Rank-19 lattices of Section 3.3 and SM Sections S1.2, S5.1: Gram matrices (integer rows) and invariants. == W512: rank 19, det 512, even, minimum 4, roots 0, kissing number 5200, L*/L = Z/2 x Z/2 x Z/128, |Aut| = 2 4 2 2 1 2 0 2 2 -2 2 -2 -1 -1 -2 2 1 2 2 -1 2 4 2 -1 2 -1 2 1 -2 0 0 -1 1 0 1 2 1 1 0 2 2 4 1 1 1 2 2 -2 0 0 -1 0 -1 2 0 2 2 -1 1 -1 1 4 1 2 1 2 1 2 0 1 -1 -2 2 -1 0 1 -2 2 2 1 1 4 1 1 2 -1 2 -1 -1 1 -1 1 0 1 0 -1 0 -1 1 2 1 4 1 2 0 1 -1 1 1 0 0 -1 0 0 -2 2 2 2 1 1 1 4 1 -2 1 0 1 1 -1 1 2 0 1 -2 2 1 2 2 2 2 1 4 0 1 -1 -1 0 -1 1 -1 1 2 -1 -2 -2 -2 1 -1 0 -2 0 4 0 1 1 0 1 -1 -1 -2 -1 1 2 0 0 2 2 1 1 1 0 4 -1 1 0 -2 1 0 1 0 -1 -2 0 0 0 -1 -1 0 -1 1 -1 4 0 1 1 0 0 -1 -1 0 -1 -1 -1 1 -1 1 1 -1 1 1 0 4 1 0 0 1 -2 -1 -1 -1 1 0 -1 1 1 1 0 0 0 1 1 4 2 -1 1 -1 -2 0 -2 0 -1 -2 -1 0 -1 -1 1 -2 1 0 2 4 -2 1 -1 -2 1 2 1 2 2 1 0 1 1 -1 1 0 0 -1 -2 4 0 1 1 -1 1 2 0 -1 0 -1 2 -1 -1 0 0 1 1 1 0 4 -1 0 0 2 1 2 0 1 0 0 1 -2 1 -1 -2 -1 -1 1 -1 4 1 0 2 1 2 1 0 0 1 2 -1 0 -1 -1 -2 -2 1 0 1 4 0 -1 0 -1 -2 -1 -2 -2 -1 1 -1 0 -1 0 1 -1 0 0 0 4 == W512': rank 19, det 512, even, minimum 4, roots 0, kissing number 5204, L*/L = Z/2 x Z/2 x Z/128, |Aut| = 2 4 -2 -2 -2 -1 -1 -1 -1 2 -2 -1 1 -1 -2 -2 2 -1 2 -1 -2 4 2 2 2 1 -1 1 -1 2 2 1 -1 0 0 -2 2 -2 -1 -2 2 4 2 1 2 0 2 0 0 0 0 0 0 1 -1 1 -2 -1 -2 2 2 4 0 2 -1 2 0 1 2 -1 -1 1 1 0 1 -2 0 -1 2 1 0 4 -1 -1 1 0 1 1 2 1 0 -1 -1 2 0 -1 -1 1 2 2 -1 4 1 2 -1 -1 0 0 0 1 0 0 -1 -2 -1 -1 -1 0 -1 -1 1 4 -1 -2 0 -2 -1 1 1 1 -1 -2 0 0 -1 1 2 2 1 2 -1 4 1 -1 1 0 0 0 -1 0 1 -2 -1 2 -1 0 0 0 -1 -2 1 4 -1 0 0 -1 -2 -1 1 0 1 0 -2 2 0 1 1 -1 0 -1 -1 4 2 0 -1 1 1 -2 1 -1 1 -1 2 0 2 1 0 -2 1 0 2 4 1 -1 0 0 0 2 -1 0 1 1 0 -1 2 0 -1 0 0 0 1 4 0 -1 -2 0 1 1 -1 -1 -1 0 -1 1 0 1 0 -1 -1 -1 0 4 2 1 0 -1 1 1 -2 0 0 1 0 