"Tr2D6 to Tr7D6 give traces of elements of orders 2 to 7 for lambda_1, lambda_5, lambda_6 and lambda_2 respectively";

w3:=RootOfUnity(3);
w4:=RootOfUnity(4);
w5:=RootOfUnity(5);
w6:=RootOfUnity(6);
w7:=RootOfUnity(7);
w8:=RootOfUnity(8);
w9:=RootOfUnity(9);

Tr2D6:={[[-12],[-32],[32],[66]],[[4],[0],[0],[2]],[[-12],[32],[-32],[66]],[[-4],[0],[0],[2]],[[12],[-32],[-32],[66]]};

Tr3D6:={[[0],[2],[2],[0]],[[-6],[14],[-13],[21]],[[9],[-16],[-16],[36]],[[-6],[-13],[14],[21]],[[3],[-4],[-4],[3]],[[-3],[-1],[-1],[6]],[[6],[8],[8],[15]]};

Tr4D6:={[[0,4],[0,0],[0,0],[-2,2]],[[4,-4],[8,0],[8,0],[10,2]],[[0,-4],[0,0],[0,0],[2,2]],[[-8,4],[-16,0],[16,0],[30,2]],[[8,4],[-16,0],[-16,0],[30,2]],[[-4,-4],[8,0],[-8,0],[10,2]],[[0,-12],[8,32],[0,-32],[6,66]],[[8,12],[0,-32],[0,-32],[26,66]],[[4,4],[0,0],[0,0],[6,2]],[[0,-12],[0,-32],[-8,32],[6,66]],[[-8,12],[0,-32],[0,-32],[26,66]],[[0,-12],[-8,32],[0,-32],[6,66]],[[-4,-4],[-8,0],[8,0],[10,2]],[[8,4],[16,0],[16,0],[30,2]],[[-8,4],[16,0],[-16,0],[30,2]],[[4,-4],[-8,0],[-8,0],[10,2]],[[-4,4],[0,0],[0,0],[6,2]],[[0,-12],[0,-32],[8,32],[6,66]],[[0,12],[0,-32],[0,-32],[-6,66]]};

