/* 1. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 -3 0 -2 0 -2 0 -2 0 -3 -3 3 0 -3 -3 1 -3 -2 -2 1 -1 3 -2 1 3 2 3] [ 4 8 0 -3 -1 0 -1 0 -1 0 0 0 3 -3 0 0 -1 0 -1 -1 -1 -2 3 -1 2 0 -2 0] [-3 0 8 -4 3 0 3 0 3 0 1 1 1 -2 1 1 -2 1 1 3 2 3 1 3 3 -2 -3 0] [ 0 -3 -4 8 0 0 0 0 0 0 1 -2 -2 1 1 -2 1 -2 1 -3 -1 0 -2 0 -3 1 0 0] [-2 -1 3 0 6 2 3 2 0 2 0 2 0 0 -1 -1 -2 0 -1 1 0 0 2 1 -1 0 0 2] [ 0 0 0 0 2 6 2 0 -3 3 -2 2 -2 2 -3 -2 -2 -2 -3 -2 2 0 1 1 0 -2 0 -1] [-2 -1 3 0 3 2 6 1 2 3 0 1 0 0 -2 -1 -2 0 1 1 0 0 1 0 0 -2 -1 1] [ 0 0 0 0 2 0 1 6 1 1 0 0 -1 1 1 -2 2 0 2 2 -2 0 2 -3 -3 1 0 0] [-2 -1 3 0 0 -3 2 1 8 1 0 -2 2 -2 4 1 -1 1 3 1 -2 0 -2 1 0 0 -1 2] [ 0 0 0 0 2 3 3 1 1 6 -2 2 0 0 -2 -1 -1 -2 -2 0 0 -2 0 0 -1 -2 1 1] [-3 0 1 1 0 -2 0 0 0 -2 6 0 -1 -1 2 2 1 1 2 2 -2 2 -1 0 -1 0 -2 -3] [-3 0 1 -2 2 2 1 0 -2 2 0 6 -1 -1 -1 2 -1 2 -1 1 1 -1 0 0 0 -3 0 -1] [ 3 3 1 -2 0 -2 0 -1 2 0 -1 -1 6 -3 -1 0 -1 1 0 0 0 -2 1 -1 1 1 0 3] [ 0 -3 -2 1 0 2 0 1 -2 0 -1 -1 -3 6 -1 -1 0 -1 0 0 0 0 0 -1 -2 1 3 -1] [-3 0 1 1 -1 -3 -2 1 4 -2 2 -1 -1 -1 8 2 0 1 3 0 -2 0 -3 2 0 0 -3 -2] [-3 0 1 -2 -1 -2 -1 -2 1 -1 2 2 0 -1 2 6 0 2 0 1 0 0 -1 1 0 -2 1 -1] [ 1 -1 -2 1 -2 -2 -2 2 -1 -1 1 -1 -1 0 0 0 6 0 1 2 0 1 0 -2 -2 0 1 -1] [-3 0 1 -2 0 -2 0 0 1 -2 1 2 1 -1 1 2 0 6 2 2 -1 -1 -1 -1 0 -1 0 0] [-2 -1 1 1 -1 -3 1 2 3 -2 2 -1 0 0 3 0 1 2 6 2 -2 0 -1 -2 -1 0 -2 -2] [-2 -1 3 -3 1 -2 1 2 1 0 2 1 0 0 0 1 2 2 2 6 -1 1 0 -1 0 0 0 -1] [ 1 -1 2 -1 0 2 0 -2 -2 0 -2 1 0 0 -2 0 0 -1 -2 -1 6 2 1 2 2 -2 0 0] [-1 -2 3 0 0 0 0 0 0 -2 2 -1 -2 0 0 0 1 -1 0 1 2 6 0 2 1 0 -1 -1] [ 3 3 1 -2 2 1 1 2 -2 0 -1 0 1 0 -3 -1 0 -1 -1 0 1 0 6 -2 0 1 1 2] [-2 -1 3 0 1 1 0 -3 1 0 0 0 -1 -1 2 1 -2 -1 -2 -1 2 2 -2 6 3 -1 -2 0] [ 1 2 3 -3 -1 0 0 -3 0 -1 -1 0 1 -2 0 0 -2 0 -1 0 2 1 0 3 6 0 -2 1] [ 3 0 -2 1 0 -2 -2 1 0 -2 0 -3 1 1 0 -2 0 -1 0 0 -2 0 1 -1 0 6 2 3] [ 2 -2 -3 0 0 0 -1 0 -1 1 -2 0 0 3 -3 1 1 0 -2 0 0 -1 1 -2 -2 2 8 4] [ 3 0 0 0 2 -1 1 0 2 1 -3 -1 3 -1 -2 -1 -1 0 -2 -1 0 -1 2 0 1 3 4 8] |Aut| = [ <2, 9>, <3, 7>, <7, 1>, <13, 1> ] Modular = true LatDB = Beis14 2. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 -3 0 -4 4 4 0 3 0 -1 1 -1 2 -2 1 -1 -1 -2 2 -3 -1 3 2 3 -2 0 3] [ 4 8 0 -3 -5 5 2 3 3 -3 -2 -1 1 1 -4 2 -2 -2 2 1 0 1 3 1 3 2 -3 0] [-3 0 8 -4 2 -2 0 2 0 -2 0 2 -2 0 -2 0 0 0 -1 1 3 2 2 -4 0 2 -4 -1] [ 0 -3 -4 8 2 -2 0 -1 -3 1 3 -1 1 0 1 -3 3 3 2 1 -3 -1 -1 2 -3 -4 2 -1] [-4 -5 2 2 8 -5 -1 -2 -2 3 2 1 -2 1 1 -1 2 0 -1 -1 0 2 -1 -1 -3 0 0 -2] [ 4 5 -2 -2 -5 8 3 0 1 -2 -2 1 0 1 -2 3 0 -2 1 2 -1 -2 0 2 4 -1 -2 0] [ 4 2 0 0 -1 3 6 -1 2 0 0 2 -2 2 -3 1 1 -1 -2 1 -1 0 3 2 3 -2 -2 1] [ 0 3 2 -1 -2 0 -1 6 -1 -2 1 -2 1 -2 -3 -1 -2 2 1 0 0 0 3 -2 1 1 -2 1] [ 3 3 0 -3 -2 1 2 -1 6 -1 -3 1 -1 2 0 1 -2 -3 -1 -1 0 2 2 1 1 1 0 2] [ 0 -3 -2 1 3 -2 0 -2 -1 8 3 1 1 2 -1 -2 -1 -1 -2 -2 1 -2 0 0 0 -2 4 0] [-1 -2 0 3 2 -2 0 1 -3 3 6 -1 2 1 -2 -3 1 3 1 0 -1 -1 1 0 -1 -2 2 0] [ 1 -1 2 -1 1 1 2 -2 1 1 -1 6 -2 2 -1 0 0 -2 -3 2 1 -1 1 0 1 -3 0 1] [-1 1 -2 1 -2 0 -2 1 -1 1 2 -2 6 0 -1 -2 -2 1 2 0 1 0 0 0 -1 0 2 -1] [ 2 1 0 0 1 1 2 -2 2 2 1 2 0 6 -1 0 0 -2 1 0 0 0 0 1 1 -1 0 -1] [-2 -4 -2 1 1 -2 -3 -3 0 -1 -2 -1 -1 -1 8 0 2 1 1 -1 -1 0 -4 1 -3 0 3 0] [ 1 2 0 -3 -1 3 1 -1 1 -2 -3 0 -2 0 0 6 0 -2 0 -1 0 1 -1 0 2 2 -3 -1] [-1 -2 0 3 2 0 1 -2 -2 -1 1 0 -2 0 2 0 6 1 2 1 -1 0 -1 1 -2 -2 0 -2] [-1 -2 0 3 0 -2 -1 2 -3 -1 3 -2 1 -2 1 -2 1 6 1 0 -1 -1 1 -1 -1 -2 0 1] [-2 2 -1 2 -1 1 -2 1 -1 -2 1 -3 2 1 1 0 2 1 8 -1 0 1 -2 1 -2 0 -1 -3] [ 2 1 1 1 -1 2 1 0 -1 -2 0 2 0 0 -1 -1 1 0 -1 6 -1 0 1 0 0 -1 -1 0] [-3 0 3 -3 0 -1 -1 0 0 1 -1 1 1 0 -1 0 -1 -1 0 -1 6 0 0 -2 1 2 -1 -1] [-1 1 2 -1 2 -2 0 0 2 -2 -1 -1 0 0 0 1 0 -1 1 0 0 6 2 0 -2 2 -2 -1] [ 3 3 2 -1 -1 0 3 3 2 0 1 1 0 0 -4 -1 -1 1 -2 1 0 2 8 -1 1 -2 -1 2] [ 2 1 -4 2 -1 2 2 -2 1 0 0 0 0 1 1 0 1 -1 1 0 -2 0 -1 6 1 -1 2 1] [ 3 3 0 -3 -3 4 3 1 1 0 -1 1 -1 1 -3 2 -2 -1 -2 0 1 -2 1 1 6 1 -2 2] [-2 2 2 -4 0 -1 -2 1 1 -2 -2 -3 0 -1 0 2 -2 -2 0 -1 2 2 -2 -1 1 8 -2 -1] [ 0 -3 -4 2 0 -2 -2 -2 0 4 2 0 2 0 3 -3 0 0 -1 -1 -1 -2 -1 2 -2 -2 8 2] [ 3 0 -1 -1 -2 0 1 1 2 0 0 1 -1 -1 0 -1 -2 1 -3 0 -1 -1 2 1 2 -1 2 6] |Aut| = [ <2, 1>, <3, 1>, <13, 1> ] Modular = true LatDB = - 3. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 -3 0 0 0 0 0 -4 0 -4 0 0 0 -4 0 1 1 4 -2 -3 -2 3 0 1 -3 0 1] [ 4 8 0 -3 0 0 0 0 -2 0 -2 0 0 0 -2 0 2 2 5 -1 -3 -1 0 -3 -1 -3 3 -1] [-3 0 8 -4 0 0 0 0 -1 0 -1 0 0 0 -1 0 -3 -3 -2 3 -1 3 1 0 2 1 0 1] [ 0 -3 -4 8 0 0 0 0 -1 0 -1 0 0 0 -1 0 0 0 -2 -3 2 -3 1 3 -1 1 -3 -2] [ 0 0 0 0 6 2 -3 -3 -2 2 -3 0 3 -3 1 -3 0 2 -1 -1 2 0 -1 -2 -2 3 -2 1] [ 0 0 0 0 2 6 0 0 0 3 -3 0 -1 -3 2 -1 2 1 -1 -2 -1 1 2 -1 -3 -1 1 3] [ 0 0 0 0 -3 0 6 1 1 -2 2 -2 -4 2 -1 2 0 -1 2 2 -3 -1 0 3 2 -4 2 -1] [ 0 0 0 0 -3 0 1 6 3 -1 3 2 -1 1 0 3 0 -3 2 -1 -1 2 2 -1 1 0 3 -1] [-4 -2 -1 -1 -2 0 1 3 8 0 6 2 -2 0 5 2 2 -1 0 1 2 2 -3 -1 -1 0 2 0] [ 0 0 0 0 2 3 -2 -1 0 6 -4 0 -1 -2 3 -3 3 2 -3 -3 2 2 2 -2 -2 1 -1 2] [-4 -2 -1 -1 -3 -3 2 3 6 -4 12 2 0 3 2 4 0 -1 1 3 -1 0 -3 0 0 -1 1 -2] [ 0 0 0 0 0 0 -2 2 2 0 2 6 0 -2 0 0 -1 -2 1 -1 -1 2 -1 -1 -1 0 -2 2] [ 0 0 0 0 3 -1 -4 -1 -2 -1 0 0 8 -2 0 -2 -2 0 0 -1 3 0 0 -2 -2 3 0 -1] [ 0 0 0 0 -3 -3 2 1 0 -2 3 -2 -2 6 -1 2 0 0 0 2 -1 -1 0 1 2 0 1 -2] [-4 -2 -1 -1 1 2 -1 0 5 3 2 0 0 -1 8 -1 3 2 -2 -1 3 3 -3 -2 -3 2 