//Standard generators of L2(81) are a and b where a has order 2, b has order 3
//and ab has order 20.
//Standard generators of the double cover 2.L2(81) = SL2(81) are preimages A and
//B where B has order 3 (and AB has order 40) and ABABAB^-1 has order 41.
_LR := rec < recformat< F: GrpFP, AI: SeqEnum, G: GrpMat > |
      F := FreeGroup(2) >;
    _LR`AI:=[[a,
       b*a*b*a*b*a*b^-1*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b*a*b^-1*a*b^-1*a^-1],
                                                    //PSL(2,81).2=PGL(2,81)
   [a^-1, a^-1*b*a*b*a*b^-1*a*b^-1*a*b^-1*a*b*a*b],//PSL(2,81).4=PSigmaL(2,81)
   [a^-1, b*a*b^-1*a*b^-1*a*b*a*b*a*b*a*b^-1*a*b]]//square of AI[2]
             where a is (_LR`F).1 where b is (_LR`F).2;

//one component (twice), mapped to inequiv rep by AI[1], fixed by AI[2]
_LR`G :=
/*
Original group: c9Group("sl281p")
Recomputed by direct ARR method
Schur index: 2
Character: ( 40, -40, -5, 4, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 
-1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 )
*/

MatrixGroup<40,K | [
Matrix(K,40,40,
[[-1,4],[-7,14],[1,-4],[3,0],[3,2],[0,1],
[0,-3],[-1,7],[4,-7],[3,4],[-2,1],[1,-6],
[3,-3],[-5,-2],[-1,-1],[1,4],[-2,0],[0,1],
[-1,1],[4,-3],[-1,3],[0,1],[-4,2],[-1,-2],
[0,0],[0,0],[-1,-1],[0,-1],[2,0],[0,0],
[1,-2],[0,0],[-1,1],[0,0],[-2,1],[0,0],
[-2,2],[0,0],[0,1],[0,0],[3,0],[3,-2],[
6,-2],[2,-1],[5,-6],[4,-2],[3,-6],[-4,-6],
[-9,5],[2,-4],[-4,3],[0,2],[3,0],[5,2],
[1,-2],[5,-2],[1,-1],[-3,3],[1,3],[-5,0],
[1,0],[1,0],[0,-2],[-5,3],[0,1],[-2,1],
[2,1],[-2,0],[0,-1],[-1,0],[0,1],[0,0],
[-2,3],[0,0],[1,-1],[0,0],[-1,1],[0,0],
[1,-1],[0,-1],[-1,3],[-7,4],[8,-8],[1,4],
[0,1],[-1,0],[-3,-3],[-10,8],[4,1],[-4,3],
[-3,3],[5,-5],[3,-2],[5,-9],[-2,-1],[1,-1],
[0,-1],[-1,4],[2,0],[-1,4],[-2,1],[1,-1],
[-3,-2],[0,2],[0,1],[-1,1],[2,-3],[-1,1],
[0,1],[-1,1],[1,0],[0,0],[0,2],[0,0],[
-1,-1],[0,0],[-1,1],[0,0],[-1,0],[-1,0],
[1,4],[-5,6],[3,-2],[8,-4],[0,1],[2,0],
[2,-3],[2,-1],[1,0],[0,0],[-1,3],[0,-2],
[-1,0],[-1,-1],[-1,1],[4,-3],[1,-1],[3,
0],[-1,-1],[-1,1],[-1,2],[0,-1],[-3,1],
[0,0],[2,0],[-2,2],[1,-1],[1,0],[-1,0],
[-1,1],[0,0],[0,0],[0,0],[0,0],[-1,0],
[0,0],[0,1],[0,0],[1,0],[-2,1],[-1,-2],
[1,-2],[-7,4],[-4,-4],[-8,4],[1,-2],[1,2],
[-1,-3],[0,3],[1,2],[4,-4],[2,4],[-5,3],
[1,3],[3,1],[-4,2],[-1,0],[1,-5],[-1,0],
[-1,1],[1,0],[-1,2],[2,2],[3,-3],[1,-3],
[1,1],[0,0],[1,0],[-1,1],[1,1],[0,1],
[0,0],[1,-1],[0,0],[1,0],[0,0],[1,-2],
[0,0],[1,-1],[2,0],[3,-1],[2,-6],[1,3],
[-3,0],[-1,-1],[-3,0],[1,-6],[-4,1],[-1,3],
[-4,-2],[0,2],[-1,3],[-1,0],[6,-3],[0,-1],
[1,-4],[1,-1],[0,1],[0,2],[-4,3],[1,-2],
[0,1],[2,-1],[-1,4],[1,-1],[0,1],[1,-1],
[-1,1],[-1,0],[0,1],[-1,1],[0,0],[0,1],
[0,0],[2,-2],[0,0],[1,0],[0,0],[0,-2],
[0,0],[3,1],[6,2],[-1,-2],[2,-2],[6,-2],
[1,1],[0,3],[6,-4],[-2,-7],[3,0],[0,1],
[-7,2],[-2,2],[-7,7],[-2,3],[1,0],[0,0],
[0,-2],[-2,3],[2,-4],[0,2],[0,0],[0,1],[
-1,-1],[-1,0],[0,-1],[-2,2],[1,-1],[2,-1],
[1,-1],[-1,0],[0,0],[-1,0],[0,0],[1,1],
[0,0],[0,0],[0,0],[0,1],[1,0],[1,0],[
-2,-2],[5,-2],[0,-1],[-4,-3],[0,2],[0,-9],