Tr5D6:={[[w5^3+w5^2+5],[4*w5^3+4*w5^2+4],[4*w5^3+4*w5^2+4],[5*w5^3+5*w5^2+11]],
[[-w5^3-w5^2+9],[16*w5^3+16*w5^2],[16*w5^3+16*w5^2],[-10*w5^3-10*w5^2+36]],
[[-6*w5^3-6*w5^2-6],[6*w5^3+6*w5^2+20],[-14*w5^3-14*w5^2-15],[15*w5^3+15*w5^2+36]],
[[3*w5^3+3*w5^2+1],[2*w5^3+2*w5^2+3],[2*w5^3+2*w5^2+3],[6]],
[[-3*w5^3-3*w5^2-2],[-2*w5^3-2*w5^2+1],[-2*w5^3-2*w5^2+1],[6]],
[[2*w5^3+2*w5^2-2],[3*w5^3+3*w5^2-4],[-2*w5^3-2*w5^2+6],[-5*w5^3-5*w5^2+6]],
[[-4*w5^3-4*w5^2-5],[-6*w5^3-6*w5^2-11],[9*w5^3+9*w5^2+9],[10*w5^3+10*w5^2+21]],
[[-6*w5^3-6*w5^2-6],[-14*w5^3-14*w5^2-15],[6*w5^3+6*w5^2+20],[15*w5^3+15*w5^2+36]],
[[-2*w5^3-2*w5^2+1],[2*w5^3+2*w5^2-2],[2*w5^3+2*w5^2-2],[-5*w5^3-5*w5^2+1]],
[[6*w5^3+6*w5^2],[-6*w5^3-6*w5^2+14],[14*w5^3+14*w5^2-1],[-15*w5^3-15*w5^2+21]],
[[6*w5^3+6*w5^2],[14*w5^3+14*w5^2-1],[-6*w5^3-6*w5^2+14],[-15*w5^3-15*w5^2+21]],
[[w5^3+w5^2],[-w5^3-w5^2-1],[-w5^3-w5^2-1],[1]],
[[-3],[-5*w5^3-5*w5^2-3],[5*w5^3+5*w5^2+2],[6]],
[[-3*w5^3-3*w5^2+3],[8*w5^3+8*w5^2-4],[8*w5^3+8*w5^2-4],[-15*w5^3-15*w5^2+6]],
[[-3],[5*w5^3+5*w5^2+2],[-5*w5^3-5*w5^2-3],[6]],
[[-5*w5^3-5*w5^2-3],[5*w5^3+5*w5^2-3],[5*w5^3+5*w5^2-3],[16]],
[[2],[2],[2],[1]],
[[4*w5^3+4*w5^2-1],[6*w5^3+6*w5^2-5],[-9*w5^3-9*w5^2],[-10*w5^3-10*w5^2+11]],
[[7],[-8],[-8],[21]],
[[-2*w5^3-2*w5^2-4],[2*w5^3+2*w5^2+8],[-3*w5^3-3*w5^2-7],[5*w5^3+5*w5^2+11]],
[[-w5^3-w5^2-1],[w5^3+w5^2],[w5^3+w5^2],[1]],
[[-w5^3-w5^2+4],[-4*w5^3-4*w5^2],[-4*w5^3-4*w5^2],[-5*w5^3-5*w5^2+6]],
[[-2*w5^3-2*w5^2+6],[-8*w5^3-8*w5^2+8],[-8*w5^3-8*w5^2+8],[-15*w5^3-15*w5^2+16]],
[[2*w5^3+2*w5^2+3],[-2*w5^3-2*w5^2-4],[-2*w5^3-2*w5^2-4],[5*w5^3+5*w5^2+6]],
[[3*w5^3+3*w5^2+6],[-8*w5^3-8*w5^2-12],[-8*w5^3-8*w5^2-12],[15*w5^3+15*w5^2+21]],
[[4*w5^3+4*w5^2-1],[-9*w5^3-9*w5^2],[6*w5^3+6*w5^2-5],[-10*w5^3-10*w5^2+11]],
[[4*w5^3+4*w5^2+4],[6*w5^3+6*w5^2+10],[6*w5^3+6*w5^2+10],[10*w5^3+10*w5^2+16]],
[[2*w5^3+2*w5^2-2],[-2*w5^3-2*w5^2+6],[3*w5^3+3*w5^2-4],[-5*w5^3-5*w5^2+6]],
[[w5^3+w5^2+10],[-16*w5^3-16*w5^2-16],[-16*w5^3-16*w5^2-16],[10*w5^3+10*w5^2+46]],
[[2*w5^3+2*w5^2+8],[8*w5^3+8*w5^2+16],[8*w5^3+8*w5^2+16],[15*w5^3+15*w5^2+31]],
[[-2*w5^3-2*w5^2-4],[-3*w5^3-3*w5^2-7],[2*w5^3+2*w5^2+8],[5*w5^3+5*w5^2+11]],
[[5*w5^3+5*w5^2+2],[-5*w5^3-5*w5^2-8],[-5*w5^3-5*w5^2-8],[16]],
[[-4*w5^3-4*w5^2-5],[9*w5^3+9*w5^2+9],[-6*w5^3-6*w5^2-11],[10*w5^3+10*w5^2+21]],
[[-4*w5^3-4*w5^2],[-6*w5^3-6*w5^2+4],[-6*w5^3-6*w5^2+4],[-10*w5^3-10*w5^2+6]]};