2 1] [ 0 0 0 0 -3 -1 2 3 2 -3 4 0 -2 2 -1 6 0 -1 1 2 -3 -1 0 1 2 -2 1 -2] [ 1 2 -3 0 0 2 0 0 2 3 0 -1 -2 0 3 0 6 3 0 -2 0 -1 0 -2 -2 -1 2 0] [ 1 2 -3 0 2 1 -1 -3 -1 2 -1 -2 0 0 2 -1 3 6 0 -1 0 -2 -1 -2 -2 -1 0 0] [ 4 5 -2 -2 -1 -1 2 2 0 -3 1 1 0 0 -2 1 0 0 8 0 -3 -1 -1 -1 1 -3 4 -1] [-2 -1 3 -3 -1 -2 2 -1 1 -3 3 -1 -1 2 -1 2 -2 -1 0 6 -1 0 -2 1 3 -1 0 0] [-3 -3 -1 2 2 -1 -3 -1 2 2 -1 -1 3 -1 3 -3 0 0 -3 -1 8 1 -1 -1 -1 5 -1 -1] [-2 -1 3 -3 0 1 -1 2 2 2 0 2 0 -1 3 -1 -1 -2 -1 0 1 6 0 -2 0 2 1 2] [ 3 0 1 1 -1 2 0 2 -3 2 -3 -1 0 0 -3 0 0 -1 -1 -2 -1 0 8 0 1 -1 0 1] [ 0 -3 0 3 -2 -1 3 -1 -1 -2 0 -1 -2 1 -2 1 -2 -2 -1 1 -1 -2 0 6 2 -2 -2 0] [ 1 -1 2 -1 -2 -3 2 1 -1 -2 0 -1 -2 2 -3 2 -2 -2 1 3 -1 0 1 2 6 0 0 -1] [-3 -3 1 1 3 -1 -4 0 0 1 -1 0 3 0 2 -2 -1 -1 -3 -1 5 2 -1 -2 0 8 -1 -1] [ 0 3 0 -3 -2 1 2 3 2 -1 1 -2 0 1 2 1 2 0 4 0 -1 1 0 -2 0 -1 8 -1] [ 1 -1 1 -2 1 3 -1 -1 0 2 -2 2 -1 -2 1 -2 0 0 -1 0 -1 2 1 0 -1 -1 -1 6] |Aut| = [ <2, 1>, <3, 1>, <13, 1> ] Modular = true LatDB = - 4. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Inner Product Matrix: [ 8 4 -3 0 0 0 0 0 -3 -1 -1 0 2 0 -2 0 -3 -3 4 4 -2 1 -3 -4 3 -1 3 -2] [ 4 8 0 -3 -3 0 0 3 0 1 1 0 1 0 -1 0 0 0 -1 2 2 2 -3 -2 0 1 3 -4] [-3 0 8 -4 1 0 0 -1 0 4 4 0 -4 0 4 0 0 0 -4 -3 2 -2 2 -1 -1 3 -4 -2] [ 0 -3 -4 8 1 0 0 -1 0 -2 -2 0 2 0 -2 0 0 0 2 3 -4 -2 2 2 2 -3 2 4] [ 0 -3 1 1 6 -2 2 -2 0 1 -1 1 0 -2 1 0 0 -1 3 -1 -3 0 1 1 -1 1 0 2] [ 0 0 0 0 -2 6 -1 0 -2 0 2 -1 0 2 -2 1 1 -1 -1 0 2 0 -2 -3 0 -2 1 0] [ 0 0 0 0 2 -1 6 2 -1 -1 0 -1 1 -2 -1 -2 2 -1 2 2 1 0 1 2 0 2 2 -2] [ 0 3 -1 -1 -2 0 2 6 -1 -1 1 1 2 -2 -2 0 1 0 0 1 1 2 0 2 0 0 3 -3] [-3 0 0 0 0 -2 -1 -1 6 0 -2 1 0 1 1 -1 1 3 -2 -3 1 0 1 2 -3 0 0 2] [-1 1 4 -2 1 0 -1 -1 0 6 3 1 -1 0 1 2 -1 -1 -1 -2 -1 -1 -1 -2 -1 1 -3 0] [-1 1 4 -2 -1 2 0 1 -2 3 6 1 -2 1 0 0 0 -2 -2 -1 2 -1 0 -1 0 1 -2 -2] [ 0 0 0 0 1 -1 -1 1 1 1 1 6 2 -1 -2 2 -2 1 2 -1 -3 -1 -1 0 0 -2 1 0] [ 2 1 -4 2 0 0 1 2 0 -1 -2 2 6 -1 -4 1 -1 0 3 1 -2 0 -2 -1 0 -2 4 0] [ 0 0 0 0 -2 2 -2 -2 1 0 1 -1 -1 6 1 0 0 0 -2 -2 2 0 0 -2 1 -1 -2 2] [-2 -1 4 -2 1 -2 -1 -2 1 1 0 -2 -4 1 8 -2 0 2 -3 -3 2 1 3 0 1 4 -3 2] [ 0 0 0 0 0 1 -2 0 -1 2 0 2 1 0 -2 6 0 0 0 0 -3 -1 -2 -2 0 -3 -1 1] [-3 0 0 0 0 1 2 1 1 -1 0 -2 -1 0 0 0 6 1 -2 0 3 2 1 2 -2 1 1 0] [-3 0 0 0 -1 -1 -1 0 3 -1 -2 1 0 0 2 0 1 6 -2 -2 1 0 0 2 -1 1 1 1] [ 4 -1 -4 2 3 -1 2 0 -2 -1 -2 2 3 -2 -3 0 -2 -2 8 2 -4 1 -2 0 2 -2 3 1] [ 4 2 -3 3 -1 0 2 1 -3 -2 -1 -1 1 -2 -3 0 0 -2 2 8 -2 -1 0 0 3 -1 2 -2] [-2 2 2 -4 -3 2 1 1 1 -1 2 -3 -2 2 2 -3 3 1 -4 -2 8 2 0 0 -2 3 0 -2] [ 1 2 -2 -2 0 0 0 2 0 -1 -1 -1 0 0 1 -1 2 0 1 -1 2 6 -1 1 -1 1 2 0] [-3 -3 2 2 1 -2 1 0 1 -1 0 -1 -2 0 3 -2 1 0 -2 0 0 -1 6 3 1 1 -2 1] [-4 -2 -1 2 1 -3 2 2 2 -2 -1 0 -1 -2 0 -2 2 2 0 0 0 1 3 8 -2 1 0 1] [ 3 0 -1 2 -1 0 0 0 -3 -1 0 0 0 1 1 0 -2 -1 2 3 -2 -1 1 -2 6 -1 0 0] [-1 1 3 -3 1 -2 2 0 0 1 1 -2 -2 -1 4 -3 1 1 -2 -1 3 1 1 1 -1 6 -1 -2] [ 3 3 -4 2 0 1 2 3 0 -3 -2 1 4 -2 -3 -1 1 1 3 2 0 2 -2 0 0 -1 8 -1] [-2 -4 -2 4 2 0 -2 -3 2 0 -2 0 0 2 2 1 0 1 1 -2 -2 0 1 1 0 -2 -1 8] |Aut| = [ <2, 1>, <3, 1>, <13, 1> ] Modular = true LatDB = - 5. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Inner Product Matrix: [ 8 4 -3 0 0 0 -3 -4 3 -4 3 1 -4 -4 2 -3 2 3 -1 2 0 -1 4 1 1 0 -4 -4] [ 4 8 0 -3 0 0 -3 -2 3 -2 3 -1 -2 -2 -2 -3 -2 3 -2 4 0 1 -1 2 2 0 1 -2] [-3 0 8 -4 0 0 -1 3 1 1 -2 -3 3 2 -2 -1 -4 -4 -3 1 -3 3 -5 -2 -1 -1 1 -1] [ 0 -3 -4 8 0 0 2 0 -2 -2 -2 0 0 2 4 2 5 -1 3 -2 3 -3 1 1 2 -1 -2 2] [ 0 0 0 0 6 2 -3 0 3 2 -3 -1 1 3 -2 -2 -2 2 2 -2 -2 -3 -2 -2 -1 2 -3 0] [ 0 0 0 0 2 6 -3 1 1 -1 -3 0 3 1 -1 -3 0 -2 0 -1 -3 -2 2 -1 1 -1 -1 0] [-3 -3 -1 2 -3 -3 8 -1 -5 1 2 2 -1 1 3 5 3 -2 0 -2 3 1 -1 2 -2 -2 3 3] [-4 -2 3 0 0 1 -1 6 -1 2 -2 -2 4 1 -2 0 -1 -3 -1 0 -2 0 -2 -2 1 -1 1 0] [ 3 3 1 -2 3 1 -5 -1 8 1 -2 -2 1 0 -3 -2 -3 4 0 2 -2 -1 0 -3 -1 3 -4 -4] [-4 -2 1 -2 2 -1 1 2 1 8 -2 1 3 3 -4 1 -3 2 2 -2 -1 0 -1 -3 -3 3 1 2] [ 3 3 -2 -2 -3 -3 2 -2 -2 -2 8 2 -5 -5 2 0 2 2 -3 3 1 1 1 2 1 -1 1 -1] [ 1 -1 -3 0 -1 0 2 -2 -2 1 2 6 -1 -2 2 1 3 0 0 -1 1 1 4 0 0 1 0 0] [-4 -2 3 0 1 3 -1 4 1 3 -5 -1 8 4 -3 -1 -2 -4 0 -2 -3 1 0 -2 -1 -1 1 0] [-4 -2 2 2 3 1 1 1 0 3 -5 -2 4 8 -2 0 -2 -1 3 -3 0 -1 -4 0 -2 0 1 4] [ 2 -2 -2 4 -2 -1 3 -2 -3 -4 2 2 -3 -2 8 1 5 -3 0 0 2 0 1 2 2 -1 -2 0] [-3 -3 -1 2 -2 -3 5 0 -2 1 0 1 -1 0 1 8 1 0 0 0 4 0 -1 1 -1 1 2 2] [ 2 -2 -4 5 -2 0 3 -1 -3 -3 2 3 -2 -2 5 1 8 -1 0 -1 2 -1 3 1 2 -2 -2 -1] [ 3 3 -4 -1 2 -2 -2 -3 4 2 2 0 -4 -1 -3 0 -1 10 2 1 2 -2 1 0 -1 4 -2 0] [-1 -2 -3 3 2 0 0 -1 0 2 -3 0 0 3 0 0 0 2 6 -2 2 -2 0 0 -1 2 0 3] [ 2 4 1 -2 -2 -1 -2 0 2 -2 3 -1 -2 -3 0 0 -1 1 -2 6 1 1 -1 1 2 1 1 -2] [ 0 0 -3 3 -2 -3 3 -2 -2 -1 1 1 -3 0 2 4 2 2 2 1 6 0 0 3 1 1 2 2] [-1 1 3 -3 -3 -2 1 0 -1 0 1 1 1 -1 0 0 -1 -2 -2 1 0 6 -1 1 0 0 3 -1] [ 4 -1 -5 1 -2 2 -1 -2 0 -1 1 4 0 -4 1 -1 3 1 0 -1 0 -1 10 0 0 0 -2 -2] [ 1 2 -2 1 -2 -1 2 -2 -3 -3 2 0 -2 0 2 1 1 0 0 1 3 1 0 6 1 -1 3 2] [ 1 2 -1 2 -1 1 -2 1 -1 -3 1 0 -1 -2 2 -1 2 -1 -1 2 1 0 0 1 6 0 0 0] [ 0 0 -1 -1 2 -1 -2 -1 3 3 -1 1 -1 0 -1 1 -2 4 2 1 1 0 0 -1 0 6 -1 0] [-4 1 1 -2 -3 -1 3 1 -4 1 1 0 1 1 -2 2 -2 -2 0 1 2 3 -2 3 0 -1 8 3] [-4 -2 -1 2 0 0 3 0 -4 2 -1 0 0 4 0 2 -1 0 3 -2 2 -1 -2 2 0 0 3 8] |Aut| = [ <2, 1>, <3, 1>, <13, 1> ] Modular = true LatDB = - 6. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 3 2 -1 3 2 -2 0 4 0 -4 0 2 -3 -2 -4 -4 4 2 2 -4 -4 4 3 -2 -2 -2] [ 4 8 0 4 1 0 -2 -4 0 2 3 -2 0 4 0 2 -2 -2 -1 -2 1 -2 -2 5 0 -4 2 2] [ 3 0 6 -2 1 2 3 1 -2 1 0 -2 2 -1 -3 0 -1 0 3 3 3 -1 -3 3 3 0 -2 -1] [ 2 4 -2 8 -2 2 0 -2 2 3 0 1 1 2 -1 2 0 -4 0 0 0 0 2 2 1 0 2 0] [-1 1 1 -2 6 -3 0 0 -2 -1 3 0 2 0 2 2 1 2 0 0 0 1 -1 2 -2 0 1 1] [ 3 0 2 2 -3 6 3 1 2 3 -1 0 1 -1 -2 -2 0 -2 2 1 0 0 -1 2 2 1 0 -1] [ 2 -2 3 0 0 3 6 3 0 2 -1 -1 3 -3 -3 -1 0 -2 4 2 0 1 -1 0 1 2 -1 -1] [-2 -4 1 -2 0 1 3 6 -1 -1 -1 2 0 -2 0 0 1 1 2 1 -1 2 1 -1 1 3 -1 0] [ 0 0 -2 2 -2 2 0 -1 6 0 -1 0 0 -1 0 -1 1 -1 0 -2 -3 1 0 -1 -1 -1 3 -1] [ 4 2 1 3 -1 3 2 -1 0 6 1 -1 0 1 -2 -2 -2 -3 3 1 1 -2 -2 1 2 -1 0 -1] [ 0 3 0 0 3 -1 -1 -1 -1 1 6 1 1 2 2 0 -1 1 -2 -1 0 1 -1 1 -2 -3 2 3] [-4 -2 -2 1 0 0 -1 2 0 -1 1 6 0 0 3 1 2 2 -3 0 -2 3 3 -2 -1 2 1 2] [ 0 0 2 1 2 1 3 0 0 0 1 0 6 -2 -1 1 2 0 1 1 0 2 1 2 -1 2 1 0] [ 2 4 -1 2 0 -1 -3 -2 -1 1 2 0 -2 6 0 1 -3 -1 -2 -1 0 -2 -1 2 1 -3 0 0] [-3 0 -3 -1 2 -2 -3 0 0 -2 2 3 -1 0 6 0 2 3 -3 -2 -2 1 2 0 -3 1 1 2] [-2 2 0 2 2 -2 -1 0 -1 -2 0 1 1 1 0 6 1 0 -2 -1 1 2 1 2 0 0 1 1] [-4 -2 -1 0 1 0 0 1 1 -2 -1 2 2 -3 2 1 6 2 -1 0 -1 3 3 0 -2 4 2 1] [-4 -2 0 -4 2 -2 -2 1 -1 -3 1 2 0 -1 3 0 2 6 -2 -1 -1 1 1 0 -1 1 1 1] [ 4 -1 3 0 0 2 4 2 0 3 -2 -3 1 -2 -3 -2 -1 -2 8 3 1 -2 -2 2 3 2 -2 -3] [ 2 -2 3 0 0 1 2 1 -2 1 -1 0 1 -1 -2 -1 0 -1 3 6 3 -1 0 0 3 2 -3 -2] [ 2 1 3 0 0 0 0 -1 -3 1 0 -2 0 0 -2 1 -1 -1 1 3 6 -1 -1 2 3 0 -2 -1] [-4 -2 -1 0 1 0 1 2 1 -2 1 3 2 -2 1 2 3 1 -2 -1 -1 6 2 -1 -2 2 2 2] [-4 -2 -3 2 -1 -1 -1 1 0 -2 -1 3 1 -1 2 1 3 1 -2 0 -1 2 6 -2 -1 3 1 1] [ 4 5 3 2 2 2 0 -1 -1 1 1 -2 2 2 0 2 0 0 2 0 2 -1 -2 10 2 1 0 -1] [ 3 0 3 1 -2 2 1 1 -1 2 -2 -1 -1 1 -3 0 -2 -1 3 3 3 -2 -1 2 6 0 -2 -3] [-2 -4 0 0 0 1 2 3 -1 -1 -3 2 2 -3 1 0 4 1 2 2 0 2 3 1 0 8 -1 -1] [-2 2 -2 2 1 0 -1 -1 3 0 2 1 1 0 1 1 2 1 -2 -3 -2 2 1 0 -2 -1 6 2] [-2 2 -1 0 1 -1 -1 0 -1 -1 3 2 0 0 2 1 1 1 -3 -2 -1 2 1 -1 -3 -1 2 6] |Aut| = [ <2, 1>, <13, 1> ] Modular = true LatDB = - 7. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 -3 0 0 0 0 0 1 0 1 1 1 -1 0 -1 -1 0 0 3 -4 -1 3 -1 1 3 4 3] [ 4 8 0 -3 0 0 0 0 -1 0 -1 -1 -1 1 0 -2 1 0 0 3 -2 -2 0 1 2 0 -1 0] [-3 0 8 -4 0 0 0 0 1 0 1 1 1 -1 0 3 -1 0 2 1 -1 -3 1 -1 3 -3 -5 1] [ 0 -3 -4 8 0 0 0 0 1 0 1 1 1 -1 0 -3 -1 0 -1 -2 -1 0 -2 -1 0 0 1 -2] [ 0 0 0 0 6 -1 -2 -3 -2 0 1 2 -3 2 -1 -2 -2 -1 -2 -2 2 2 0 3 -2 -2 -2 -1] [ 0 0 0 0 -1 6 0 0 -1 2 2 1 3 0 -1 -2 2 -2 3 0 -3 -3 -1 -1 -2 1 -1 1] [ 0 0 0 0 -2 0 6 -1 3 1 2 -3 0 0 1 3 2 3 0 -1 1 -2 0 0 -1 1 2 2] [ 0 0 0 0 -3 0 -1 6 -1 -1 -3 0 0 0 2 0 0 -1 1 3 -3 0 1 -2 1 2 0 1] [ 1 -1 1 1 -2 -1 3 -1 6 -1 3 0 2 -1 1 2 0 2 0 1 -1 -1 1 -1 2 1 2 2] [ 0 0 0 0 0 2 1 -1 -1 6 -1 -1 2 -1 -2 -2 0 -2 3 -1 -2 -3 1 0 -2 0 2 0] [ 1 -1 1 1 1 2 2 -3 3 -1 8 2 2 1 0 1 0 0 1 -1 -1 -1 1 -1 1 1 -2 2] [ 1 -1 1 1 2 1 -3 0 0 -1 2 6 0 -1 0 -2 -3 -3 1 1 -2 0 2 0 1 -1 -2 1] [ 1 -1 1 1 -3 3 0 0 2 2 2 0 8 -3 0 -1 0 -1 4 2 -3 -4 0 -3 2 1 2 1] [-1 1 -1 -1 2 0 0 0 -1 -1 1 -1 -3 6 1 0 2 0 -2 -1 1 3 0 1 -1 1 -2 -1] [ 0 0 0 0 -1 -1 1 2 1 -2 0 0 0 1 6 2 -1 2 -1 1 -1 1 1 1 0 0 1 0] [-1 -2 3 -3 -2 -2 3 0 2 -2 1 -2 -1 0 2 10 1 4 -1 0 2 2 2 -1 1 1 0 1] [-1 1 -1 -1 -2 2 2 0 0 0 0 -3 0 2 -1 1 6 1 -1 -1 1 -1 -2 0 0 2 -1 0] [ 0 0 0 0 -1 -2 3 -1 2 -2 0 -3 -1 0 2 4 1 6 -2 -1 2 1 -1 1 0 0 1 0] [ 0 0 2 -1 -2 3 0 1 0 3 1 1 4 -2 -1 -1 -1 -2 6 2 -3 -3 1 -2 0 1 0 1] [ 3 3 1 -2 -2 0 -1 3 1 -1 -1 1 2 -1 1 0 -1 -1 2 6 -3 -1 2 -1 2 2 1 2] [-4 -2 -1 -1 2 -3 1 -3 -1 -2 -1 -2 -3 1 -1 2 1 2 -3 -3 10 4 -3 3 -2 -2 0 -2] [-1 -2 -3 0 2 -3 -2 0 -1 -3 -1 0 -4 3 1 2 -1 1 -3 -1 4 8 0 2 -2 1 1 -2] [ 3 0 1 -2 0 -1 0 1 1 1 1 2 0 0 1 2 -2 -1 1 2 -3 0 6 -1 1 2 2 3] [-1 1 -1 -1 3 -1 0 -2 -1 0 -1 0 -3 1 1 -1 0 1 -2 -1 3 2 -1 6 -3 -1 0 -1] [ 1 2 3 0 -2 -2 -1 1 2 -2 1 1 2 -1 0 1 0 0 0 2 -2 -2 1 -3 8 -1 -3 0] [ 3 0 -3 0 -2 1 1 2 1 0 1 -1 1 1 0 1 2 0 1 2 -2 1 2 -1 -1 6 3 2] [ 4 -1 -5 1 -2 -1 2 0 2 2 -2 -2 2 -2 1 0 -1 1 0 1 0 1 2 0 -3 3 10 2] [ 3 0 1 -2 -1 1 2 1 2 0 2 1 1 -1 0 1 0 0 1 2 -2 -2 3 -1 0 2 2 6] |Aut| = [ <2, 1>, <13, 1> ] Modular = true LatDB = - 8. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 -3 0 0 0 0 0 0 0 0 0 0 0 3 3 -3 -3 1 -2 -2 3 4 0 0 -2 -1 -1] [ 4 8 0 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 -4 0 5 -3 0 -1 -2 1] [-3 0 8 -4 0 0 0 0 0 0 0 0 0 -3 0 -2 3 1 2 3 2 1 -2 -4 -1 1 -3 2] [ 0 -3 -4 8 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 -1 0 2 -2 -2 2 2 -2 3 -1] [ 0 0 0 0 6 -1 2 2 2 -2 3 -2 2 -2 -3 2 0 0 -1 2 -1 -1 1 -2 -3 1 -1 -2] [ 0 0 0 0 -1 6 1 1 2 3 2 3 1 1 -2 1 -1 -1 -2 0 -2 0 2 0 -1 -3 3 -2] [ 0 0 0 0 2 1 6 3 1 -1 3 0 3 1 -4 2 -1 2 1 0 -3 1 -1 0 -3 1 0 -1] [ 0 0 0 0 2 1 3 6 1 -1 3 1 0 -2 -4 1 -2 1 -2 1 -3 0 -1 -2 -3 1 0 0] [ 0 0 0 0 2 2 1 1 6 2 4 -1 0 0 -1 -1 -1 -2 -3 3 0 1 0 0 0 -2 0 -1] [ 0 0 0 0 -2 3 -1 -1 2 6 0 1 -2 1 0 0 -2 -2 -2 0 1 0 1 2 0 -1 3 1] [ 0 0 0 0 3 2 3 3 4 0 8 -2 0 0 -3 -1 0 0 -2 4 -1 1 1 -1 -1 -1 -1 -3] [ 0 0 0 0 -2 3 0 1 -1 1 -2 6 0 1 0 1 -1 1 -1 -1 -1 0 0 1 0 0 2 -1] [ 0 0 0 0 2 1 3 0 0 -2 0 0 6 0 -2 2 0 0 2 -2 -3 -1 0 0 -2 0 0 -1] [ 0 0 -3 0 -2 1 1 -2 0 1 0 1 0 6 0 0 1 1 0 -2 0 1 1 4 2 0 2 -2] [ 3 0 0 0 -3 -2 -4 -4 -1 0 -3 0 -2 0 8 -1 0 -2 1 -1 3 2 0 2 4 -1 -2 1] [ 3 0 -2 1 2 1 2 1 -1 0 -1 1 2 0 -1 6 -2 -1 0 -3 -2 0 2 0 -3 0 2 -1] [-3 0 3 -3 0 -1 -1 -2 -1 -2 0 -1 0 1 0 -2 6 1 1 1 1 0 0 -2 1 1 -2 -1] [-3 0 1 1 0 -1 2 1 -2 -2 0 1 0 1 -2 -1 1 6 2 2 0 -1 -2 0 0 2 0 0] [ 1 2 2 -1 -1 -2 1 -2 -3 -2 -2 -1 2 0 1 0 1 2 6 -1 0 1 0 -1 0 1 -2 1] [-2 2 3 0 2 0 0 1 3 0 4 -1 -2 -2 -1 -3 1 2 -1 8 1 -1 0 -3 1 -1 -2 0] [-2 -4 2 2 -1 -2 -3 -3 0 1 -1 -1 -3 0 3 -2 1 0 0 1 8 1 -3 1 3 0 0 0] [ 3 0 1 -2 -1 0 1 0 1 0 1 0 -1 1 2 0 0 -1 1 -1 1 6 0 0 0 0 -2 -1] [ 4 5 -2 -2 1 2 -1 -1 0 1 1 0 0 1 0 2 0 -2 0 0 -3 0 8 -2 -1 -2 0 -2] [ 0 -3 -4 2 -2 0 0 -2 0 2 -1 1 0 4 2 0 -2 0 -1 -3 1 0 -2 8 2 1 3 -1] [ 0 0 -1 2 -3 -1 -3 -3 0 0 -1 0 -2 2 4 -3 1 0 0 1 3 0 -1 2 6 -2 0 0] [-2 -1 1 -2 1 -3 1 1 -2 -1 -1 0 0 0 -1 0 1 2 1 -1 0 0 -2 1 -2 6 -1 1] [-1 -2 -3 3 -1 3 0 0 0 3 -1 2 0 2 -2 2 -2 0 -2 -2 0 -2 0 3 0 -1 6 -1] [-1 1 2 -1 -2 -2 -1 0 -1 1 -3 -1 -1 -2 1 -1 -1 0 1 0 0 -1 -2 -1 0 1 -1 6] |Aut| = [ <2, 1>, <13, 1> ] Modular = true LatDB = - 9. Standard Lattice of rank 28 and degree 28 Determinant: 4782969 Factored Determinant: 3^14 Minimum: 6 Kissing Number: 17472 Inner Product Matrix: [ 8 4 -3 0 2 0 0 -2 2 2 2 1 2 0 2 1 0 1 0 -2 1 -4 4 0 0 -3 -3 -4] [ 4 8 0 -3 1 0 0 -1 1 1 -2 2 1 3 1 -1 0 -1 -3 -1 2 -2 2 -3 3 0 -3 -5] [-3 0 8 -4 -3 0 0 3 -3 -3 -3 2 -3 4 -3 2 0 -3 0 -1 3 4 -2 -4 1 4 1 -2] [ 0 -3 -4 8 3 0 0 -3 0 3 3 -1 0 -5 0 -1 0 0 3 -1 0 -2 1 5 -2 -2 1 1] [ 2 1 -3 3 6 -1 2 -3 -1 2 2 0 0 -1 0 -1 -2 2 2 0 1 -1 1 2 -2 -2 0 -2] [ 0 0 0 0 -1 6 2 -1 0 -1 -2 -2 0 2 0 0 2 -2 2 -3 -1 2 1 -2 1 0 2 -1] [ 0 0 0 0 2 2 6 -1 -2 -2 -2 -1 1 1 -1 -1 -2 -1 3 -2 1 0 2 1 1 0 1 -3] [-2 -1 3 -3 -3 -1 -1 6 1 -1 -1 2 1 0 0 2 1 1 -1 1 0 0 -1 -2 1 3 -1 0] [ 2 1 -3 0 -1 0 -2 1 6 3 0 1 2 -3 3 1 2 1 -3 0 -3 -3 2 -1 2 -2 -2 2] [ 2 1 -3 3 2 -1 -2 -1 3 6 2 2 0 -2 1 1 0 2 0 0 -1 -3 2 0 -1 -2 -2 1] [ 2 -2 -3 3 2 -2 -2 -1 0 2 6 -1 1 -3 0 1 -1 3 2 2 0 -1 0 2 -3 -1 -1 2] [ 1 2 2 -1 0 -2 -1 2 1 2 -1 6 0 1 1 2 0 -1 -1 0 2 -2 0 -2 1 1 -1 -2] [ 2 1 -3 0 0 0 1 1 2 0 1 0 6 -3 3 0 1 2 -1 1 0 -2 1 1 2 -1 -2 -1] [ 0 3 4 -5 -1 2 1 0 -3 -2 -3 1 -3 10 -1 0 0 -3 -1 -2 2 2 0 -5 1 2 0 -3] [ 2 1 -3 0 0 0 -1 0 3 1 0 1 3 -1 6 1 3 0 -3 0 0 -3 0 0 2 -1 0 1] [ 1 -1 2 -1 -1 0 -1 2 1 1 1 2 0 0 1 6 0 0 0 0 1 1 -1 -2 0 1 1 1] [ 0 0 0 0 -2 2 -2 1 2 0 -1 0 1 0 3 0 6 -2 -2 -2 0 -1 0 -2 1 1 0 1] [ 1 -1 -3 0 2 -2 -1 1 1 2 3 -1 2 -3 0 0 -2 8 0 4 -3 0 0 2 -3 -2 -2 1] [ 0 -3 0 3 2 2 3 -1 -3 0 2 -1 -1 -1 -3 0 -2 0 8 -2 1 1 1 2 -3 0 2 -1] [-2 -1 -1 -1 0 -3 -2 1 0 0 2 0 1 -2 0 0 -2 4 -2 6 -2 1 -3 1 -1 0 0 3] [ 1 2 3 0 1 -1 1 0 -3 -1 0 2 0 2 0 1 0 -3 1 -2 6 0 0 -1 1 2 0 -4] [-4 -2 4 -2 -1 2 0 0 -3 -3 -1 -2 -2 2 -3 1 -1 0 1 1 0 8 -4 -2 -1 1 3 1] [ 4 2 -2 1 1 1 2 -1 2 2 0 0 1 0 0 -1 0 0 1 -3 0 -4 6 0 1 -2 -3 -3] [ 0 -3 -4 5 2 -2 1 -2 -1 0 2 -2 1 -5 0 -2 -2 2 2 1 -1 -2 0 8 -2 -2 1 1] [ 0 3 1 -2 -2 1 1 1 2 -1 -3 1 2 1 2 0 1 -3 -3 -1 1 -1 1 -2 6 1 -1 -2] [-3 0 4 -2 -2 0 0 3 -2 -2 -1 1 -1 2 -1 1 1 -2 0 0 2 1 -2 -2 1 6 1 0] [-3 -3 1 1 0 2 1 -1 -2 -2 -1 -1 -2 0 0 1 0 -2 2 0 0 3 -3 1 -1 1 6 2] [-4 -5 -2 1 -2 -1 -3 0 2 1 2 -2 -1 -3 1 1 1 1 -1 3 -4 1 -3 1 -2 0 2 10] |Aut| = [ <2, 1>, <13, 1> ] Modular = true LatDB = - */ // Data Liste:=[ PowerStructure(Lat) | LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, -2, 0, -2, 0, -2, 0, -3, -3, 3, 0, -3, -3, 1, -3, -2, -2, 1, -1, 3, -2, 1, 3, 2, 3, 4, 8, 0, -3, -1, 0, -1, 0, -1, 0, 0, 0, 3, -3, 0, 0, -1, 0, -1, -1, -1, -2, 3, -1, 2, 0, -2, 0, -3, 0, 8, -4, 3, 0, 3, 0, 3, 0, 1, 1, 1, -2, 1, 1, -2, 1, 1, 3, 2, 3, 1, 3, 3, -2, -3, 0, 0, -3, -4, 8, 0, 0, 0, 0, 0, 0, 1, -2, -2, 1, 1, -2, 1, -2, 1, -3, -1, 0, -2, 0, -3, 1, 0, 0, -2, -1, 3, 0, 6, 2, 3, 2, 0, 2, 0, 2, 0, 0, -1, -1, -2, 0, -1, 1, 0, 0, 2, 1, -1, 0, 0, 2, 0, 0, 0, 0, 2, 6, 2, 0, -3, 3, -2, 2, -2, 2, -3, -2, -2, -2, -3, -2, 2, 0, 1, 1, 0, -2, 0, -1, -2, -1, 3, 0, 3, 2, 6, 1, 2, 3, 0, 1, 0, 0, -2, -1, -2, 0, 1, 1, 0, 0, 1, 0, 0, -2, -1, 1, 0, 0, 0, 0, 2, 0, 1, 6, 1, 1, 0, 0, -1, 1, 1, -2, 2, 0, 2, 2, -2, 0, 2, -3, -3, 1, 0, 0, -2, -1, 3, 0, 0, -3, 2, 1, 8, 1, 0, -2, 2, -2, 4, 1, -1, 1, 3, 1, -2, 0, -2, 1, 0, 0, -1, 2, 0, 0, 0, 0, 2, 3, 3, 1, 1, 6, -2, 2, 0, 0, -2, -1, -1, -2, -2, 0, 0, -2, 0, 0, -1, -2, 1, 1, -3, 0, 1, 1, 0, -2, 0, 0, 0, -2, 6, 0, -1, -1, 2, 2, 1, 1, 2, 2, -2, 2, -1, 0, -1, 0, -2, -3, -3, 0, 1, -2, 2, 2, 1, 0, -2, 2, 0, 6, -1, -1, -1, 2, -1, 2, -1, 1, 1, -1, 0, 0, 0, -3, 0, -1, 3, 3, 1, -2, 0, -2, 0, -1, 2, 0, -1, -1, 6, -3, -1, 0, -1, 1, 0, 0, 0, -2, 1, -1, 1, 1, 0, 3, 0, -3, -2, 1, 0, 2, 0, 1, -2, 0, -1, -1, -3, 6, -1, -1, 0, -1, 0, 0, 0, 0, 0, -1, -2, 1, 3, -1, -3, 0, 1, 1, -1, -3, -2, 1, 4, -2, 2, -1, -1, -1, 8, 2, 0, 1, 3, 0, -2, 0, -3, 2, 0, 0, -3, -2, -3, 0, 1, -2, -1, -2, -1, -2, 1, -1, 2, 2, 0, -1, 2, 6, 0, 2, 0, 1, 0, 0, -1, 1, 0, -2, 1, -1, 1, -1, -2, 1, -2, -2, -2, 2, -1, -1, 1, -1, -1, 0, 0, 0, 6, 0, 1, 2, 0, 1, 0, -2, -2, 0, 1, -1, -3, 0, 1, -2, 0, -2, 0, 0, 1, -2, 1, 2, 1, -1, 1, 2, 0, 6, 2, 2, -1, -1, -1, -1, 0, -1, 0, 0, -2, -1, 1, 1, -1, -3, 1, 2, 3, -2, 2, -1, 0, 0, 3, 0, 1, 2, 6, 2, -2, 0, -1, -2, -1, 0, -2, -2, -2, -1, 3, -3, 1, -2, 1, 2, 1, 0, 2, 1, 0, 0, 0, 1, 2, 2, 2, 6, -1, 1, 0, -1, 0, 0, 0, -1, 1, -1, 2, -1, 0, 2, 0, -2, -2, 0, -2, 1, 0, 0, -2, 0, 0, -1, -2, -1, 6, 2, 1, 2, 2, -2, 0, 0, -1, -2, 3, 0, 0, 0, 0, 0, 0, -2, 2, -1, -2, 0, 0, 0, 1, -1, 0, 1, 2, 6, 0, 2, 1, 0, -1, -1, 3, 3, 1, -2, 