Q(rt7) Disc=28 -------------------- n=2 Gram Matrix A= [2,rt7] [rt7,4] h=1 Automorphism group size: [8] Trivial case. -------------------- n=4 Gram Matrix A oplus A h=4 Automorphism group sizes: [128, 72, 1152, 192] Neighbour Matrices: N(P)=2 [4 0 1 4] [0 9 0 0] [9 0 0 0] [6 0 0 3] CharPoly = (x-1)(x+3)(x-9)^2 N(P)=3 [ 0 16 0 0] [ 9 0 1 6] [ 0 16 0 0] [ 0 16 0 0] CharPoly = x^2(x+16)(x-16) N(P)=25 [484 0 16 176] [ 0 676 0 0] [144 0 196 336] [264 0 56 356] CharPoly = (x-100)(x-260)(x-676)^2 N(P)=7 [ 0 64 0 0] [36 0 4 24] [ 0 64 0 0] [ 0 64 0 0] CharPoly = x^2(x-64)(x+64) -------------------- n=6 Gram Matrix A oplus A oplus A h=25 Automorphism group sizes: [3072, 576, 96, 96, 9216, 1536, 64, 288, 288, 512, 256, 2304, 384, 1344, 96, 2304, 576, 576, 64, 336, 10080, 10080, 46080, 46080, 1536] Neighbour Matrices: N(P)=2 [ 6 0 0 0 0 0 0 0 0 0 3 12 0 0 6 0 0 0 0 0 0 0 0 8 0] [ 0 11 0 3 3 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 12 3 0 12 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 3 18 3 9 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 3 0 9 3 0 0 0 18 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 2 8 0 0 13 0 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 35 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 21 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 8 0 3 12 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 9 0 0 0 0 0 0 0 0 0 2 0 0 0 18 0 0 3 0 0 0 0 3 0 0] [ 6 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 6 0 0 6 0 0 0 12 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 16 18 0 0 1 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 2 6 0 18 9 0 0 0 0 0 0 0 0] [ 1 0 0 0 0 0 0 0 0 0 1 0 4 0 1 8 8 0 0 0 0 4 0 8 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 18 0 0 8 0 4 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 1 0 8 4 0 2 0 8 0 8 0 0 0 4] [ 0 0 0 0 0 0 0 0 0 0 15 0 20 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 12 3 0 16 1 0 0 0 3 0] [ 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 16 13 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 9 0 0 0 6 2 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0 16 0 1 0 0] [ 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 20 0 0 0] [ 1 0 0 0 0 0 0 0 0 0 0 3 0 0 6 0 0 0 12 0 0 0 0 9 4] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 14 0] CharPoly = (x-35)^2(x-23)(x-19)^2(x-14)^2(x-10)^2(x-3)(x-2)^2(x+2)^2(x+5)(x+6)(x+12)(x+14)(x+21)(x^2-20x+92)(x^2-4x-68)^2 N(P)=3 [ 0 48 32 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 9 0 0 0 0 0 0 0 0 0 1 6 0 12 0 72 0 0 0 0 12 0 0 0 0] [ 1 0 0 0 0 0 0 0 0 0 0 0 3 18 6 36 12 0 24 0 0 0 0 8 4] [ 0 0 0 0 0 0 0 0 0 0 3 0 8 28 18 36 18 1 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 3 0 0 0 18 36 18 0 0 0 28 8 1 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 4 0 8 2 40 8 0 32 2 8 0 0 8 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 35 70 0 0 0 7 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 42 0 0 56 14 0 0 0 0 0] [ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 6 36 12 0 24 0 18 3 0 8 4] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 70 35 7 0 0] [ 0 16 0 48 48 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 16 0 0 0 96 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 72 32 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 6 54 14 0 36 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 32 16 16 16 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 8 24 4 4 40 0 8 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 32 8 8 32 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 80 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 24 0 0 48 0 16 24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 48 0 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 6 0 0 14 36 0 0 54 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 32 0 0 0 72 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 80 0 0 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 32 0 0 48 0 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 56 0 0 0 0 0 56 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 CharPoly = x^9(x-112)(x-48)^2(x-28)(x-20)(x-16)(x+16)(x+20)(x+28)(x+48)^2(x+112)(x^4-1280x^2+335872) -------------------- n=8 Gram Matrix A oplus A oplus A oplus A Mass = 208.6 Too big.