Charge-22 flux on K3 x K3: arithmetic data (Section 3.4; SM Section S6). Field: K = Q(zeta), zeta = zeta_66, [K:Q] = 20, |d_K| = 3^10 11^18; Phi_66(x) = x^20 + x^19 - x^17 - x^16 + x^14 + x^13 - x^11 - x^10 - x^9 + x^7 + x^6 - x^4 - x^3 + x + 1 Real places sigma_k, k in [1, 5, 7, 13, 17, 19, 23, 25, 29, 31] delta = -55*zeta^19 - 85*zeta^18 + 270*zeta^17 - 107*zeta^16 - 83*zeta^15 + 54*zeta^14 - 28*zeta^13 - 2*zeta^12 + 18*zeta^11 + 20*zeta^10 + 10*zeta^9 - 35*zeta^8 + 150*zeta^7 - 145*zeta^6 - 127*zeta^5 + 186*zeta^4 - 17*zeta^3 - 8*zeta^2 - 16*zeta - 19 signs of sigma_k(delta^-1): [-1, 1, 1, -1, -1, 1, 1, -1, -1, 1] eps_S = -u_7 u_17 u_19 u_23 u_29 = 1806*zeta^19 + 3522*zeta^18 + 3186*zeta^17 + 1014*zeta^16 - 1087*zeta^15 - 1170*zeta^14 + 582*zeta^13 + 2227*zeta^12 + 1869*zeta^11 - 358*zeta^10 - 2451*zeta^9 - 4374*zeta^8 - 4304*zeta^7 - 2331*zeta^6 - 462*zeta^5 - 566*zeta^4 - 2505*zeta^3 - 4320*zeta^2 - 4096*zeta - 2016 signs of sigma_k(eps_S delta^-1): [1, -1, -1, -1, -1, -1, -1, -1, -1, -1] (positive only at k = 1); min |sigma_k(eps_S delta^-1)| = 8.9165415791729897621647662860158793141931851080186110784686644444344550230248e-6 Gram matrix B of L = (Z[zeta], Tr(eps_S delta^-1 x ybar)) in the power basis: symmetric Toeplitz, B_ij = tau(|i-j|), tau(0..19) = [12726, 12746, 12769, 12744, 12623, 12359, 11879, 11146, 10182, 9031, 7736, 6363, 5010, 3738, 2562, 1477, 480, -480, -1477, -2562] det B = 1, signature (2,18), all diagonal entries 12726 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 -480 -1477 -2562 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 -480 -1477 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 -480 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 -480 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 -1477 -480 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 -2562 -1477 -480 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 M_zeta (multiplication by zeta, 20x20): 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 Lambda = U + L, Gram d (22x22), det -1, signature (3,19): 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 -480 -1477 -2562 0 0 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 -480 -1477 0 0 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 -480 0 0 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 480 0 0 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 1477 0 0 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 2562 0 0 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 3738 0 0 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 5010 0 0 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 6363 0 0 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 7736 0 0 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 9031 0 0 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 10182 0 0 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 11146 0 0 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 11879 0 0 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 12359 0 0 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 12623 0 0 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 12744 0 0 -480 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 12769 0 0 -1477 -480 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 12746 0 0 -2562 -1477 -480 480 1477 2562 3738 5010 6363 7736 9031 10182 11146 11879 12359 12623 12744 12769 12746 12726 U block: d_U = [[0,1],[1,0]], gtilde_U = [[1, 1], [1, 2]], g_U = [[2, 1], [1, 1]], S_U = g_U gtilde_U = [[3, 4], [2, 3]], charpoly x^2 - 6x + 1, eigenvalues 3 +- 2 sqrt 2 M_(1+zeta) (= gtilde on L): 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 M_(1+zeta^-1) (= g on L): 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 gtilde (22x22): 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 g (22x22): 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 S = g gtilde (22x22), tr S = 44, det S = 1, N_flux = 22, n_M2 = 2: 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 N with g = N d (22x22; basis dependent; max |N_ij| = 3846, 398 nonzero entries): 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1072 -2144 544 2890 749 -1639 -1062 -449 -339 1647 2237 -93 -575 -733 -1695 -10 2711 1395 -1818 -1616 0 0 544 -1600 -1600 1818 2023 -890 -1085 105 -788 -308 2268 528 -668 308 -812 -1705 1085 2490 -423 -1818 0 0 1818 2362 -1600 -3418 0 2023 928 733 105 -2606 -2126 450 528 1150 2126 -812 -3523 -733 2490 1395 0 0 -323 2567 1818 -3095 -2772 1639 1690 -18 1072 -147 -3448 -638 1025 -134 1450 2136 -2128 -3523 1085 2711 0 0 -1639 -890 2023 1639 -1133 -1133 -10 -572 321 2136 327 -644 -63 -953 -1150 1460 2136 -812 -1705 -10 0 0 10 -1629 -890 2013 1629 -1133 -1123 0 -572 311 2126 317 -644 -53 -943 -1150 1450 2126 -812 -1695 0 0 623 -439 -1085 305 1067 -10 -500 123 -339 -620 853 338 -258 318 -53 -953 -134 1150 308 -733 0 0 -339 -788 105 1072 321 -572 -339 -216 -216 575 884 27 -237 -258 -644 -63 1025 528 -668 -575 0 0 575 236 -788 -470 497 321 3 236 -216 -791 0 309 27 338 317 -644 -638 450 528 -93 0 0 1165 2812 -308 -3771 -1312 2136 1476 545 575 -1956 -3121 0 884 853 2126 327 -3448 -2126 2268 2237 0 0 -1165 1072 2268 -961 -2283 327 961 -312 884 1165 -1956 -791 575 -620 311 2136 -147 -2606 -308 1647 0 0 -575 -668 528 1025 -63 -644 -258 -237 27 884 575 -216 -216 -339 -572 321 1072 105 -788 -339 0 0 339 -236 -668 189 686 -63 -305 81 -237 -312 545 236 -216 123 0 -572 -18 733 105 -449 0 0 -623 -1356 308 1773 489 -953 -676 -305 -258 961 1476 3 -339 -500 -1123 -10 1690 928 -1085 -1062 0 0 -10 -1705 -812 2136 1460 -1150 -953 -63 -644 327 2136 321 -572 -10 -1133 -1133 1639 2023 -890 -1639 0 0 1639 1629 -1705 -2451 497 1460 489 686 -63 -2283 -1312 497 321 1067 1629 -1133 -2772 0 2023 749 0 0 323 3034 1085 -3846 -2451 2136 1773 189 1025 -961 -3771 -470 1072 305 2013 1639 -3095 -3418 1818 2890 0 0 -1818 -423 2490 1085 -1705 -812 308 -668 528 2268 -308 -788 105 -1085 -890 2023 1818 -1600 -1600 544 0 0 -544 -2362 -423 3034 1629 -1705 -1356 -236 -668 1072 2812 236 -788 -439 -1629 -890 2567 2362 -1600 -2144 0 0 1072 -544 -1818 323 1639 -10 -623 339 -575 -1165 1165 575 -339 623 10 -1639 -323 1818 544 -1072 det(x - S) = (x^2 - 6x + 1) m(x)^2, m(x) = x^10 - 19*x^9 + 152*x^8 - 666*x^7 + 1742*x^6 - 2782*x^5 + 2665*x^4 - 1443*x^3 + 390*x^2 - 40*x + 1, disc(m) = 572981288913 expanded: x^22 - 44*x^21 + 894*x^20 - 11136*x^19 + 95209*x^18 - 592708*x^17 + 2781410*x^16 - 10049472*x^15 + 28311500*x^14 - 62601840*x^13 + 108847544*x^12 - 148482242*x^11 + 157932863*x^10 - 129649518*x^9 + 80941466*x^8 - 37668104*x^7 + 12725687*x^6 - 3015610*x^5 + 479766*x^4 - 48446*x^3 + 2861*x^2 - 86*x + 1 Eigenplanes of S on L (k, lambda_k = 2 + 2 cos(2 pi k/66), sign of b on P_k): k = 1 lambda = 3.9909438451461692094525105622598612315150... sign + k = 5 lambda = 3.7776708973098469326231977859017091047356... sign - k = 7 lambda = 3.5721061894855749395135921122944407320797... sign - k = 13 lambda = 2.6541359266348432726834987403169048156145... sign - k = 17 lambda = 1.9048361683525154051004255119370263302909... sign - k = 19 lambda = 1.5284821289811455434989793593970248311472... sign - k = 23 lambda = 0.8398861808576036416060377361993851755329... sign - k = 25 lambda = 0.5525319237898596767202845264703197707278... sign - k = 29 lambda = 0.1432641339678547795988225504728199303381... sign - k = 31 lambda = 0.0361426054745865992026511147505080780178... sign - U: 3+2 sqrt 2 = 5.8284271247461900976033774484193961571393... (+), 3-2 sqrt 2 = 0.1715728752538099023966225515806038428606... (-) => exactly three positive directions. Kondo identification (K3Groups entry 0.66.0.1): G_BH (22x22): -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 2 -2 4 -4 2 -2 0 0 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 2 -2 4 -4 2 0 0 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 2 -2 4 -4 0 0 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 2 -2 4 0 0 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 2 -2 0 0 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 2 0 0 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 -3 0 0 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 2 0 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 -2 0 0 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 1 0 0 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 0 0 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 -1 0 0 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 -1 0 0 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 -1 0 0 2 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 3 0 0 -2 2 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 -3 0 0 4 -2 2 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 1 0 0 -4 4 -2 2 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 -3 0 0 2 -4 4 -2 2 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 3 0 0 -2 2 -4 4 -2 2 -3 2 -2 1 0 -1 -1 -1 3 -3 1 -3 3 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 M_BH (row convention, M_BH G_BH M_BH^T = G_BH): 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 0 1 1 0 -1 -1 0 1 1 1 0 -1 -1 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 P (det 1, P^T G_BH P = d, (M_BH^T)^5 P = P h, h = 1_U + M_zeta): 0 0 9 6 9 10 5 0 2 3 -1 -2 3 6 3 3 7 7 1 -1 1 -1 0 0 12 13 16 11 4 1 1 -4 -8 -5 0 0 0 5 8 4 -1 -1 -4 -11 0 0 5 8 4 -1 -1 -4 -11 -16 -13 -12 -13 -11 -3 0 -2 -2 0 -3 -11 -13 0 0 -9 -8 -11 -10 -8 -11 -15 -15 -12 -14 -14 -10 -4 -4 -3 1 4 1 -1 1 0 0 -13 -9 -8 -6 -4 -1 -1 -1 0 1 1 1 4 6 8 9 13 14 15 14 0 0 6 8 9 13 14 15 14 16 15 14 13 14 14 13 14 15 16 14 15 14 0 0 22 20 24 26 19 15 16 16 8 6 9 10 4 4 8 7 0 -2 0 -5 0 0 13 14 16 10 3 0 -3 -10 -16 -14 -13 -14 -15 -9 -8 -11 -15 -14 -18 -25 0 0 -9 -8 -11 -15 -14 -18 -25 -29 -27 -27 -29 -25 -18 -14 -15 -11 -8 -9 -15 -14 0 0 -23 -21 -20 -18 -14 -15 -16 -16 -13 -14 -13 -9 -3 0 3 9 13 14 13 16 0 0 -9 -3 0 3 9 13 14 13 16 16 15 14 18 20 21 23 28 30 29 29 0 0 11 15 14 18 25 29 27 27 29 25 18 14 15 11 8 9 15 14 13 14 0 0 11 8 9 15 14 13 14 16 10 3 0 -3 -10 -16 -14 -13 -14 -15 -9 -8 0 0 -7 -8 -4 -4 -10 -9 -6 -8 -16 -16 -15 -19 -26 -24 -20 -22 -24 -19 -13 -16 0 0 -15 -14 -13 -14 -14 -13 -14 -15 -16 -14 -15 -14 -13 -9 -8 -6 -4 -1 -1 -1 0 0 -9 -8 -6 -4 -1 -1 -1 0 1 1 1 4 6 8 9 13 14 15 14 16 0 0 -1 3 4 4 10 14 14 12 15 15 11 8 10 11 8 9 13 16 13 14 0 0 2 2 0 3 11 13 12 13 16 11 4 1 1 -4 -8 -5 0 0 0 5 0 0 -4 -8 -5 0 0 0 5 8 4 -1 -1 -4 -11 -16 -13 -12 -13 -11 -3 0 0 0 -7 -7 -3 -3 -6 -3 2 1 -3 -2 0 -5 -10 -9 -6 -9 -10 -5 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Admissible powers a with an isometry h -> (M_BH^T)^a: [5, 61] Whether W = 0 at this vacuum (supersymmetry) is not decided by these data.