2, 1, 1, 2, -2, 0, -1, 0, 1, 0, -3, -1, 0, -1, -1, 0, 1, 0, 6, -2, 0, 1, 1, 2, -2, -1, 3, 0, 1, 1, 0, -3, 1, 0, 0, 0, -1, -1, 2, 1, -2, -1, -2, -1, 2, 2, -2, 6, 3, -1, -2, 0, 1, 2, 3, -3, -1, 0, 0, -3, 0, -1, -1, 0, 1, -2, 0, 0, -2, 0, -1, 0, 2, 1, 0, 3, 6, 0, -2, 1, 3, 0, -2, 1, 0, -2, -2, 1, 0, -2, 0, -3, 1, 1, 0, -2, 0, -1, 0, 0, -2, 0, 1, -1, 0, 6, 2, 3, 2, -2, -3, 0, 0, 0, -1, 0, -1, 1, -2, 0, 0, 3, -3, 1, 1, 0, -2, 0, 0, -1, 1, -2, -2, 2, 8, 4, 3, 0, 0, 0, 2, -1, 1, 0, 2, 1, -3, -1, 3, -1, -2, -1, -1, 0, -2, -1, 0, -1, 2, 0, 1, 3, 4, 8 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, -4, 4, 4, 0, 3, 0, -1, 1, -1, 2, -2, 1, -1, -1, -2, 2, -3, -1, 3, 2, 3, -2, 0, 3, 4, 8, 0, -3, -5, 5, 2, 3, 3, -3, -2, -1, 1, 1, -4, 2, -2, -2, 2, 1, 0, 1, 3, 1, 3, 2, -3, 0, -3, 0, 8, -4, 2, -2, 0, 2, 0, -2, 0, 2, -2, 0, -2, 0, 0, 0, -1, 1, 3, 2, 2, -4, 0, 2, -4, -1, 0, -3, -4, 8, 2, -2, 0, -1, -3, 1, 3, -1, 1, 0, 1, -3, 3, 3, 2, 1, -3, -1, -1, 2, -3, -4, 2, -1, -4, -5, 2, 2, 8, -5, -1, -2, -2, 3, 2, 1, -2, 1, 1, -1, 2, 0, -1, -1, 0, 2, -1, -1, -3, 0, 0, -2, 4, 5, -2, -2, -5, 8, 3, 0, 1, -2, -2, 1, 0, 1, -2, 3, 0, -2, 1, 2, -1, -2, 0, 2, 4, -1, -2, 0, 4, 2, 0, 0, -1, 3, 6, -1, 2, 0, 0, 2, -2, 2, -3, 1, 1, -1, -2, 1, -1, 0, 3, 2, 3, -2, -2, 1, 0, 3, 2, -1, -2, 0, -1, 6, -1, -2, 1, -2, 1, -2, -3, -1, -2, 2, 1, 0, 0, 0, 3, -2, 1, 1, -2, 1, 3, 3, 0, -3, -2, 1, 2, -1, 6, -1, -3, 1, -1, 2, 0, 1, -2, -3, -1, -1, 0, 2, 2, 1, 1, 1, 0, 2, 0, -3, -2, 1, 3, -2, 0, -2, -1, 8, 3, 1, 1, 2, -1, -2, -1, -1, -2, -2, 1, -2, 0, 0, 0, -2, 4, 0, -1, -2, 0, 3, 2, -2, 0, 1, -3, 3, 6, -1, 2, 1, -2, -3, 1, 3, 1, 0, -1, -1, 1, 0, -1, -2, 2, 0, 1, -1, 2, -1, 1, 1, 2, -2, 1, 1, -1, 6, -2, 2, -1, 0, 0, -2, -3, 2, 1, -1, 1, 0, 1, -3, 0, 1, -1, 1, -2, 1, -2, 0, -2, 1, -1, 1, 2, -2, 6, 0, -1, -2, -2, 1, 2, 0, 1, 0, 0, 0, -1, 0, 2, -1, 2, 1, 0, 0, 1, 1, 2, -2, 2, 2, 1, 2, 0, 6, -1, 0, 0, -2, 1, 0, 0, 0, 0, 1, 1, -1, 0, -1, -2, -4, -2, 1, 1, -2, -3, -3, 0, -1, -2, -1, -1, -1, 8, 0, 2, 1, 1, -1, -1, 0, -4, 1, -3, 0, 3, 0, 1, 2, 0, -3, -1, 3, 1, -1, 1, -2, -3, 0, -2, 0, 0, 6, 0, -2, 0, -1, 0, 1, -1, 0, 2, 2, -3, -1, -1, -2, 0, 3, 2, 0, 1, -2, -2, -1, 1, 0, -2, 0, 2, 0, 6, 1, 2, 1, -1, 0, -1, 1, -2, -2, 0, -2, -1, -2, 0, 3, 0, -2, -1, 2, -3, -1, 3, -2, 1, -2, 1, -2, 1, 6, 1, 0, -1, -1, 1, -1, -1, -2, 0, 1, -2, 2, -1, 2, -1, 1, -2, 1, -1, -2, 1, -3, 2, 1, 1, 0, 2, 1, 8, -1, 0, 1, -2, 1, -2, 0, -1, -3, 2, 1, 1, 1, -1, 2, 1, 0, -1, -2, 0, 2, 0, 0, -1, -1, 1, 0, -1, 6, -1, 0, 1, 0, 0, -1, -1, 0, -3, 0, 3, -3, 0, -1, -1, 0, 0, 1, -1, 1, 1, 0, -1, 0, -1, -1, 0, -1, 6, 0, 0, -2, 1, 2, -1, -1, -1, 1, 2, -1, 2, -2, 0, 0, 2, -2, -1, -1, 0, 0, 0, 1, 0, -1, 1, 0, 0, 6, 2, 0, -2, 2, -2, -1, 3, 3, 2, -1, -1, 0, 3, 3, 2, 0, 1, 1, 0, 0, -4, -1, -1, 1, -2, 1, 0, 2, 8, -1, 1, -2, -1, 2, 2, 1, -4, 2, -1, 2, 2, -2, 1, 0, 0, 0, 0, 1, 1, 0, 1, -1, 1, 0, -2, 0, -1, 6, 1, -1, 2, 1, 3, 3, 0, -3, -3, 4, 3, 1, 1, 0, -1, 1, -1, 1, -3, 2, -2, -1, -2, 0, 1, -2, 1, 1, 6, 1, -2, 2, -2, 2, 2, -4, 0, -1, -2, 1, 1, -2, -2, -3, 0, -1, 0, 2, -2, -2, 0, -1, 2, 2, -2, -1, 1, 8, -2, -1, 0, -3, -4, 2, 0, -2, -2, -2, 0, 4, 2, 0, 2, 0, 3, -3, 0, 0, -1, -1, -1, -2, -1, 2, -2, -2, 8, 2, 3, 0, -1, -1, -2, 0, 1, 1, 2, 0, 0, 1, -1, -1, 0, -1, -2, 1, -3, 0, -1, -1, 2, 1, 2, -1, 2, 6 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, 0, 0, 0, 0, -4, 0, -4, 0, 0, 0, -4, 0, 1, 1, 4, -2, -3, -2, 3, 0, 1, -3, 0, 1, 4, 8, 0, -3, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, -2, 0, 2, 2, 5, -1, -3, -1, 0, -3, -1, -3, 3, -1, -3, 0, 8, -4, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -3, -3, -2, 3, -1, 3, 1, 0, 2, 1, 0, 1, 0, -3, -4, 8, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, -2, -3, 2, -3, 1, 3, -1, 1, -3, -2, 0, 0, 0, 0, 6, 2, -3, -3, -2, 2, -3, 0, 3, -3, 1, -3, 0, 2, -1, -1, 2, 0, -1, -2, -2, 3, -2, 1, 0, 0, 0, 0, 2, 6, 0, 0, 0, 3, -3, 0, -1, -3, 2, -1, 2, 1, -1, -2, -1, 1, 2, -1, -3, -1, 1, 3, 0, 0, 0, 0, -3, 0, 6, 1, 1, -2, 2, -2, -4, 2, -1, 2, 0, -1, 2, 2, -3, -1, 0, 3, 2, -4, 2, -1, 0, 0, 0, 0, -3, 0, 1, 6, 3, -1, 3, 2, -1, 1, 0, 3, 0, -3, 2, -1, -1, 2, 2, -1, 1, 0, 3, -1, -4, -2, -1, -1, -2, 0, 1, 3, 8, 0, 6, 2, -2, 0, 5, 2, 2, -1, 0, 1, 2, 2, -3, -1, -1, 0, 2, 0, 0, 0, 0, 0, 2, 3, -2, -1, 0, 6, -4, 0, -1, -2, 3, -3, 3, 2, -3, -3, 2, 2, 2, -2, -2, 1, -1, 2, -4, -2, -1, -1, -3, -3, 2, 3, 6, -4, 12, 2, 0, 3, 2, 4, 0, -1, 1, 3, -1, 0, -3, 0, 0, -1, 1, -2, 0, 0, 0, 0, 0, 0, -2, 2, 2, 0, 2, 6, 0, -2, 0, 0, -1, -2, 1, -1, -1, 2, -1, -1, -1, 0, -2, 2, 0, 0, 0, 0, 3, -1, -4, -1, -2, -1, 0, 0, 8, -2, 0, -2, -2, 0, 0, -1, 3, 0, 0, -2, -2, 3, 0, -1, 0, 0, 0, 0, -3, -3, 2, 1, 0, -2, 3, -2, -2, 6, -1, 2, 0, 0, 0, 2, -1, -1, 0, 1, 2, 0, 1, -2, -4, -2, -1, -1, 1, 2, -1, 0, 5, 3, 2, 0, 0, -1, 8, -1, 3, 2, -2, -1, 3, 3, -3, -2, -3, 2, 2, 1, 0, 0, 0, 0, -3, -1, 2, 3, 2, -3, 4, 0, -2, 2, -1, 6, 0, -1, 1, 2, -3, -1, 0, 1, 2, -2, 1, -2, 1, 2, -3, 0, 0, 2, 0, 0, 2, 3, 0, -1, -2, 0, 3, 0, 6, 3, 0, -2, 0, -1, 0, -2, -2, -1, 2, 0, 1, 2, -3, 0, 2, 1, -1, -3, -1, 2, -1, -2, 0, 0, 2, -1, 3, 6, 0, -1, 0, -2, -1, -2, -2, -1, 0, 0, 4, 5, -2, -2, -1, -1, 2, 2, 0, -3, 1, 1, 0, 0, -2, 1, 0, 0, 8, 0, -3, -1, -1, -1, 1, -3, 4, -1, -2, -1, 3, -3, -1, -2, 2, -1, 1, -3, 3, -1, -1, 