[-6,4],[-2,5],[-4,1],[0,4],[4,0],[-1,-1],
[7,-6],[0,-3],[4,-5],[1,-3],[0,3],[2,1],
[-4,4],[2,-2],[1,1],[1,-2],[-1,4],[2,-2],
[-1,1],[2,-3],[-1,0],[-1,0],[1,1],[0,0],
[0,0],[-1,2],[0,0],[1,-3],[0,0],[0,1],
[0,0],[1,-2],[-2,0],[1,0],[-3,-3],[6,1],
[-1,5],[0,6],[-1,-4],[-1,-1],[-2,1],[1,3],
[0,-6],[-1,0],[3,-3],[1,4],[6,-5],[-1,-1],
[2,-4],[0,1],[-2,3],[3,-2],[-3,5],[-1,-1],
[3,-4],[2,-5],[-1,2],[-3,2],[0,0],[2,0],
[0,1],[-2,1],[1,-2],[0,1],[0,0],[1,0],
[0,0],[0,-1],[0,0],[0,0],[0,0],[-2,0],
[-1,0],[-4,8],[-1,12],[2,-5],[1,0],[0,4],
[-1,5],[-9,4],[-1,10],[9,-5],[3,5],[-2,
2],[6,-11],[-1,-3],[-8,-4],[-1,-2],[2,3],
[-2,1],[2,0],[-2,-1],[4,-1],[0,0],[0,1],
[-5,4],[0,-2],[1,-1],[1,0],[-3,-2],[0,0],
[2,0],[0,1],[2,-3],[0,0],[1,0],[0,0],
[-4,2],[0,0],[-1,2],[0,0],[0,0],[-1,0],
[6,0],[-1,-5],[10,2],[1,4],[11,-2],[-5,
2],[7,-8],[1,-3],[-2,-3],[-1,-5],[-3,3],
[-4,3],[1,5],[5,0],[1,-1],[4,-2],[2,-1],
[-4,3],[-1,5],[-4,1],[-1,0],[1,-1],[2,-4],
[-4,3],[-1,2],[-1,0],[0,3],[0,-1],[0,-1],
[0,-1],[-1,1],[0,0],[-2,1],[0,0],[2,-2],
[0,0],[-1,1],[0,0],[-1,0],[0,-1],[2,2],
[11,4],[-9,-1],[4,-11],[1,-6],[6,0],[3,4],
[10,-8],[-7,-4],[7,2],[2,1],[-8,5],[-4,0],
[-12,16],[0,4],[1,3],[-1,-1],[3,-6],[-4,
3],[2,-8],[3,2],[-2,3],[-1,5],[-1,-3],[
1,-2],[-1,0],[-3,2],[1,-2],[3,-3],[1,-1],
[-1,-1],[0,0],[-2,0],[0,0],[1,1],[0,0],
[0,0],[0,0],[3,1],[1,0],[-4,4],[-3,2],
[8,-6],[4,0],[-2,-5],[3,-1],[-1,-7],[-10,
3],[-4,10],[-1,-1],[-5,5],[7,-2],[3,-4],
[8,-6],[0,-3],[5,-2],[1,-2],[-1,6],[3,-1],
[-6,3],[1,-1],[1,0],[-2,-2],[-3,4],[2,0],
[-3,2],[4,-3],[-3,1],[0,-1],[-1,1],[1,0],
[0,0],[-1,3],[0,0],[0,-2],[0,0],[-1,2],
[0,0],[1,-1],[-2,-1],[-4,7],[-7,4],[7,-1],
[-1,-4],[-7,4],[-3,3],[0,-11],[-14,4],[6,
7],[-8,6],[-3,2],[10,-3],[0,-2],[9,-11],
[3,-5],[-1,0],[2,-4],[1,1],[-4,2],[-4,6],
[0,-2],[-3,4],[-2,-1],[0,1],[4,-3],[-1,3],
[3,-5],[-1,0],[-2,2],[-1,2],[2,0],[0,0],
[-2,2],[0,0],[0,-3],[0,0],[-1,1],[0,0],
[1,-3],[-1,0],[-10,8],[-13,1],[3,7],[-8,
12],[-9,15],[-1,-5],[1,-4],[-11,8],[10,6],
[3,-3],[-4,-4],[17,-13],[5,-1],[12,-13],
[4,-8],[2,5],[-3,4],[-5,5],[1,-3],[-3,
6],[-3,-3],[3,-2],[-1,-4],[-2,-1],[-3,3],
[0,1],[2,-1],[-3,3],[-3,2],[-3,0],[2,-1],
[0,0],[0,2],[0,0],[-4,0],[0,0],[-3,2],
[0,0],[0,-2],[-1,-1],[-3,-2],[1,-3],[0,3],
[-6,1],[-6,2],[-4,-3],[-8,0],[-8,7],[3,8],
[-5,-1],[0,0],[4,-1],[1,-3],[6,-8],[0,-2],
[-3,-1],[-1,2],[1,0],[2,-3],[-4,6],[1,-4],
[1,-1],[2,-1],[1,3],[-1,-1],[3,0],[1,-2],
[-2,4],[-1,1],[1,0],[1,0],[0,0],[3,-1],
[0,0],[0,-1],[0,0],[1,-1],[0,0],[-2,-1],
[1,-1],[4,-1],[20,-10],[1,7],[9,-8],[19,
-21],[-8,7],[10,-4],[15,-19],[-16,2],[-1,
-12],[-6,7],[-15,14],[3,-6],[-3,14],[3,1],
[8,-4],[6,1],[0,1],[-4,2],[-5,-5],[4,-1],
[-5,0],[1,1],[-8,6],[1,5],[-1,-2],[2,3],
[1,-1],[1,-4],[-4,1],[-2,1],[0,0],[-2,-1
],[0,0],[4,0],[0,0],[1,1],[0,0],[3,1],
[0,-2],[-5,-2],[-12,-4],[5,0],[-3,4],[-9,
10],[-2,-7],[-3,3],[-11,1],[4,14],[-5,-2],
[1,-5],[10,-3],[3,3],[12,-11],[1,-1],[-5,
-2],[0,1],[-1,2],[4,-7],[-4,10],[-3,-2],
[1,-5],[0,-5],[3,0],[-2,2],[0,2],[5,-1],
[0,3],[-5,4],[-1,-1],[2,2],[0,0],[3,-1],