1 1 0 -2 1 0 -1 2 4 1 0 -1 -1 1 -2 0 1 1 -1 0 1 -1 -1 1 0 -2 1 1 4 -1 0 0 2 2 -2 -1 0 -1 0 -1 0 1 -2 0 0 0 0 -1 4 -1 1 -1 -1 2 1 1 2 -1 -2 1 0 1 2 1 -1 -1 0 -1 4 -1 0 2 -2 -2 -2 0 -2 0 -2 1 -1 -1 1 1 -1 0 1 -1 4 1 -1 -1 -1 0 -1 -1 0 -1 0 1 0 -1 1 1 2 -1 0 1 4 == W1024: rank 19, det 1024, even, minimum 4, roots 0, kissing number 3664, L*/L = Z/2 x Z/2 x Z/256, |Aut| = 2 4 -1 -1 2 2 2 2 2 2 -1 -2 2 2 -1 -2 2 -2 2 2 -1 4 2 0 -2 1 1 -2 -1 -1 2 0 -1 2 2 0 2 -2 0 -1 2 4 1 -1 0 0 -2 -2 0 2 1 0 2 0 -1 1 -2 1 2 0 1 4 2 2 2 0 1 0 0 1 2 -1 -2 1 -1 1 2 2 -2 -1 2 4 0 1 2 1 1 -1 0 1 -2 -2 0 -2 1 1 2 1 0 2 0 4 1 0 2 -2 0 2 2 0 0 1 0 1 1 2 1 0 2 1 1 4 1 1 -1 -1 0 0 -1 -1 2 0 1 1 2 -2 -2 0 2 0 1 4 2 -1 -2 0 1 -2 -1 0 -2 1 1 2 -1 -2 1 1 2 1 2 4 -2 -2 1 1 -1 0 1 -1 2 1 -1 -1 0 0 1 -2 -1 -1 -2 4 0 -1 -1 -1 -1 0 -1 0 -1 -2 2 2 0 -1 0 -1 -2 -2 0 4 0 0 1 1 -2 2 -2 -1 2 0 1 1 0 2 0 0 1 -1 0 4 2 1 -1 1 -1 1 1 2 -1 0 2 1 2 0 1 1 -1 0 2 4 -1 -2 0 -1 1 2 -1 2 2 -1 -2 0 -1 -2 -1 -1 1 1 -1 4 2 0 1 -2 0 -2 2 0 -2 -2 0 -1 -1 0 -1 1 -1 -2 2 4 -1 2 -2 -1 2 0 -1 1 0 1 2 0 1 0 -2 1 0 0 -1 4 -1 2 0 -2 2 1 -1 -2 0 0 -2 -1 -1 2 -1 -1 1 2 -1 4 -1 -1 2 -2 -2 1 1 1 1 1 2 0 -2 1 1 -2 -2 2 -1 4 0 2 0 1 2 1 1 1 1 1 -1 -1 1 2 0 -1 0 -1 0 4 == Lambda_19 (LLL-reduced basis): rank 19, det 128, even, minimum 4, roots 0, kissing number 10668, L*/L = Z/2 x Z/2 x Z/2 x Z/2 x Z/8, |Aut| = 23592960 4 2 2 -2 2 -2 -2 2 0 0 -2 -2 1 0 -1 -1 -1 1 -2 2 4 2 -2 2 0 0 2 1 -1 -2 -2 2 -1 -2 1 -2 1 -1 2 2 4 0 2 0 0 2 -1 -1 -1 -1 2 -1 -2 1 -1 2 -2 -2 -2 0 4 0 0 0 0 -1 1 2 2 -1 1 1 0 1 0 1 2 2 2 0 4 0 0 2 1 -1 -1 -1 1 -1 -1 1 0 2 -1 -2 0 0 0 0 4 2 -1 1 -2 1 0 0 -1 0 2 1 1 1 -2 0 0 0 0 2 4 -1 1 -2 1 0 1 -1 -1 2 1 0 0 2 2 2 0 2 -1 -1 4 1 -1 -2 0 0 -1 0 1 0 2 -1 0 1 -1 -1 1 1 1 1 4 -2 0 -1 0 