],[-1/4,3/8,27/16,3/8,-67/8,-25/8,185/8,-77/16,
-195/8,273/16,65/16,-143/16,65/16,-13/16,1/16],[3/16,-5/16,
-15/8,55/8,-21/16,-385/16,25,299/16,-637/16,199/16,209/16,-13,
39/8,-7/8,1/16],[-1/16,7/8,27/16,-115/16,-115/16,89/4,21/16,
-425/16,233/16,25/4,-153/16,33/8,-13/16,1/16,0],[-3/8,11/16,
43/8,-47/16,-345/16,153/16,69/2,-341/16,-363/16,363/16,3/4,
-131/16,4,-13/16,1/16],[1/16,-15/16,37/16,53/16,-141/8,3/8,
573/16,-275/16,-407/16,187/8,11/16,-131/16,4,-13/16,1/16],[
1/16,7/8,-67/16,-47/8,95/4,57/16,-45,37/2,473/16,-209/8,0,
65/8,-4,13/16,-1/16],[3/16,5/8,-1/8,-3/2,-91/16,-3/16,
321/16,-91/16,-91/4,33/2,33/8,-143/16,65/16,-13/16,1/16],[
1/16,7/8,1/8,-159/16,121/16,28,-547/16,-139/8,703/16,-243/16,
-99/8,207/16,-39/8,7/8,-1/16],[1/16,-3/8,3/2,97/16,-67/8,
-57/4,141/8,77/8,-137/8,17/8,89/16,-53/16,3/4,-1/16,0],[1/4,
23/16,-11/2,-43/4,393/16,77/4,-395/8,-13/8,351/8,-171/8,-9,
195/16,-77/16,7/8,-1/16],[-1/16,-7/16,13/16,21/16,-65/16,
-7/8,49/8,-35/16,-5/2,35/16,-5/8,1/16,0,0,0],[0,5/16,
27/16,11/16,-139/16,35/16,105/8,-21/2,-45/16,55/8,-55/16,3/4,
-1/16,0,0],[1/8,-9/8,-5/16,153/16,-71/16,-347/16,289/16,
111/8,-159/8,45/16,11/2,-53/16,3/4,-1/16,0],[-1/4,-3/4,9/2,
89/16,-295/16,-217/16,629/16,49/16,-159/4,149/8,155/16,-49/4,
77/16,-7/8,1/16],[-5/16,-1/16,17/4,-29/16,-107/8,39/4,203/16,
-59/4,-1/16,99/16,-27/8,3/4,-1/16,0,0],[0,11/16,31/16,
-13/2,-29/16,71/4,-71/8,-243/16,63/4,-1/16,-99/16,27/8,-3/4,
1/16,0]])
]> where w := K.1 where K := ext<K|Polynomial(K, [1, -5, -40, 75, 235, -379, 
-406, 825, 66, -737, 352, 143, -195, 77, -14, 1])> where K is RationalField();

return _LR;