[0,0],[-1,-1],[0,0],[0,-1],[0,0],[-3,0],
[0,0],[2,-7],[-1,-8],[-1,7],[-2,3],[0,7],
[1,-8],[9,3],[6,-17],[-5,2],[-1,-8],[3,-8],
[-6,6],[2,7],[5,6],[0,4],[-5,-4],[2,1],
[-3,-2],[0,-2],[1,-1],[-1,0],[-1,-5],[6,
-7],[1,-2],[-4,4],[0,-1],[2,3],[3,-2],[
-3,3],[0,-2],[-2,4],[0,0],[0,-2],[0,0],
[2,1],[0,0],[1,-4],[0,0],[-1,0],[1,2],
[-8,4],[-15,4],[8,-8],[0,0],[-12,7],[7,
-2],[-7,7],[-9,3],[7,7],[-4,11],[1,-3],[
15,-6],[0,2],[1,-6],[1,-1],[-7,7],[-2,-2],
[3,-3],[1,-3],[-1,6],[-5,1],[1,0],[-3,-2],
[6,-5],[0,-2],[-1,2],[2,-2],[-1,2],[-3,3],
[-1,0],[3,0],[0,0],[0,1],[0,0],[-4,-1],
[0,0],[0,-2],[0,0],[-2,2],[-1,1],[3,-2],
[-1,2],[7,-11],[5,3],[5,-11],[-3,6],[-14,
2],[-1,9],[0,0],[-8,4],[-2,8],[-4,0],[
3,-10],[-4,-7],[-8,2],[3,-6],[0,0],[5,4],
[5,-2],[-1,4],[-4,2],[2,-2],[-5,1],[1,7],
[1,1],[0,0],[2,-2],[-2,5],[0,-1],[-3,2],
[-1,0],[0,0],[2,2],[0,0],[-1,-1],[0,0],
[2,2],[0,0],[-3,2],[-2,0],[-6,1],[0,1],
[-1,-6],[8,-8],[-4,-5],[6,0],[0,3],[3,-5],
[-5,5],[0,4],[3,0],[3,1],[-1,0],[-2,2],
[2,0],[-1,1],[1,-2],[2,-1],[1,-4],[1,-1],
[2,0],[-2,0],[-3,1],[2,-3],[2,-1],[-2,0],
[1,-1],[1,-2],[0,-1],[1,-1],[2,-1],[0,0],
[-1,-1],[0,0],[-1,0],[0,0],[-1,0],[0,0],
[2,1],[-2,1],[-1,4],[-17,0],[-8,14],[-6,
4],[-10,25],[-8,-8],[11,-4],[-5,13],[16,
-3],[2,-2],[4,-5],[7,-7],[-4,11],[9,-11],
[5,-1],[-5,5],[-2,1],[-1,-2],[-1,-3],[0,
6],[-1,-1],[1,-1],[1,-1],[4,-5],[-2,0],
[1,2],[-2,0],[3,0],[-2,2],[3,-3],[2,-1],
[0,0],[3,-4],[0,0],[0,-2],[0,0],[-2,0],
[0,0],[-1,-1],[1,0],[0,9],[5,13],[-8,3],
[-5,-4],[-1,3],[-1,-5],[4,-12],[-6,1],[6,
-4],[4,-6],[-3,2],[-3,-7],[0,-7],[3,-1],[
0,-4],[9,-6],[-2,5],[-1,-1],[-7,4],[-2,0],
[2,0],[-1,2],[-2,7],[-6,4],[2,-2],[2,2],
[0,-3],[-1,2],[2,1],[-2,5],[-2,-1],[0,0],
[1,1],[0,0],[0,4],[0,0],[0,2],[0,0],[
5,-6],[2,0],[-6,0],[1,-8],[-2,9],[-7,8],
[1,1],[4,6],[-1,9],[9,-9],[-6,-2],[4,7],
[3,-9],[-1,8],[-3,8],[-8,9],[2,1],[-10,
14],[0,-1],[-4,-2],[-2,3],[3,-8],[-2,-2],
[1,3],[5,-4],[3,-8],[-3,-1],[0,-4],[-5,
8],[0,-3],[2,-3],[3,-6],[0,0],[0,0],[
-4,-1],[0,0],[1,-2],[0,0],[-2,-1],[0,0],
[-3,3],[3,-3],[-4,-7],[8,-11],[-13,6],[-5,
-7],[-9,-8],[-4,9],[2,1],[6,-10],[-7,1],
[-16,15],[11,-4],[-14,21],[-11,1],[-4,6],[
0,7],[-15,1],[4,-4],[4,-9],[-5,1],[4,-5],
[3,-3],[-7,6],[5,1],[10,-3],[4,-5],[2,-3],
[-4,0],[5,-3],[3,-1],[4,1],[-2,2],[0,0],
[0,-5],[0,0],[6,-3],[0,0],[2,-5],[0,0],
[1,-1],[4,0],[-5,-4],[-5,-6],[-4,0],[-3,
-3],[-14,0],[4,-11],[4,0],[-15,5],[-3,15],
[-1,1],[2,1],[9,1],[0,-3],[11,-3],[3,-2],
[0,1],[-1,0],[-1,-1],[4,-4],[-5,7],[1,1],
[1,-1],[-1,1],[1,1],[0,0],[0,1],[6,-4],
[1,2],[-3,2],[-2,3],[3,-1],[0,0],[2,0],
[0,0],[0,-1],[0,0],[-1,-1],[0,0],[2,0],
[0,-1],[3,1],[16,-14],[-14,8],[-2,-6],[-18,
6],[15,-17],[1,3],[-2,-6],[-11,19],[17,-18],
[3,0],[4,1],[-9,6],[10,8],[1,1],[12,-11],
[-3,3],[0,0],[6,-4],[-13,6],[6,-4],[6,-3],
[4,2],[-4,4],[0,-3],[-3,5],[3,1],[-3,4],
[-4,-3],[1,0],[-2,2],[0,0],[3,2],[0,0],
[1,0],[0,0],[2,1],[0,0],[4,-5],[-2,0],
[2,-4],[8,-6],[3,-5],[7,-14],[-4,-16],[0,
-3],[-4,-6],[-5,3],[-10,14],[-8,0],[2,10],
[-8,10],[-3,-8],[4,-1],[-3,1],[4,-9],[3,
-4],[6,0],[2,-1],[-10,5],[4,-3],[-2,1],[