0 1 1 1 1 1 0 -1 -1 1 -1 -2 -2 -1 -2 4 1 0 -1 2 0 -2 -1 -2 1 -2 -2 -1 2 -1 1 1 -2 0 1 4 0 0 2 0 0 1 -1 2 -2 -2 -1 2 -1 0 0 0 -1 0 0 4 -1 -1 1 1 1 0 1 1 2 2 -1 1 0 1 0 0 -1 0 -1 4 -1 -2 1 -2 1 -1 0 -1 -1 1 -1 -1 -1 -1 0 2 2 -1 -1 4 0 -2 0 -2 1 -1 -2 -2 1 -1 0 -1 0 1 0 0 1 -2 0 4 -1 1 0 1 -1 1 1 0 1 2 2 1 1 -2 0 1 1 -2 -1 4 1 2 0 -1 -2 -1 1 0 1 1 0 1 -1 1 1 -2 0 1 1 4 1 0 1 1 2 0 2 1 0 2 1 -2 -1 0 1 -2 0 2 1 4 -1 -2 -1 -2 1 -1 1 0 -1 1 1 2 1 -1 1 1 0 0 -1 4 == Lambda_19, Gram matrix in the construction basis (complement of sqrt(2)D5 in the Leech lattice) 4 2 2 2 2 2 -2 0 0 1 3 0 2 1 -2 -4 1 0 2 2 4 2 2 2 2 -2 0 1 1 3 0 1 2 -2 -2 -1 1 -1 2 2 4 2 2 2 0 0 -1 1 3 -1 1 1 -1 -3 2 1 2 2 2 2 4 2 2 0 0 1 0 3 -1 3 0 -3 -1 2 1 2 2 2 2 2 4 2 0 -1 1 -2 3 -2 0 1 -2 -2 0 1 1 2 2 2 2 2 4 0 1 1 -1 2 0 0 2 -4 -2 3 3 2 -2 -2 0 0 0 0 4 -2 -1 -2 -2 -2 -3 3 -2 0 2 3 1 0 0 0 0 -1 1 -2 6 2 1 1 3 4 -7 2 4 2 -2 2 0 1 -1 1 1 1 -1 2 4 -2 1 1 1 -3 -1 3 -1 0 0 1 1 1 0 -2 -1 -2 1 -2 6 1 2 3 0 2 -2 0 -2 0 3 3 3 3 3 2 -2 1 1 1 6 0 4 -2 0 -2 1 -1 2 0 0 -1 -1 -2 0 -2 3 1 2 0 4 1 -2 1 1 0 -1 0 2 1 1 3 0 0 -3 4 1 3 4 1 10 -9 3 3 2 -5 3 1 2 1 0 1 2 3 -7 -3 0 -2 -2 -9 18 -9 -9 0 9 -3 -2 -2 -1 -3 -2 -4 -2 2 -1 2 0 1 3 -9 10 4 -3 -7 -1 -4 -2 -3 -1 -2 -2 0 4 3 -2 -2 1 3 -9 4 10 -1 -3 -1 1 -1 2 2 0 3 2 2 -1 0 1 0 2 0 -3 -1 8 3 5 0 1 1 1 1 3 3 -2 0 -2 -1 -1 -5 9 -7 -3 3 8 0 2 -1 2 2 1 2 1 2 0 0 2 0 3 -3 -1 -1 5 0 10 == T with T * (construction Gram) * T^T = (LLL-reduced Gram), det T = -1 1 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 0 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 1 1 -1 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 -1 -1 1 0 0 1 -1 -1 1 1 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 1 0 0 -1 0 0 0 0 0 1 1 0 0 -1 0 