2, -1, 2, -2, -1, 0, 6, -1, 0, -2, 1, 3, -1, 0, 0, -3, -3, -1, 2, 2, -1, -3, -1, 2, 2, -1, -1, 3, -1, 3, -3, 0, 0, -3, -1, 8, 1, -1, -1, -1, 5, -1, -1, -2, -1, 3, -3, 0, 1, -1, 2, 2, 2, 0, 2, 0, -1, 3, -1, -1, -2, -1, 0, 1, 6, 0, -2, 0, 2, 1, 2, 3, 0, 1, 1, -1, 2, 0, 2, -3, 2, -3, -1, 0, 0, -3, 0, 0, -1, -1, -2, -1, 0, 8, 0, 1, -1, 0, 1, 0, -3, 0, 3, -2, -1, 3, -1, -1, -2, 0, -1, -2, 1, -2, 1, -2, -2, -1, 1, -1, -2, 0, 6, 2, -2, -2, 0, 1, -1, 2, -1, -2, -3, 2, 1, -1, -2, 0, -1, -2, 2, -3, 2, -2, -2, 1, 3, -1, 0, 1, 2, 6, 0, 0, -1, -3, -3, 1, 1, 3, -1, -4, 0, 0, 1, -1, 0, 3, 0, 2, -2, -1, -1, -3, -1, 5, 2, -1, -2, 0, 8, -1, -1, 0, 3, 0, -3, -2, 1, 2, 3, 2, -1, 1, -2, 0, 1, 2, 1, 2, 0, 4, 0, -1, 1, 0, -2, 0, -1, 8, -1, 1, -1, 1, -2, 1, 3, -1, -1, 0, 2, -2, 2, -1, -2, 1, -2, 0, 0, -1, 0, -1, 2, 1, 0, -1, -1, -1, 6 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, 0, 0, 0, 0, -3, -1, -1, 0, 2, 0, -2, 0, -3, -3, 4, 4, -2, 1, -3, -4, 3, -1, 3, -2, 4, 8, 0, -3, -3, 0, 0, 3, 0, 1, 1, 0, 1, 0, -1, 0, 0, 0, -1, 2, 2, 2, -3, -2, 0, 1, 3, -4, -3, 0, 8, -4, 1, 0, 0, -1, 0, 4, 4, 0, -4, 0, 4, 0, 0, 0, -4, -3, 2, -2, 2, -1, -1, 3, -4, -2, 0, -3, -4, 8, 1, 0, 0, -1, 0, -2, -2, 0, 2, 0, -2, 0, 0, 0, 2, 3, -4, -2, 2, 2, 2, -3, 2, 4, 0, -3, 1, 1, 6, -2, 2, -2, 0, 1, -1, 1, 0, -2, 1, 0, 0, -1, 3, -1, -3, 0, 1, 1, -1, 1, 0, 2, 0, 0, 0, 0, -2, 6, -1, 0, -2, 0, 2, -1, 0, 2, -2, 1, 1, -1, -1, 0, 2, 0, -2, -3, 0, -2, 1, 0, 0, 0, 0, 0, 2, -1, 6, 2, -1, -1, 0, -1, 1, -2, -1, -2, 2, -1, 2, 2, 1, 0, 1, 2, 0, 2, 2, -2, 0, 3, -1, -1, -2, 0, 2, 6, -1, -1, 1, 1, 2, -2, -2, 0, 1, 0, 0, 1, 1, 2, 0, 2, 0, 0, 3, -3, -3, 0, 0, 0, 0, -2, -1, -1, 6, 0, -2, 1, 0, 1, 1, -1, 1, 3, -2, -3, 1, 0, 1, 2, -3, 0, 0, 2, -1, 1, 4, -2, 1, 0, -1, -1, 0, 6, 3, 1, -1, 0, 1, 2, -1, -1, -1, -2, -1, -1, -1, -2, -1, 1, -3, 0, -1, 1, 4, -2, -1, 2, 0, 1, -2, 3, 6, 1, -2, 1, 0, 0, 0, -2, -2, -1, 2, -1, 0, -1, 0, 1, -2, -2, 0, 0, 0, 0, 1, -1, -1, 1, 1, 1, 1, 6, 2, -1, -2, 2, -2, 1, 2, -1, -3, -1, -1, 0, 0, -2, 1, 0, 2, 1, -4, 2, 0, 0, 1, 2, 0, -1, -2, 2, 6, -1, -4, 1, -1, 0, 3, 1, -2, 0, -2, -1, 0, -2, 4, 0, 0, 0, 0, 0, -2, 2, -2, -2, 1, 0, 1, -1, -1, 6, 1, 0, 0, 0, -2, -2, 2, 0, 0, -2, 1, -1, -2, 2, -2, -1, 4, -2, 1, -2, -1, -2, 1, 1, 0, -2, -4, 1, 8, -2, 0, 2, -3, -3, 2, 1, 3, 0, 1, 4, -3, 2, 0, 0, 0, 0, 0, 1, -2, 0, -1, 2, 0, 2, 1, 0, -2, 6, 0, 0, 0, 0, -3, -1, -2, -2, 0, -3, -1, 1, -3, 0, 0, 0, 0, 1, 2, 1, 1, -1, 0, -2, -1, 0, 0, 0, 6, 1, -2, 0, 3, 2, 1, 2, -2, 1, 1, 0, -3, 0, 0, 0, -1, -1, -1, 0, 3, -1, -2, 1, 0, 0, 2, 0, 1, 6, -2, -2, 1, 0, 0, 2, -1, 1, 1, 1, 4, -1, -4, 2, 3, -1, 2, 0, -2, -1, -2, 2, 3, -2, -3, 0, -2, -2, 8, 2, -4, 1, -2, 0, 2, -2, 3, 1, 4, 2, -3, 3, -1, 0, 2, 1, -3, -2, -1, -1, 1, -2, -3, 0, 0, -2, 2, 8, -2, -1, 0, 0, 3, -1, 2, -2, -2, 2, 2, -4, -3, 2, 1, 1, 1, -1, 2, -3, -2, 2, 2, -3, 3, 1, -4, -2, 8, 2, 0, 0, -2, 3, 0, -2, 1, 2, -2, -2, 0, 0, 0, 2, 0, -1, -1, -1, 0, 0, 1, -1, 2, 0, 1, -1, 2, 6, -1, 1, -1, 1, 2, 0, -3, -3, 2, 2, 1, -2, 1, 0, 1, -1, 0, -1, -2, 0, 3, -2, 1, 0, -2, 0, 0, -1, 6, 3, 1, 1, -2, 1, -4, -2, -1, 2, 1, -3, 2, 2, 2, -2, -1, 0, -1, -2, 0, -2, 2, 2, 0, 0, 0, 1, 3, 8, -2, 1, 0, 1, 3, 0, -1, 2, -1, 0, 0, 0, -3, -1, 0, 0, 0, 1, 1, 0, -2, -1, 2, 3, -2, -1, 1, -2, 6, -1, 0, 0, -1, 1, 3, -3, 1, -2, 2, 0, 0, 1, 1, -2, -2, -1, 4, -3, 1, 1, -2, -1, 3, 1, 1, 1, -1, 6, -1, -2, 3, 3, -4, 2, 0, 1, 2, 3, 0, -3, -2, 1, 4, -2, -3, -1, 1, 1, 3, 2, 0, 2, -2, 0, 0, -1, 8, -1, -2, -4, -2, 4, 2, 0, -2, -3, 2, 0, -2, 0, 0, 2, 2, 1, 0, 1, 1, -2, -2, 0, 1, 1, 0, -2, -1, 8 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, 0, 0, -3, -4, 3, -4, 3, 1, -4, -4, 2, -3, 2, 3, -1, 2, 0, -1, 4, 1, 1, 0, -4, -4, 4, 8, 0, -3, 0, 0, -3, -2, 3, -2, 3, -1, -2, -2, -2, -3, -2, 3, -2, 4, 0, 1, -1, 2, 2, 0, 1, -2, -3, 0, 8, -4, 0, 0, -1, 3, 1, 1, -2, -3, 3, 2, -2, -1, -4, -4, -3, 1, -3, 3, -5, -2, -1, -1, 1, -1, 0, -3, -4, 8, 0, 0, 2, 0, -2, -2, -2, 0, 0, 2, 4, 2, 5, -1, 3, -2, 3, -3, 1, 1, 2, -1, -2, 2, 0, 0, 0, 0, 6, 2, -3, 0, 3, 2, -3, -1, 1, 3, -2, -2, -2, 2, 2, -2, -2, -3, -2, -2, -1, 2, -3, 0, 0, 0, 0, 0, 2, 6, -3, 1, 1, -1, -3, 0, 3, 1, -1, -3, 0, -2, 0, -1, -3, -2, 2, -1, 1, -1, -1, 0, -3, -3, -1, 2, -3, -3, 8, -1, -5, 1, 2, 2, -1, 1, 3, 5, 3, -2, 0, -2, 3, 1, -1, 2, -2, -2, 3, 3, -4, -2, 3, 0, 0, 1, -1, 6, -1, 2, -2, -2, 4, 1, -2, 0, -1, -3, -1, 0, -2, 0, -2, -2, 1, -1, 1, 0, 3, 3, 1, -2, 3, 1, -5, -1, 8, 1, -2, -2, 1, 0, -3, -2, -3, 4, 0, 2, -2, -1, 0, -3, -1, 3, -4, -4, -4, -2, 1, -2, 2, -1, 1, 2, 1, 8, -2, 1, 3, 3, -4, 1, -3, 2, 2, -2, -1, 0, -1, -3, -3, 3, 1, 2, 3, 3, -2, -2, -3, -3, 2, -2, -2, -2, 8, 2, -5, -5, 2, 0, 2, 2, -3, 3, 1, 1, 1, 2, 1, -1, 1, -1, 1, -1, -3, 0, -1, 0, 2, -2, -2, 1, 2, 6, -1, -2, 2, 1, 3, 0, 0, -1, 1, 1, 4, 0, 0, 1, 0, 0, -4, -2, 3, 0, 1, 3, -1, 4, 1, 3, -5, -1, 8, 4, -3, -1, -2, -4, 0, -2, -3, 1, 0, -2, -1, -1, 1, 0, -4, -2, 2, 2, 3, 1, 1, 1, 0, 3, -5, -2, 4, 8, -2, 0, -2, -1, 3, -3, 0, -1, -4, 0, -2, 0, 1, 4, 2, -2, -2, 4, -2, -1, 3, -2, -3, -4, 2, 2, -3, -2, 8, 1, 5, -3, 0, 0, 2, 0, 1, 2, 2, -1, -2, 0, -3, -3, -1, 2, -2, -3, 5, 0, -2, 1, 0, 1, -1, 0, 1, 8, 1, 0, 0, 0, 4, 0, -1, 1, -1, 1, 2, 2, 2, -2, -4, 5, -2, 0, 3, -1, -3, -3, 2, 3, -2, -2, 5, 1, 8, -1, 0, -1, 2, -1, 3, 1, 2, -2, -2, -1, 3, 