-2,3],[-2,10],[5,-3],[-1,1],[3,-2],[-1,3],
[0,-3],[1,1],[0,-1],[0,0],[1,0],[0,0],
[3,-3],[0,0],[1,2],[0,0],[1,-1],[-2,0],
[-6,-5],[10,-6],[-10,-5],[-5,-3],[-12,0],
[9,-5],[-13,17],[-1,-2],[-3,8],[4,3],[5,
-5],[3,1],[-4,-1],[-4,5],[-2,3],[-7,3],
[-4,2],[3,-5],[4,-5],[0,0],[1,-2],[1,1],
[1,3],[5,-3],[0,-4],[1,0],[-1,1],[-3,3],
[0,0],[2,-1],[1,0],[0,0],[3,-1],[0,0],
[-1,3],[0,0],[2,-3],[0,0],[-1,1],[2,1],
[-6,4],[-24,7],[-1,6],[2,5],[1,10],[-17,
6],[19,-16],[10,5],[10,-9],[-6,-2],[6,-5],
[1,-2],[4,7],[9,-12],[4,-2],[0,0],[0,0],
[-4,5],[1,-6],[3,3],[1,-2],[-1,-3],[3,-7],
[4,-3],[-2,3],[-1,-1],[0,-1],[4,-4],[0,0],
[4,-6],[-1,-1],[0,0],[-1,-5],[0,0],[2,-4],
[0,0],[-3,1],[0,0],[1,1],[-1,0],[10,-7],
[17,-17],[0,-5],[-8,-4],[-7,-10],[13,5],
[-6,8],[2,-22],[-11,2],[-6,14],[11,-4],[
-6,18],[-13,8],[-6,17],[-1,5],[-6,-1],[3,
-6],[1,-10],[-5,10],[-2,-1],[-1,2],[-1,6],
[4,0],[6,-3],[2,-5],[0,-1],[-1,2],[4,-4],
[-2,0],[0,2],[-3,4],[0,0],[-4,2],[0,0],
[2,-2],[0,0],[3,-5],[0,1],[1,-1],[1,1],
[4,0],[-25,10],[20,-12],[6,7],[7,-1],[-3,
4],[-3,-6],[-16,16],[10,-4],[-10,7],[-6,
5],[16,-10],[9,2],[8,-20],[2,-5],[-1,3],
[2,-3],[-1,7],[5,0],[2,10],[-6,6],[3,-3],
[-5,-4],[2,0],[-2,3],[0,1],[6,-7],[1,0],
[-2,4],[-2,1],[4,0],[0,0],[0,2],[0,0],
[-3,-4],[0,0],[0,0],[0,0],[-3,3],[-3,-1
],[13,-8],[25,0],[1,-4],[-1,2],[25,-22],
[-11,20],[-19,3],[17,6],[-8,-17],[1,0],[0,
7],[-21,2],[4,-10],[-22,6],[-8,-2],[8,-5],
[1,3],[1,3],[-2,7],[8,-10],[3,-2],[0,2],
[-1,6],[-8,9],[-2,2],[6,-8],[-9,5],[-2,-1],
[8,-6],[3,-3],[-2,-5],[1,-1],[-1,0],[0,-1],
[0,3],[1,-1],[0,5],[1,-1],[-2,1],[1,-2],
[-4,6],[-11,22],[6,-8],[3,6],[4,-3],[-1,9],
[-7,-15],[-11,14],[3,-8],[-4,10],[-6,2],[7,
-6],[5,-6],[2,-14],[-1,-3],[-2,3],[-2,-1],
[-2,8],[2,3],[5,-4],[1,2],[0,3],[-4,-1],
[0,0],[2,-2],[0,1],[0,-7],[-3,-2],[5,0],
[1,3],[0,1],[0,0],[-2,5],[0,0],[-1,-3],
[0,0],[-1,2],[0,0],[0,-2],[0,-1],[-4,14],
[-4,22],[11,-8],[13,-6],[5,-6],[-10,23],
[-20,-1],[9,7],[14,-11],[-13,17],[-3,7],
[2,-3],[-5,-8],[-15,-10],[-3,0],[-2,0],[
5,-2],[11,-1],[-7,1],[5,0],[-5,3],[-4,3],
[-5,5],[6,-2],[7,-5],[1,1],[-2,-4],[2,0],
[2,-1],[1,4],[0,0],[1,0],[0,-2],[1,-1],
[-2,-1],[0,1],[3,1],[0,0],[-2,1],[-3,0],
[8,-2],[13,3],[5,1],[-2,0],[13,-9],[-12,
22],[-15,-5],[14,-4],[-2,-10],[-8,8],[3,0],
[-11,10],[-1,-3],[-11,-1],[-3,1],[-1,-2],[
1,-2],[3,-1],[-4,6],[2,-3],[1,-4],[-2,5],
[1,1],[2,1],[3,-3],[1,-1],[-6,3],[-1,-2],
[2,-4],[0,-2],[-3,1],[0,0],[-4,1],[0,0],
[0,-2],[0,0],[2,1],[0,0],[-2,-1],[0,0],
[2,16],[-9,7],[-13,13],[-20,5],[-19,44],
[10,-26],[27,-9],[-17,4],[24,-16],[24,-13],
[-4,-8],[20,-23],[-8,18],[16,3],[10,-6],[6,
6],[-10,4],[-10,-7],[-8,10],[-2,4],[-1,4],
[5,2],[6,-1],[-5,-10],[-5,-5],[1,6],[1,-3],
[0,-1],[-4,8],[0,4],[0,1],[-1,1],[-2,5],
[0,0],[-1,4],[0,0],[-2,-3],[0,0],[6,-7],
[3,3],[0,-9],[-14,-6],[2,-7],[5,3],[-4,-5],
[9,-2],[12,6],[6,-14],[-10,4],[1,2],[5,-5],
[2,9],[0,6],[3,8],[2,4],[-1,3],[1,-2],[
-2,-1],[7,-4],[0,0],[-4,6],[2,-2],[2,-3],
[6,-5],[0,2],[-4,0],[4,3],[3,-2],[-3,1],
[-2,1],[-1,3],[0,0],[0,-1],[0,0],[0,1],
[0,0],[1,-4],[0,0],[1,4],[0,1],[2,11],[