1 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 -1 0 -1 2 0 0 -1 0 1 1 0 0 0 0 0 0 1 2 0 -1 0 -1 2 0 1 0 0 0 0 0 0 0 1 -1 0 -9 -7 1 3 2 2 -10 0 0 1 0 -2 0 0 -1 -2 -1 2 1 == gluing of W512(-1) into Gamma_(3,19): overlattice Gram G (22x22, even, det -1, inertia (3, 19, 0)) -4 -2 -2 -1 -2 0 -2 -2 2 -2 2 1 1 2 -2 -1 -2 -2 1 -5 -9 -9 -2 -4 -2 1 -2 1 -2 -1 2 0 0 1 -1 0 -1 -2 -1 -1 0 -1 -7 -8 -2 -2 -4 -1 -1 -1 -2 -2 2 0 0 1 0 1 -2 0 -2 -2 1 -4 -8 -7 -1 1 -1 -4 -1 -2 -1 -2 -1 -2 0 -1 1 2 -2 1 0 -1 2 -6 -5 -6 -2 -2 -1 -1 -4 -1 -1 -2 1 -2 1 1 -1 1 -1 0 -1 0 1 -3 -8 -9 0 1 -1 -2 -1 -4 -1 -2 0 -1 1 -1 -1 0 0 1 0 0 2 -3 -5 -3 -2 -2 -2 -1 -1 -1 -4 -1 2 -1 0 -1 -1 1 -1 -2 0 -1 2 -3 -8 -7 -2 -1 -2 -2 -2 -2 -1 -4 0 -1 1 1 0 1 -1 1 -1 -2 1 -5 -8 -8 2 2 2 -1 1 0 2 0 -4 0 -1 -1 0 -1 1 1 2 1 -1 1 5 2 -2 0 0 -2 -2 -1 -1 -1 0 -4 1 -1 0 2 -1 0 -1 0 1 -5 -6 -8 2 0 0 0 1 1 0 1 -1 1 -4 0 -1 -1 0 0 1 1 0 2 3 1 1 1 1 -1 1 -1 -1 1 -1 -1 0 -4 -1 0 0 -1 2 1 1 -1 1 0 1 -1 0 1 -1 -1 -1 0 0 0 -1 -1 -4 -2 1 -1 1 2 0 2 -2 -3 2 0 1 2 1 0 1 1 -1 2 -1 0 -2 -4 2 -1 1 2 -1 5 3 3 -2 -1 -2 -2 -1 0 -1 -1 1 -1 0 0 1 2 -4 0 -1 -1 1 -5 -5 -7 -1 -2 0 1 0 1 -2 1 1 0 0 -1 -1 -1 0 -4 1 0 0 1 -3 -4 -2 -1 -2 0 -1 0 0 -1 2 -1 1 2 1 1 -1 1 -4 -1 0 -3 -5 -4 -2 -1 -2 -1 0 0 -1 -2 1 0 1 1 2 2 -1 0 -1 -4 0 -4 -4 -3 1 0 1 2 1 2 2 1 -1 1 0 1 0 -1 1 0 0 0 -4 3 5 3 -5 -1 -4 -6 -3 -3 -3 -5 1 -5 2 -1 2 5 -5 1 -3 -4 3 -14 -16 -18 -9 -7 -8 -5 -8 -5 -8 -8 5 -6 3 1 -2 3 -5 -3 -5 -4 5 -16 -34 -35 -9 -8 -7 -6 -9 -3 -7 -8 2 -8 1 0 -3 3 -7 -4 -4 -3 3 -18 -35 -44 -- embedding X (19x22), X G X^T = -W512 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 0 -- complement basis K (3x22), K G K^T = diag(2, 2, 128), glue index 512 0 0 0 -1 0 0 0 -1 0 -1 0 -1 0 0 -1 0 -1 -1 0 2 0 0 -1 -1 -1 -1 -1 -1 -1 -1 0 -1 0 0 0 -1 0 -1 -1 0 0 0 2 0 -81 -95 -31 -27 -95 -56 -22 -77 -124 -108 -69 -35 -35 -42 -101 -116 -95 -12 -47 0 0 128 == gluing of W512'(-1) into Gamma_(3,19): overlattice Gram G (22x22, even, det -1, inertia (3, 19, 0)) -4 2 2 2 1 1 1 1 -2 2 1 -1 1 2 2 -2 1 -2 1 2 1 3 2 -4 -2 -2 -2 -1 1 -1 1 -2 -2 -1 1 0 0 2 -2 2 1 -2 0 -4 2 -2 -4 -2 -1 -2 0 -2 0 0 0 0 0 0 -1 1 -1 2 1 -2 -1 -5 2 -2 -2 -4 0 -2 1 -2 0 -1 -2 1 1 -1 -1 0 -1 2 0 -1 -2 -4 1 -2 -1 0 -4 1 1 -1 0 -1 -1 -2 -1 0 1 1 -2 0 1 -3 -1 -4 1 -1 -2 -2 1 -4 -1 -2 1 1 0 0 0 -1 0 0 1 2 1 1 -1 -4 1 1 0 1 1 -1 -4 1 2 0 2 1 -1 -1 -1 1 2 0 0 2 2 2 1 -1 -2 -2 -1 -2 1 -4 -1 1 -1 0 0 0 1 0 -1 2 1 -1 -2 -4 -2 1 0 0 0 1 2 -1 -4 1 0 0 1 2 1 -1 0 -1 0 -1 -1 1 2 -2 0 -1 -1 1 0 1 1 -4 -2 0 1 -1 -1 2 -1 1 -1 -2 0 0 1 -2 0 -2 -1 0 2 -1 0 -2 -4 -1 1 0 0 0 -2 1 0 -2 -2 -3 -1 -1 0 1 -2 0 1 0 0 0 -1 -4 0 1 2 0 -1 -1 1 -2 -1 -4 1 1 0 1 -1 0 -1 0 1 1 1 0 -4 -2 -1 0 1 -1 -1 -1 -2 -2 2 0 0 -1 0 -1 -1 0 2 -1 0 1 -2 -4 -1 0 1 1 -1 0 -2 -2 2 0 -1 -1 1 0 -1 1 1 -1 0 2 -1 -1 -4 1 0 0 -2 -1 -1 0 -2 2 1 0 1 0 1 0 -1 2 0 0 0 0 1 -4 1 -1 1 2 -1 0 1 -2 -1 -1 -2 1 2 -1 0 -1 -2 -1 1 1 0 1 -4 1 0 -3 -1 -3 -2 2 2 2 0 2 0 2 -1 1 1 -1 -1 1 0 -1 1 -4 -1 0 0 2 1 1 1 0 1 1 0 1 0 -1 0 1 -1 -1 -2 1 0 -1 -4 -2 -2 1 2 -2 -2 -1 -3 1 2 -1 -1 -2 -2 -2 -1 0 -1 2 -3 0 -2 -6 -4 -6 1 0 -1 -2 -1 -1 2 -2 -1 0 -2 -1 -2 -2 -1 -1 -1 0 -2 -4 -6 -7 3 -4 -5 -4 -4 -4 2 -4 1 0 -3 -4 -2 -2 0 0 -3 2 1 -6 -7 -16 -- embedding X (19x22), X G X^T = -W512' 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 0 -- complement basis K (3x22), K G K^T = diag(2, 2, 128), glue index 512 0 0 -1 0 0 0 0 0 -1 -1 0 -1 -1 0 0 0 -1 0 -1 2 0 0 -1 0 0 0 0 -1 0 -1 -1 -1 0 -1 -1 -1 -1 -1 -1 0 -1 0 2 0 -58 -26 -106 -43 -55 -96 -22 -3 -8 -2 -25 -102 -53 -61 -12 -61 -76 -15 -56 0 0 128 == gluing of W1024(-1) into Gamma_(3,19): overlattice Gram G (22x22, even, det -1, inertia (3, 19, 0)) -4 1 1 -2 -2 -2 -2 -2 -2 1 2 -2 -2 1 2 -2 2 -2 -2 -6 -5 -8 1 -4 -2 0 2 -1 -1 2 1 1 -2 0 1 -2 -2 0 -2 2 0 1 0 -2 1 -2 -4 -1 1 0 0 2 2 0 -2 -1 0 -2 0 1 -1 2 -1 -1 -1 -4 -2 0 -1 -4 -2 -2 -2 0 -1 0 0 -1 -2 1 2 -1 1 -1 -2 -6 -5 -10 -2 2 1 -2 -4 0 -1 -2 -1 -1 1 0 -1 2 2 0 2 -1 -1 -3 -2 -4 -2 -1 0 -2 0 -4 -1 0 -2 2 0 -2 -2 0 0 -1 0 -1 -1 -5 -5 -7 -2 -1 0 -2 -1 -1 -4 -1 -1 1 1 0 0 1 1 -2 0 -1 -1 -3 -3 -7 -2 2 2 0 -2 0 -1 -4 -2 1 2 0 -1 2 1 0 2 -1 -1 -1 -2 -1 -2 1 2 -1 -1 -2 -1 -2 -4 2 2 -1 -1 1 0 -1 1 -2 -1 -4 -4 -3 1 1 0 0 -1 2 1 1 2 -4 0 1 1 1 1 0 1 0 1 2 3 3 2 -2 -2 0 1 0 1 2 2 0 -4 0 0 -1 -1 2 -2 2 1 2 1 0 -2 0 -1 -1 0 -2 0 0 -1 1 0 -4 -2 -1 1 -1 1 -1 -1 -6 -5 -6 -2 1 0 -2 -1 -2 0 -1 -1 1 0 -2 -4 1 2 0 1 -1 -2 -5 -5 -7 1 -2 -2 1 2 0 1 2 1 1 -1 -1 1 -4 -2 0 -1 2 0 0 1 1 2 -2 0 2 2 0 1 1 0 1 -1 1 2 -2 -4 1 -2 2 1 4 3 5 -2 0 1 -1 0 -1 -2 0 -1 0 2 -1 0 0 1 -4 1 -2 0 -4 -2 -4 2 -2 -1 1 2 0 0 2 1 1 -2 1 1 -1 -2 1 -4 1 1 3 2 1 -2 2 2 -1 -1 -1 -1 -1 -2 0 2 -1 -1 2 2 -2 1 -4 0 -4 -3 -3 -2 0 -1 -2 -1 -1 -1 -1 -1 1 1 -1 -2 0 1 0 1 0 -4 -4 -4 -8 -6 1 -1 -6 -3 -5 -3 -1 -4 2 2 -6 -5 0 4 -4 3 -4 -4 -16 -13 -20 -5 0 -1 -5 -2 -5 -3 -2 -4 3 1 -5 -5 1 3 -2 2 -3 -4 -13 -12 -18 -8 -2 -4 -10 -4 -7 -7 -1 -3 3 0 -6 -7 1 5 -4 1 -3 -8 -20 -18 -36 -- embedding X (19x22), X G X^T = -W1024 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 0 -- complement basis K (3x22), K G K^T = diag(2, 2, 256), glue index 1024 0 0 -1 -1 -1 0 0 0 -1 0 0 -1 -1 -1 0 -1 0 -1 0 2 0 0 0 -1 -1 -1 0 0 0 -1 -1 0 0 -1 -1 0 0 0 0 -1 0 0 2 0 -177 -39 -246 -208 -73 -64 -53 -212 -30 -132 -200 -29 -112 -43 -50 -221 -227 -136 -239 0 0 256