3, -4, -1, 2, -2, -2, -3, 4, 2, 2, 0, -4, -1, -3, 0, -1, 10, 2, 1, 2, -2, 1, 0, -1, 4, -2, 0, -1, -2, -3, 3, 2, 0, 0, -1, 0, 2, -3, 0, 0, 3, 0, 0, 0, 2, 6, -2, 2, -2, 0, 0, -1, 2, 0, 3, 2, 4, 1, -2, -2, -1, -2, 0, 2, -2, 3, -1, -2, -3, 0, 0, -1, 1, -2, 6, 1, 1, -1, 1, 2, 1, 1, -2, 0, 0, -3, 3, -2, -3, 3, -2, -2, -1, 1, 1, -3, 0, 2, 4, 2, 2, 2, 1, 6, 0, 0, 3, 1, 1, 2, 2, -1, 1, 3, -3, -3, -2, 1, 0, -1, 0, 1, 1, 1, -1, 0, 0, -1, -2, -2, 1, 0, 6, -1, 1, 0, 0, 3, -1, 4, -1, -5, 1, -2, 2, -1, -2, 0, -1, 1, 4, 0, -4, 1, -1, 3, 1, 0, -1, 0, -1, 10, 0, 0, 0, -2, -2, 1, 2, -2, 1, -2, -1, 2, -2, -3, -3, 2, 0, -2, 0, 2, 1, 1, 0, 0, 1, 3, 1, 0, 6, 1, -1, 3, 2, 1, 2, -1, 2, -1, 1, -2, 1, -1, -3, 1, 0, -1, -2, 2, -1, 2, -1, -1, 2, 1, 0, 0, 1, 6, 0, 0, 0, 0, 0, -1, -1, 2, -1, -2, -1, 3, 3, -1, 1, -1, 0, -1, 1, -2, 4, 2, 1, 1, 0, 0, -1, 0, 6, -1, 0, -4, 1, 1, -2, -3, -1, 3, 1, -4, 1, 1, 0, 1, 1, -2, 2, -2, -2, 0, 1, 2, 3, -2, 3, 0, -1, 8, 3, -4, -2, -1, 2, 0, 0, 3, 0, -4, 2, -1, 0, 0, 4, 0, 2, -1, 0, 3, -2, 2, -1, -2, 2, 0, 0, 3, 8 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, 3, 2, -1, 3, 2, -2, 0, 4, 0, -4, 0, 2, -3, -2, -4, -4, 4, 2, 2, -4, -4, 4, 3, -2, -2, -2, 4, 8, 0, 4, 1, 0, -2, -4, 0, 2, 3, -2, 0, 4, 0, 2, -2, -2, -1, -2, 1, -2, -2, 5, 0, -4, 2, 2, 3, 0, 6, -2, 1, 2, 3, 1, -2, 1, 0, -2, 2, -1, -3, 0, -1, 0, 3, 3, 3, -1, -3, 3, 3, 0, -2, -1, 2, 4, -2, 8, -2, 2, 0, -2, 2, 3, 0, 1, 1, 2, -1, 2, 0, -4, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, -1, 1, 1, -2, 6, -3, 0, 0, -2, -1, 3, 0, 2, 0, 2, 2, 1, 2, 0, 0, 0, 1, -1, 2, -2, 0, 1, 1, 3, 0, 2, 2, -3, 6, 3, 1, 2, 3, -1, 0, 1, -1, -2, -2, 0, -2, 2, 1, 0, 0, -1, 2, 2, 1, 0, -1, 2, -2, 3, 0, 0, 3, 6, 3, 0, 2, -1, -1, 3, -3, -3, -1, 0, -2, 4, 2, 0, 1, -1, 0, 1, 2, -1, -1, -2, -4, 1, -2, 0, 1, 3, 6, -1, -1, -1, 2, 0, -2, 0, 0, 1, 1, 2, 1, -1, 2, 1, -1, 1, 3, -1, 0, 0, 0, -2, 2, -2, 2, 0, -1, 6, 0, -1, 0, 0, -1, 0, -1, 1, -1, 0, -2, -3, 1, 0, -1, -1, -1, 3, -1, 4, 2, 1, 3, -1, 3, 2, -1, 0, 6, 1, -1, 0, 1, -2, -2, -2, -3, 3, 1, 1, -2, -2, 1, 2, -1, 0, -1, 0, 3, 0, 0, 3, -1, -1, -1, -1, 1, 6, 1, 1, 2, 2, 0, -1, 1, -2, -1, 0, 1, -1, 1, -2, -3, 2, 3, -4, -2, -2, 1, 0, 0, -1, 2, 0, -1, 1, 6, 0, 0, 3, 1, 2, 2, -3, 0, -2, 3, 3, -2, -1, 2, 1, 2, 0, 0, 2, 1, 2, 1, 3, 0, 0, 0, 1, 0, 6, -2, -1, 1, 2, 0, 1, 1, 0, 2, 1, 2, -1, 2, 1, 0, 2, 4, -1, 2, 0, -1, -3, -2, -1, 1, 2, 0, -2, 6, 0, 1, -3, -1, -2, -1, 0, -2, -1, 2, 1, -3, 0, 0, -3, 0, -3, -1, 2, -2, -3, 0, 0, -2, 2, 3, -1, 0, 6, 0, 2, 3, -3, -2, -2, 1, 2, 0, -3, 1, 1, 2, -2, 2, 0, 2, 2, -2, -1, 0, -1, -2, 0, 1, 1, 1, 0, 6, 1, 0, -2, -1, 1, 2, 1, 2, 0, 0, 1, 1, -4, -2, -1, 0, 1, 0, 0, 1, 1, -2, -1, 2, 2, -3, 2, 1, 6, 2, -1, 0, -1, 3, 3, 0, -2, 4, 2, 1, -4, -2, 0, -4, 2, -2, -2, 1, -1, -3, 1, 2, 0, -1, 3, 0, 2, 6, -2, -1, -1, 1, 1, 0, -1, 1, 1, 1, 4, -1, 3, 0, 0, 2, 4, 2, 0, 3, -2, -3, 1, -2, -3, -2, -1, -2, 8, 3, 1, -2, -2, 2, 3, 2, -2, -3, 2, -2, 3, 0, 0, 1, 2, 1, -2, 1, -1, 0, 1, -1, -2, -1, 0, -1, 3, 6, 3, -1, 0, 0, 3, 2, -3, -2, 2, 1, 3, 0, 0, 0, 0, -1, -3, 1, 0, -2, 0, 0, -2, 1, -1, -1, 1, 3, 6, -1, -1, 2, 3, 0, -2, -1, -4, -2, -1, 0, 1, 0, 1, 2, 1, -2, 1, 3, 2, -2, 1, 2, 3, 1, -2, -1, -1, 6, 2, -1, -2, 2, 2, 2, -4, -2, -3, 2, -1, -1, -1, 1, 0, -2, -1, 3, 1, -1, 2, 1, 3, 1, -2, 0, -1, 2, 6, -2, -1, 3, 1, 1, 4, 5, 3, 2, 2, 2, 0, -1, -1, 1, 1, -2, 2, 2, 0, 2, 0, 0, 2, 0, 2, -1, -2, 10, 2, 1, 0, -1, 3, 0, 3, 1, -2, 2, 1, 1, -1, 2, -2, -1, -1, 1, -3, 0, -2, -1, 3, 3, 3, -2, -1, 2, 6, 0, -2, -3, -2, -4, 0, 0, 0, 1, 2, 3, -1, -1, -3, 2, 2, -3, 1, 0, 4, 1, 2, 2, 0, 2, 3, 1, 0, 8, -1, -1, -2, 2, -2, 2, 1, 0, -1, -1, 3, 0, 2, 1, 1, 0, 1, 1, 2, 1, -2, -3, -2, 2, 1, 0, -2, -1, 6, 2, -2, 2, -1, 0, 1, -1, -1, 0, -1, -1, 3, 2, 0, 0, 2, 1, 1, 1, -3, -2, -1, 2, 1, -1, -3, -1, 2, 6 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, -1, 0, -1, -1, 0, 0, 3, -4, -1, 3, -1, 1, 3, 4, 3, 4, 8, 0, -3, 0, 0, 0, 0, -1, 0, -1, -1, -1, 1, 0, -2, 1, 0, 0, 3, -2, -2, 0, 1, 2, 0, -1, 0, -3, 0, 8, -4, 0, 0, 0, 0, 1, 0, 1, 1, 1, -1, 0, 3, -1, 0, 2, 1, -1, -3, 1, -1, 3, -3, -5, 1, 0, -3, -4, 8, 0, 0, 0, 0, 1, 0, 1, 1, 1, -1, 0, -3, -1, 0, -1, -2, -1, 0, -2, -1, 0, 0, 1, -2, 0, 0, 0, 0, 6, -1, -2, -3, -2, 0, 1, 2, -3, 2, -1, -2, -2, -1, -2, -2, 2, 2, 0, 3, -2, -2, -2, -1, 0, 0, 0, 0, -1, 6, 0, 0, -1, 2, 2, 1, 3, 0, -1, -2, 2, -2, 3, 0, -3, -3, -1, -1, -2, 1, -1, 1, 0, 0, 0, 0, -2, 0, 6, -1, 3, 1, 2, -3, 0, 0, 1, 3, 2, 3, 0, -1, 1, -2, 0, 0, -1, 1, 2, 2, 0, 0, 0, 0, -3, 0, -1, 6, -1, -1, -3, 0, 0, 0, 2, 0, 0, -1, 1, 3, -3, 0, 1, -2, 1, 2, 0, 1, 1, -1, 1, 1, -2, -1, 3, -1, 6, -1, 3, 0, 2, -1, 1, 2, 0, 2, 0, 1, -1, -1, 1, -1, 2, 1, 2, 2, 0, 0, 0, 0, 0, 2, 1, -1, -1, 6, -1, -1, 2, -1, -2, -2, 0, -2, 3, -1, -2, -3, 1, 0, -2, 0, 2, 0, 1, -1, 1, 1, 1, 2, 2, -3, 3, -1, 8, 2, 2, 1, 0, 1, 0, 0, 1, -1, -1, -1, 1, -1, 1, 1, -2, 2, 1, -1, 1, 1, 2, 1, -3, 0, 0, -1, 2, 6, 0, -1, 0, -2, -3, -3, 1, 1, -2, 0, 2, 0, 1, -1, -2, 1, 1, -1, 1, 1, -3, 3, 0, 0, 2, 2, 2, 0, 8, -3, 0, -1, 0, -1, 4, 2, -3, -4, 0, -3, 2, 1, 2, 1, -1, 1, -1, -1, 2, 0, 0, 0, -1, -1, 1, -1, -3, 6, 1, 0, 2, 0, -2, -1, 1, 3, 0, 1, -1, 1, -2, -1, 0, 0, 0, 0, -1, -1, 1, 2, 1, -2, 0, 0, 0, 1, 6, 2, -1, 2, -1, 1, -1, 1, 1, 1, 0, 0, 1, 0, -1, -2, 3, -3, -2, -2, 3, 0, 2, -2, 