7,-27],[10,21],[-12,7],[-13,20],[-8,-6],[6,
-9],[-1,-7],[2,19],[-1,-19],[0,2],[7,-3],
[-7,11],[20,-7],[1,-7],[15,-14],[4,0],[-3,
3],[-3,0],[-18,16],[1,-12],[5,-4],[9,-10],
[-6,9],[-3,3],[-3,2],[2,3],[0,3],[-9,-1],
[-1,-4],[-2,1],[0,0],[-1,0],[0,0],[1,-4],
[0,0],[0,2],[0,0],[0,-6],[-5,0]])    ,
Matrix(K,40,40,
[[-11,6],[-3,0],[0,-3],[-3,3],[1,2],[0,
-3],[2,-4],[-7,7],[6,-4],[-2,3],[-3,0],
[5,-5],[1,1],[2,-6],[3,-3],[-5,8],[-4,2],
[-2,2],[-1,0],[2,1],[0,-2],[-3,4],[-5,1],
[1,-2],[-1,-1],[1,-2],[1,-4],[-2,0],[1,
2],[-2,0],[2,-1],[-3,3],[-2,2],[0,2],[0,
-1],[-1,-2],[-1,1],[-1,2],[1,-1],[1,-1],
[-10,4],[1,1],[5,-3],[2,-3],[2,1],[0,0],
[0,-2],[6,-12],[4,3],[-9,6],[3,-3],[1,1],
[-4,2],[-4,-1],[2,-1],[-9,6],[0,-1],[3,
-3],[-5,-3],[0,1],[-2,-2],[-5,2],[-4,-1],
[5,-5],[1,-1],[-1,-1],[2,-2],[0,-1],[-3,
3],[0,-3],[1,1],[-3,3],[-2,-2],[-1,3],[
0,0],[-1,-1],[0,-1],[-3,4],[-1,1],[0,1],
[-10,6],[-4,3],[6,-3],[-2,2],[3,-1],[-1,
0],[2,-7],[-6,-2],[8,-3],[-5,7],[-1,-4],
[7,-1],[2,3],[2,-2],[5,-3],[-8,9],[-2,0],
[-3,1],[-4,3],[1,0],[-1,-1],[-5,3],[-2,-2],
[1,-4],[-1,0],[0,0],[2,-2],[-1,-2],[0,3],
[-1,-1],[1,1],[-2,2],[-5,2],[1,2],[1,-2],
[0,-1],[-1,0],[-1,3],[1,0],[1,-1],[-7,8],
[5,3],[1,2],[-2,-5],[1,2],[-6,5],[0,-2],
[13,-9],[4,-1],[-3,4],[2,-3],[1,-1],[-5,1],
[-7,1],[3,-3],[-5,6],[-1,0],[3,-3],[-4,-2],
[2,-3],[-1,-3],[-4,4],[0,2],[2,-4],[2,-2],
[-2,2],[-2,2],[0,-1],[-2,1],[0,-2],[0,0],
[-1,2],[-2,-1],[1,1],[0,1],[0,1],[1,0],
[-2,3],[0,0],[0,2],[4,-1],[2,-5],[-7,3],
[0,1],[-10,6],[1,-4],[-1,10],[5,-2],[1,1],
[8,-6],[0,-2],[-1,-3],[-4,4],[-2,5],[-4,3],
[4,-4],[-1,2],[2,-1],[4,-7],[-2,1],[-2,2],
[5,-5],[6,-2],[0,-1],[-1,-1],[1,3],[1,3],
[1,3],[-2,0],[1,0],[0,0],[2,-1],[4,-2],
[2,-3],[0,1],[2,1],[1,-2],[3,-1],[-2,2],
[0,1],[5,0],[-1,5],[-1,1],[5,-2],[3,-3],
[1,2],[4,-2],[4,-9],[0,-3],[2,-2],[-2,-1],
[-1,-1],[2,-2],[0,3],[0,0],[4,-4],[2,0],
[0,0],[1,-1],[0,-2],[-2,4],[0,-2],[3,-1],
[-2,0],[2,0],[-1,4],[2,2],[1,0],[-1,1],
[-1,2],[-1,2],[2,-2],[0,0],[2,-2],[1,1],
[2,1],[1,-1],[1,0],[1,0],[0,1],[-4,-1],
[-6,1],[2,3],[3,3],[7,-5],[-7,4],[5,-5],
[9,-4],[-7,1],[-6,-2],[-3,1],[-1,3],[6,-5
],[4,-6],[3,-2],[-2,2],[1,2],[-1,4],[5,
-6],[-1,-1],[-1,-1],[-1,-1],[1,-5],[1,1],
[-2,3],[0,-2],[1,1],[-1,1],[0,-1],[0,-1],
[0,2],[0,0],[1,-1],[0,-1],[1,-2],[0,0],
[0,-1],[-1,0],[-1,1],[1,-1],[3,3],[-2,1],
[-5,9],[5,-5],[2,-1],[-4,4],[8,-4],[7,-13],
[-2,2],[1,-5],[-2,-3],[-3,4],[2,-1],[3,2],
[1,1],[5,-5],[3,1],[0,0],[0,-3],[-3,-1],
[-2,2],[1,-3],[5,-2],[-3,1],[2,0],[-2,5],
[3,3],[1,1],[-3,1],[-2,1],[-2,3],[3,-2],
[0,-1],[3,-4],[3,-1],[2,2],[1,0],[2,-1],
[1,0],[1,0],[-1,1],[-1,7],[3,6],[-2,-3],
[1,8],[-3,5],[5,-4],[6,-9],[8,-3],[-2,3],
[1,-3],[0,-1],[-3,2],[-5,2],[2,0],[-5,2],
[1,-1],[1,-5],[-9,0],[3,-2],[0,1],[-4,-1],
[1,-3],[1,-4],[0,0],[3,0],[1,-1],[4,-4],
[-2,4],[1,-1],[1,-1],[0,-2],[-2,-3],[-2,0],
[-1,1],[3,-2],[-1,-1],[-1,0],[1,1],[1,1],
[-3,4],[-1,-8],[1,-1],[-3,-1],[1,1],[-4,
-4],[5,-9],[-15,5],[2,-7],[-4,-3],[-5,3],
[-2,7],[6,5],[11,0],[4,-1],[-2,4],[-1,0],
[-3,1],[-6,10],[-4,5],[2,-3],[-5,7],[-2,
0],[-3,3],[-1,-1],[2,-5],[2,-5],[-1,-1],