Tr6D6:={[[-7,9,-4],[0,-16,0],[0,-16,0],[20,36,2]],
[[10,6,4],[24,8,0],[24,8,0],[47,15,2]],
[[-7,3,-4],[12,-4,0],[-12,-4,0],[23,3,2]],
[[-3,3,-12],[-4,-4,32],[4,-4,-32],[3,3,66]],
[[5,-3,-4],[9,-1,0],[9,-1,0],[14,6,2]],
[[-10,6,-4],[24,8,0],[-24,8,0],[47,15,2]],
[[6,-6,-12],[-14,14,-32],[-13,-13,32],[21,21,66]],
[[-10,6,-4],[-24,8,0],[24,8,0],[47,15,2]],
[[-9,9,-12],[-16,-16,32],[16,-16,-32],[36,36,66]],
[[-6,6,-12],[-8,8,-32],[8,8,32],[15,15,66]],
[[0,0,-12],[2,2,32],[-2,2,-32],[0,0,66]],
[[10,6,4],[-24,8,0],[-24,8,0],[47,15,2]],
[[-5,-3,4],[-9,-1,0],[9,-1,0],[14,6,2]],
[[-1,3,-4],[0,-4,0],[0,-4,0],[-1,3,2]],
[[-6,-6,12],[13,-13,-32],[-14,14,-32],[21,21,66]],
[[8,0,-4],[18,2,0],[18,2,0],[32,0,2]],
[[2,-6,-4],[3,-13,0],[6,14,0],[5,21,2]],
[[2,6,-4],[0,8,0],[0,8,0],[-1,15,2]],
[[1,9,4],[0,-16,0],[0,-16,0],[-4,36,2]],
[[3,3,12],[4,-4,-32],[4,-4,-32],[3,3,66]],
[[-2,-6,4],[-6,14,0],[3,-13,0],[5,21,2]],
[[1,3,4],[0,-4,0],[0,-4,0],[-1,3,2]],
[[-4,6,-4],[0,8,0],[0,8,0],[5,15,2]],
[[6,-6,-12],[-13,-13,32],[-14,14,-32],[21,21,66]],
[[-2,-6,4],[6,14,0],[-3,-13,0],[5,21,2]],
[[0,0,-12],[-2,2,-32],[2,2,32],[0,0,66]],
[[-1,-3,-4],[-3,-1,0],[3,-1,0],[2,6,2]],
[[-5,-3,4],[9,-1,0],[-9,-1,0],[14,6,2]],
[[4,6,4],[0,8,0],[0,8,0],[5,15,2]],
[[-2,0,4],[0,2,0],[0,2,0],[2,0,2]],
[[-5,3,4],[0,-4,0],[0,-4,0],[11,3,2]],
[[4,0,4],[-6,2,0],[-6,2,0],[8,0,2]],
[[3,-3,-12],[1,-1,-32],[-1,-1,32],[6,6,66]],
[[9,9,12],[16,-16,-32],[16,-16,-32],[36,36,66]],
[[6,-6,-12],[14,14,32],[13,-13,-32],[21,21,66]],
[[3,-3,-12],[-1,-1,32],[1,-1,-32],[6,6,66]],
[[8,0,-4],[-18,2,0],[-18,2,0],[32,0,2]],
[[1,-3,4],[3,-1,0],[3,-1,0],[2,6,2]],
[[7,3,4],[12,-4,0],[12,-4,0],[23,3,2]],
[[-7,3,-4],[-12,-4,0],[12,-4,0],[23,3,2]],
[[-6,6,-12],[8,8,32],[-8,8,-32],[15,15,66]],
[[4,0,4],[6,2,0],[6,2,0],[8,0,2]],
[[-2,6,4],[0,8,0],[0,8,0],[-1,15,2]],
[[-8,0,4],[-18,2,0],[18,2,0],[32,0,2]],
[[-6,-6,12],[-14,14,-32],[13,-13,-32],[21,21,66]],
[[6,6,12],[-8,8,-32],[-8,8,-32],[15,15,66]],
[[2,-6,-4],[-6,14,0],[-3,-13,0],[5,21,2]],
[[-1,9,-4],[0,-16,0],[0,-16,0],[-4,36,2]],
[[-1,-3,-4],[3,-1,0],[-3,-1,0],[2,6,2]],
[[-8,0,4],[18,2,0],[-18,2,0],[32,0,2]],
[[-4,0,-4],[-6,2,0],[6,2,0],[8,0,2]],
[[-2,-6,4],[-3,-13,0],[6,14,0],[5,21,2]],
[[7,3,4],[-12,-4,0],[-12,-4,0],[23,3,2]],
[[-9,9,-12],[16,-16,-32],[-16,-16,32],[36,36,66]],
[[1,-3,4],[-3,-1,0],[-3,-1,0],[2,6,2]],
[[7,9,4],[0,-16,0],[0,-16,0],[20,36,2]],
[[-3,-3,12],[1,-1,-32],[1,-1,-32],[6,6,66]],
[[2,0,-4],[0,2,0],[0,2,0],[2,0,2]],
[[-4,0,-4],[6,2,0],[-6,2,0],[8,0,2]],
[[6,-6,-12],[13,-13,-32],[14,14,32],[21,21,66]],
[[5,-3,-4],[-9,-1,0],[-9,-1,0],[14,6,2]],
[[2,-6,-4],[6,14,0],[3,-13,0],[5,21,2]],
[[0,0,12],[-2,2,-32],[-2,2,-32],[0,0,66]],
[[5,3,-4],[0,-4,0],[0,-4,0],[11,3,2]],
[[2,-6,-4],[-3,-13,0],[-6,14,0],[5,21,2]],
[[-2,-6,4],[3,-13,0],[-6,14,0],[5,21,2]],
[[-3,3,-12],[4,-4,-32],[-4,-4,32],[3,3,66]]};