[3,0],[-2,0],[-1,1],[-2,4],[-4,3],[1,1],
[3,-3],[-3,-2],[0,1],[3,-2],[2,-2],[1,-2],
[-5,-4],[0,2],[0,-1],[-5,-1],[-1,3],[-1,1],
[6,-7],[0,-11],[2,3],[-8,6],[3,-6],[3,1],
[-3,0],[4,-3],[4,-2],[-9,4],[-2,-1],[-1,
-3],[-2,-2],[0,1],[0,-1],[-4,3],[0,-3],
[4,-4],[2,-2],[0,1],[2,-1],[0,-2],[-3,4],
[0,-1],[0,3],[-2,1],[-2,-1],[-1,2],[2,0],
[1,-1],[-1,-2],[-3,3],[1,-1],[3,1],[-1,-3
],[-8,3],[4,-3],[7,0],[9,-10],[-5,4],[4,
-2],[5,-3],[-10,1],[-9,-3],[-8,5],[-1,1],
[9,-13],[6,-11],[1,-2],[0,0],[4,0],[1,6],
[7,-8],[-2,2],[-4,2],[-2,1],[-3,-4],[1,3],
[0,3],[-1,-3],[5,-3],[-2,3],[0,-1],[-3,0
],[1,2],[-1,1],[2,0],[-1,-2],[1,-2],[-1,
0],[0,-1],[-1,-1],[-1,1],[0,-1],[-11,12],
[-7,2],[2,2],[2,2],[5,1],[-4,0],[4,-4],
[4,-5],[9,-5],[-2,2],[0,-6],[3,0],[4,4],
[-1,1],[4,-2],[-3,8],[-1,3],[-2,1],[-4,2],
[1,-1],[-4,-1],[-3,1],[-1,0],[0,-4],[-2,2],
[-2,0],[1,1],[-1,0],[-1,2],[-2,-2],[-1,1],
[-1,3],[-4,1],[3,1],[1,-1],[-2,1],[0,1],
[0,3],[0,1],[0,-1],[1,-5],[1,-5],[0,-1],
[-2,2],[-1,4],[5,-5],[13,-2],[-2,-15],[
9,-4],[5,-7],[-2,-8],[2,2],[3,7],[7,9],
[4,2],[-2,1],[-1,-1],[-3,-2],[-2,3],[-3,
0],[-2,2],[-4,-1],[6,-5],[-3,-1],[2,-1],
[0,4],[6,2],[0,-2],[-3,4],[-3,-1],[-3,4],
[0,-1],[-4,1],[2,0],[3,1],[4,-2],[1,-1],
[1,1],[3,0],[1,1],[-5,-4],[9,0],[0,-11],
[-3,-15],[-21,11],[17,-16],[-7,5],[-21,9],
[9,12],[-3,11],[10,1],[4,-1],[-18,10],[-6,
5],[-3,6],[-13,0],[-2,-10],[8,-11],[-11,5],
[2,6],[8,-3],[-6,5],[-10,10],[8,-5],[6,
-8],[-1,0],[0,-11],[3,-5],[-1,3],[2,0],
[3,-4],[-6,4],[-1,-2],[-6,8],[-3,2],[-2,
-3],[0,0],[-3,2],[2,-2],[-4,4],[15,-3],
[3,-4],[-4,0],[0,0],[1,5],[4,-6],[1,9],
[-14,-1],[11,-15],[9,-5],[-2,-4],[-6,-1],
[3,7],[-1,13],[-4,5],[3,-2],[2,0],[-2,
-4],[-9,10],[1,1],[-4,8],[-1,-1],[2,1],[
-5,-1],[-2,0],[5,-1],[3,-2],[3,-2],[2,3],
[-1,1],[0,-1],[2,-1],[-1,0],[2,-3],[1,2],
[1,-1],[0,-2],[6,-3],[0,2],[1,0],[5,2],
[11,-8],[-8,-3],[4,-1],[3,-13],[-1,-2],[-5,
6],[14,-7],[-19,7],[5,-4],[7,1],[-16,11],
[0,-4],[-8,16],[-6,3],[13,-2],[1,2],[2,
-1],[2,5],[-3,-7],[1,-2],[5,4],[-2,12],[
-3,3],[1,4],[-9,-1],[-11,8],[-5,4],[4,-9],
[-1,0],[-6,-1],[2,4],[2,1],[2,2],[-1,5],
[-8,6],[0,2],[1,1],[0,-1],[-1,1],[-3,-10],
[17,-10],[4,-5],[-13,-5],[-11,13],[13,-13],
[-2,9],[-12,-6],[16,2],[3,7],[9,-9],[0,3],
[-16,18],[-10,15],[0,6],[-19,10],[-4,-7],[
2,-13],[-16,7],[2,0],[4,-2],[-8,3],[-1,1],
[4,-9],[1,-7],[5,-1],[0,-4],[3,-7],[-2,6],
[3,-5],[3,-4],[-4,1],[-5,-3],[-5,6],[-2,
3],[3,-5],[-2,-2],[-2,3],[0,2],[1,3],[1,
-16],[11,-7],[10,4],[-11,1],[-2,3],[4,2],
[-1,5],[13,-11],[0,13],[-4,3],[11,-5],[-2,
9],[-14,7],[-10,7],[0,5],[-14,1],[0,-6],
[2,-7],[-5,-2],[0,-3],[5,-5],[-1,-5],[6,
-6],[6,-3],[-1,-2],[3,-1],[-3,4],[3,-5],[
-5,2],[6,-5],[-1,-1],[-2,-4],[-1,-6],[-8,5],
[-2,2],[5,-3],[0,-2],[-7,2],[-2,3],[1,2],
[-6,-12],[2,-8],[10,-13],[-10,-8],[-17,8],
[15,-15],[-8,7],[-27,0],[11,14],[-10,10],[
8,-8],[15,1],[-6,6],[10,-5],[2,1],[-19,2],
[-1,-9],[0,-7],[-2,0],[-5,13],[2,-4],[-6,
3],[-2,-4],[10,-4],[3,-7],[3,-1],[8,-8],
[1,-3],[-5,7],[2,-4],[4,1],[-6,1],[-2,-1],
[-4,4],[0,-1],[1,-4],[1,-5],[-3,2],[-1,0],
[0,2],[-5,2],[-2,9],[-7,-3],[4,-5],[-1,
-8],[3,-6],[-4,-7],[-8,11],[-3,3],[-1,7],
[2,1],[1,-1],[2,-6],[-1,-4],[1,-2],[0,1],
[-3,0],[1,1],[5,-2],[3,-3],[3,-1],[-1,4],
[-5,9],[2,-1],[4,-3],[-4,4],[-4,-2],[-3,1],
[4,-2],[-1,4],[2,-1],[0,2],[1,2],[2,1],
[-1,0],[-3,2],[1,0],[0,2],[1,-3],[-1,1],
[2,0],[2,-5],[4,2],[2,1],[-2,-1],[-3,7],
[-6,5],[9,-9],[-6,10],[-1,-2],[1,-1],[-2,
5],[-2,0],[-1,1],[-4,3],[3,-4],[3,0],[
3,1],[1,-4],[-5,2],[-2,-1],[3,-4],[2,-4],
[0,2],[0,2],[-2,1],[2,2],[0,2],[-3,-1],
[0,-3],[-1,1],[2,-1],[1,-1],[0,-2],[0,-2],
[1,1],[0,1],[1,-1],[-2,2],[-1,-1],[9,-2],
[12,7],[3,-9],[-2,-10],[-5,5],[6,5],[7,
0],[-2,-12],[9,-12],[4,3],[-8,5],[0,-13],
[-12,0],[-10,7],[-1,-2],[1,0],[1,-5],[5,
-7],[-12,1],[2,0],[0,9],[-7,5],[-4,-1],
[-4,-2],[5,-4],[7,1],[6,-8],[5,-3],[-2,
7],[-2,3],[4,-3],[-1,-2],[-1,0],[-4,-1],
[-2,3],[7,-5],[-3,0],[1,0],[4,0],[1,3],
[-3,23],[-3,-6],[-16,5],[-8,15],[2,2],[
-13,1],[1,5],[9,6],[7,-13],[8,2],[1,-4],
[-2,-3],[-1,16],[-11,11],[-2,1],[5,11],[-7,
8],[-1,3],[-2,4],[8,-5],[-9,1],[8,0],[3,
10],[-1,-9],[-6,-1],[-9,6],[-10,7],[-1,2],
[3,-3],[-4,2],[-2,-1],[5,8],[-1,1],[9,0],
[1,-1],[-6,9],[2,1],[5,3],[-3,3],[-1,-1
],[4,-34],[-6,-3],[10,-8],[9,-6],[-4,-8],
[12,-4],[0,-5],[-13,11],[-21,21],[-17,-1],
[1,12],[1,10],[4,-12],[17,-19],[1,3],[-9,
-13],[5,-9],[4,2],[13,-8],[-5,10],[10,-3],
[-4,-3],[-5,-10],[7,11],[2,1],[6,-9],[8,
-9],[2,-2],[-1,-1],[5,-2],[3,2],[-5,-5],[
5,-3],[-10,3],[0,-4],[3,-8],[0,-1],[-6,-4],
[0,-1],[-2,-1],[25,-25],[-4,-12],[-6,15],[
10,10],[6,-21],[-13,14],[8,1],[17,-7],[-29,
11],[2,-20],[-5,2],[-11,20],[12,-10],[16,0],
[-3,7],[16,-22],[8,1],[-3,13],[23,-11],[-11,
0],[-1,4],[11,-16],[21,-15],[-6,14],[-2,6],
[-1,5],[3,14],[1,5],[-2,-8],[2,1],[-7,9],
[9,-10],[7,-3],[3,-9],[7,-5],[7,4],[3,-1],
[4,-7],[-3,4],[1,-4],[-6,13],[16,-10],[-14,
-4],[1,-10],[-12,7],[4,-6],[-12,22],[4,-9],
[8,2],[6,10],[11,-9],[-5,-2],[-21,13],[-20,
17],[-9,7],[-2,4],[-4,1],[7,-11],[-10,-2],
[3,-1],[-4,3],[3,2],[-5,12],[5,-12],[2,
-6],[-5,5],[-5,1],[1,2],[-3,2],[-1,-1],
[2,-4],[1,5],[1,-3],[3,1],[-1,4],[-4,5],
[-1,-1],[3,4],[-3,4],[0,4],[-14,23],[-18,
27],[-10,13],[8,-4],[-5,13],[-16,9],[3,2],
[22,3],[16,-8],[-2,11],[-3,1],[5,-14],[-2,
-6],[-19,-6],[1,-2],[-2,10],[1,4],[10,-4],
[-6,-14],[13,-6],[-8,6],[0,-4],[-3,5],[5,
-12],[-1,3],[-4,6],[-3,-1],[6,2],[-1,2],
[-2,2],[5,-5],[5,0],[3,-6],[3,-3],[-5,1],
[0,5],[-1,0],[1,1],[-2,5],[-3,2],[8,2],
[4,-15],[-13,1],[-1,4],[11,-8],[-9,7],[4,
7],[2,-17],[0,-11],[-3,3],[-1,-9],[-11,10],
[2,4],[-1,12],[-2,4],[4,5],[-1,5],[0,-4],
[-4,6],[0,-1],[-12,9],[2,4],[1,4],[-3,-3],
[-1,0],[-5,4],[-1,3],[-2,4],[-1,3],[-8,2],
[-2,4],[7,3],[-2,2],[7,-4],[5,-1],[-3,6],
[1,-2],[6,1],[-2,4],[4,0],[7,-1],[-9,-5],
[0,-2],[2,10],[-1,-1],[3,-7],[-13,13],[-12,
22],[-3,-3],[6,-5],[-4,5],[4,-5],[11,-3],
[5,-6],[-5,0],[9,-5],[1,4],[-3,7],[11,0],
[-1,5],[-4,3],[10,-7],[1,-2],[-2,5],[-8,5],
[2,-4],[0,0],[-2,6],[3,-3],[1,1],[2,-1],
[3,-1],[5,3],[2,-4],[-2,-2],[-3,2],[1,-1],
[4,-4],[-5,2],[-2,-3],[16,-2],[-8,18],[-5,
17],[4,7],[14,-3],[-10,25],[18,-13],[12,0],
[-9,-14],[11,-8],[-18,8],[-7,-4],[3,-8],[
-2,-3],[0,-1],[16,-9],[8,2],[-6,11],[-2,1],
[6,-8],[2,9],[3,-7],[2,-5],[-12,6],[0,7],
[4,-2],[1,2],[7,-4],[4,-1],[-1,4],[-1,0],
[5,-8],[1,-1],[-3,-6],[1,-2],[8,-1],[-6,8],
[3,-7],[5,0],[3,-7],[-9,-14],[-2,0],[6,7],
[17,-7],[0,-25],[-4,17],[-4,-17],[16,-15],
[-37,34],[-25,8],[0,13],[1,19],[-3,-16],[9,
-18],[3,-3],[-2,-11],[6,-5],[8,5],[16,-20],
[-10,2],[6,-4],[3,-4],[4,-12],[8,6],[5,-2],
[-4,3],[4,2],[-1,3],[-4,-6],[4,1],[2,6],
[2,-5],[4,-4],[-3,-1],[4,-9],[3,0],[2,-2],
[-5,0],[-2,0],[-1,-2],[-4,18],[10,11],[9,
3],[3,-7],[-1,15],[4,5],[-5,-5],[3,-23],
[19,-9],[7,0],[-2,-5],[3,-14],[-7,5],[-8,
7],[-1,-6],[2,0],[2,2],[0,-6],[-18,3],[-2,
-1],[-2,2],[-7,3],[-1,-4],[-4,-5],[3,-2],
[8,0],[7,-2],[3,-4],[-3,6],[2,-2],[2,-2],
[-3,-1],[-4,-1],[1,-2],[-1,3],[4,-5],[-2,
0],[2,2],[2,-2],[1,1],[34,-15],[-10,-8],
[-5,2],[5,7],[19,-15],[-4,6],[4,-9],[-30,
24],[-26,-8],[2,-14],[-13,17],[-17,13],[24,
-9],[25,-7],[-6,4],[25,-20],[7,2],[-9,11],
[8,19],[-3,5],[2,7],[10,-1],[-2,3],[-15,
20],[-3,7],[0,-6],[-1,-3],[-1,2],[10,-7],
[-5,9],[-3,2],[8,-3],[3,7],[2,-7],[4,-5],
[-5,3],[-1,4],[9,-13],[2,-4],[1,-6],[-14,
20],[-17,10],[9,16],[8,10],[2,6],[-8,5],
[4,-19],[4,-11],[20,-3],[0,-9],[-8,-6],[
12,-6],[13,4],[9,-8],[8,-7],[-1,3],[1,8],
[-3,9],[-5,-5],[-8,3],[-5,-4],[-5,-7],[8,
-14],[-4,0],[-4,3],[7,3],[11,2],[-1,1],[
-4,4],[1,-2],[-1,4],[-1,-2],[-4,0],[5,-3],
[2,-5],[6,-5],[2,1],[2,2],[0,-1],[0,-5],
[20,-1],[-2,-13],[-9,20],[-3,10],[1,4],[-7,
2],[7,0],[7,-13],[-5,-8],[21,-26],[-6,-11],
[-1,5],[23,5],[20,13],[3,-1],[15,-6],[0,
9],[-8,5],[10,6],[-8,-5],[-6,1],[6,-3],
[24,-10],[-14,7],[-5,4],[0,7],[4,14],[-5,
2],[0,-4],[-1,-1],[-7,7],[8,-3],[-2,6],
[13,-12],[7,-3],[3,3],[6,-4],[10,-6],[1,
-2],[1,-1],[18,-22],[-5,4],[1,5],[22,-1],
[10,-26],[9,6],[7,-24],[-3,0],[-38,10],[
-2,-13],[-13,22],[-12,14],[15,-16],[16,-6],
[1,-2],[19,-21],[9,-2],[2,10],[15,1],[-8,
-3],[10,3],[2,-3],[0,-4],[-10,21],[3,6],
[1,-3],[3,0],[-2,1],[7,-8],[1,7],[-2,5],
[4,-8],[4,4],[-2,-3],[2,-4],[4,-5],[3,3],
[2,-7],[5,-6],[-2,-4],[-31,28],[-11,13],
[-6,0],[-3,-7],[-37,29],[2,-16],[0,11],
[20,-14],[24,15],[-1,8],[8,-11],[26,-27],
[-20,6],[-11,-6],[1,-4],[-13,8],[-8,2],
[10,-7],[3,-32],[-1,6],[-6,-4],[2,-6],[3,
-4],[17,-19],[1,-7],[-4,12],[5,-2],[2,5],
[-13,8],[1,-1],[4,0],[-5,5],[6,-7],[2,1],
[-5,3],[2,2],[3,-8],[-4,9],[-3,2],[-3,8],
[-24,10],[7,0],[-9,9],[-2,5],[-12,5],[-6,
1],[-22,10],[21,25],[-6,14],[1,9],[11,1],
[5,-7],[-19,-2],[-14,-15],[-5,-3],[-2,0],
[-6,5],[1,6],[15,-18],[6,-3],[7,-12],[12,
-6],[0,4],[11,-5],[-2,-2],[-3,-2],[-13,8],
[-1,5],[-1,-7],[9,-4],[2,-4],[-3,2],[7,
-5],[-1,4],[-3,0],[-4,5],[-2,4],[-6,5],
[-7,1],[-2,-1],[18,-28],[10,10],[2,1],[7,
-36],[2,-1],[8,4],[23,-8],[3,-27],[-11,6],
[-16,10],[6,4],[-15,22],[-13,-1],[-5,14],
[5,10],[-13,-8],[11,-20],[11,-22],[-19,12],
[7,-4],[10,7],[-15,7],[-5,7],[3,-2],[12,
-5],[-4,1],[-1,-7],[12,-14],[-3,5],[-1,2],
[-1,1],[1,-5],[-5,-7],[-10,5],[0,5],[3,-1],
[0,-2],[-5,-4],[8,0],[-2,9]])
]> where w := K.1 where K := ext<K|Polynomial(K,[1,-1,1])> where K
is RationalField();

return _LR;