1, -2, -1, 0, 2, 10, 1, 4, -1, 0, 2, 2, 2, -1, 1, 1, 0, 1, -1, 1, -1, -1, -2, 2, 2, 0, 0, 0, 0, -3, 0, 2, -1, 1, 6, 1, -1, -1, 1, -1, -2, 0, 0, 2, -1, 0, 0, 0, 0, 0, -1, -2, 3, -1, 2, -2, 0, -3, -1, 0, 2, 4, 1, 6, -2, -1, 2, 1, -1, 1, 0, 0, 1, 0, 0, 0, 2, -1, -2, 3, 0, 1, 0, 3, 1, 1, 4, -2, -1, -1, -1, -2, 6, 2, -3, -3, 1, -2, 0, 1, 0, 1, 3, 3, 1, -2, -2, 0, -1, 3, 1, -1, -1, 1, 2, -1, 1, 0, -1, -1, 2, 6, -3, -1, 2, -1, 2, 2, 1, 2, -4, -2, -1, -1, 2, -3, 1, -3, -1, -2, -1, -2, -3, 1, -1, 2, 1, 2, -3, -3, 10, 4, -3, 3, -2, -2, 0, -2, -1, -2, -3, 0, 2, -3, -2, 0, -1, -3, -1, 0, -4, 3, 1, 2, -1, 1, -3, -1, 4, 8, 0, 2, -2, 1, 1, -2, 3, 0, 1, -2, 0, -1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 2, -2, -1, 1, 2, -3, 0, 6, -1, 1, 2, 2, 3, -1, 1, -1, -1, 3, -1, 0, -2, -1, 0, -1, 0, -3, 1, 1, -1, 0, 1, -2, -1, 3, 2, -1, 6, -3, -1, 0, -1, 1, 2, 3, 0, -2, -2, -1, 1, 2, -2, 1, 1, 2, -1, 0, 1, 0, 0, 0, 2, -2, -2, 1, -3, 8, -1, -3, 0, 3, 0, -3, 0, -2, 1, 1, 2, 1, 0, 1, -1, 1, 1, 0, 1, 2, 0, 1, 2, -2, 1, 2, -1, -1, 6, 3, 2, 4, -1, -5, 1, -2, -1, 2, 0, 2, 2, -2, -2, 2, -2, 1, 0, -1, 1, 0, 1, 0, 1, 2, 0, -3, 3, 10, 2, 3, 0, 1, -2, -1, 1, 2, 1, 2, 0, 2, 1, 1, -1, 0, 1, 0, 0, 1, 2, -2, -2, 3, -1, 0, 2, 2, 6 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -3, 1, -2, -2, 3, 4, 0, 0, -2, -1, -1, 4, 8, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 0, 5, -3, 0, -1, -2, 1, -3, 0, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -2, 3, 1, 2, 3, 2, 1, -2, -4, -1, 1, -3, 2, 0, -3, -4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 1, -1, 0, 2, -2, -2, 2, 2, -2, 3, -1, 0, 0, 0, 0, 6, -1, 2, 2, 2, -2, 3, -2, 2, -2, -3, 2, 0, 0, -1, 2, -1, -1, 1, -2, -3, 1, -1, -2, 0, 0, 0, 0, -1, 6, 1, 1, 2, 3, 2, 3, 1, 1, -2, 1, -1, -1, -2, 0, -2, 0, 2, 0, -1, -3, 3, -2, 0, 0, 0, 0, 2, 1, 6, 3, 1, -1, 3, 0, 3, 1, -4, 2, -1, 2, 1, 0, -3, 1, -1, 0, -3, 1, 0, -1, 0, 0, 0, 0, 2, 1, 3, 6, 1, -1, 3, 1, 0, -2, -4, 1, -2, 1, -2, 1, -3, 0, -1, -2, -3, 1, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 6, 2, 4, -1, 0, 0, -1, -1, -1, -2, -3, 3, 0, 1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, -2, 3, -1, -1, 2, 6, 0, 1, -2, 1, 0, 0, -2, -2, -2, 0, 1, 0, 1, 2, 0, -1, 3, 1, 0, 0, 0, 0, 3, 2, 3, 3, 4, 0, 8, -2, 0, 0, -3, -1, 0, 0, -2, 4, -1, 1, 1, -1, -1, -1, -1, -3, 0, 0, 0, 0, -2, 3, 0, 1, -1, 1, -2, 6, 0, 1, 0, 1, -1, 1, -1, -1, -1, 0, 0, 1, 0, 0, 2, -1, 0, 0, 0, 0, 2, 1, 3, 0, 0, -2, 0, 0, 6, 0, -2, 2, 0, 0, 2, -2, -3, -1, 0, 0, -2, 0, 0, -1, 0, 0, -3, 0, -2, 1, 1, -2, 0, 1, 0, 1, 0, 6, 0, 0, 1, 1, 0, -2, 0, 1, 1, 4, 2, 0, 2, -2, 3, 0, 0, 0, -3, -2, -4, -4, -1, 0, -3, 0, -2, 0, 8, -1, 0, -2, 1, -1, 3, 2, 0, 2, 4, -1, -2, 1, 3, 0, -2, 1, 2, 1, 2, 1, -1, 0, -1, 1, 2, 0, -1, 6, -2, -1, 0, -3, -2, 0, 2, 0, -3, 0, 2, -1, -3, 0, 3, -3, 0, -1, -1, -2, -1, -2, 0, -1, 0, 1, 0, -2, 6, 1, 1, 1, 1, 0, 0, -2, 1, 1, -2, -1, -3, 0, 1, 1, 0, -1, 2, 1, -2, -2, 0, 1, 0, 1, -2, -1, 1, 6, 2, 2, 0, -1, -2, 0, 0, 2, 0, 0, 1, 2, 2, -1, -1, -2, 1, -2, -3, -2, -2, -1, 2, 0, 1, 0, 1, 2, 6, -1, 0, 1, 0, -1, 0, 1, -2, 1, -2, 2, 3, 0, 2, 0, 0, 1, 3, 0, 4, -1, -2, -2, -1, -3, 1, 2, -1, 8, 1, -1, 0, -3, 1, -1, -2, 0, -2, -4, 2, 2, -1, -2, -3, -3, 0, 1, -1, -1, -3, 0, 3, -2, 1, 0, 0, 1, 8, 1, -3, 1, 3, 0, 0, 0, 3, 0, 1, -2, -1, 0, 1, 0, 1, 0, 1, 0, -1, 1, 2, 0, 0, -1, 1, -1, 1, 6, 0, 0, 0, 0, -2, -1, 4, 5, -2, -2, 1, 2, -1, -1, 0, 1, 1, 0, 0, 1, 0, 2, 0, -2, 0, 0, -3, 0, 8, -2, -1, -2, 0, -2, 0, -3, -4, 2, -2, 0, 0, -2, 0, 2, -1, 1, 0, 4, 2, 0, -2, 0, -1, -3, 1, 0, -2, 8, 2, 1, 3, -1, 0, 0, -1, 2, -3, -1, -3, -3, 0, 0, -1, 0, -2, 2, 4, -3, 1, 0, 0, 1, 3, 0, -1, 2, 6, -2, 0, 0, -2, -1, 1, -2, 1, -3, 1, 1, -2, -1, -1, 0, 0, 0, -1, 0, 1, 2, 1, -1, 0, 0, -2, 1, -2, 6, -1, 1, -1, -2, -3, 3, -1, 3, 0, 0, 0, 3, -1, 2, 0, 2, -2, 2, -2, 0, -2, -2, 0, -2, 0, 3, 0, -1, 6, -1, -1, 1, 2, -1, -2, -2, -1, 0, -1, 1, -3, -1, -1, -2, 1, -1, -1, 0, 1, 0, 0, -1, -2, -1, 0, 1, -1, 6 ]:CheckPositive:=false), LatticeWithGram(MatrixRing(IntegerRing(), 28) ! \[ 8, 4, -3, 0, 2, 0, 0, -2, 2, 2, 2, 1, 2, 0, 2, 1, 0, 1, 0, -2, 1, -4, 4, 0, 0, -3, -3, -4, 4, 8, 0, -3, 1, 0, 0, -1, 1, 1, -2, 2, 1, 3, 1, -1, 0, -1, -3, -1, 2, -2, 2, -3, 3, 0, -3, -5, -3, 0, 8, -4, -3, 0, 0, 3, -3, -3, -3, 2, -3, 4, -3, 2, 0, -3, 0, -1, 3, 4, -2, -4, 1, 4, 1, -2, 0, -3, -4, 8, 3, 0, 0, -3, 0, 3, 3, -1, 0, -5, 0, -1, 0, 0, 3, -1, 0, -2, 1, 5, -2, -2, 1, 1, 2, 1, -3, 3, 6, -1, 2, -3, -1, 2, 2, 0, 0, -1, 0, -1, -2, 2, 2, 0, 1, -1, 1, 2, -2, -2, 0, -2, 0, 0, 0, 0, -1, 6, 2, -1, 0, -1, -2, -2, 0, 2, 0, 0, 2, -2, 2, -3, -1, 2, 1, -2, 1, 0, 2, -1, 0, 0, 0, 0, 2, 2, 6, -1, -2, -2, -2, -1, 1, 1, -1, -1, -2, -1, 3, -2, 1, 0, 2, 1, 1, 0, 1, -3, -2, -1, 3, -3, -3, -1, -1, 6, 1, -1, -1, 2, 1, 0, 0, 2, 1, 1, -1, 1, 0, 0, -1, -2, 1, 3, -1, 0, 2, 1, -3, 0, -1, 0, -2, 1, 6, 3, 0, 1, 2, -3, 3, 1, 2, 1, -3, 0, -3, -3, 2, -1, 2, -2, -2, 2, 2, 1, -3, 3, 2, -1, -2, -1, 3, 6, 2, 2, 0, -2, 1, 1, 0, 2, 0, 0, -1, -3, 2, 0, -1, -2, -2, 1, 2, -2, -3, 3, 2, -2, -2, -1, 0, 2, 6, -1, 1, -3, 0, 1, -1, 3, 2, 2, 0, -1, 0, 2, -3, -1, -1, 2, 1, 2, 2, -1, 0, -2, -1, 2, 1, 2, -1, 6, 0, 1, 1, 2, 0, -1, -1, 0, 2, -2, 0, -2, 1, 1, -1, -2, 2, 1, -3, 0, 0, 0, 1, 1, 2, 0, 1, 0, 6, -3, 3, 0, 1, 2, -1, 1, 0, -2, 1, 1, 2, -1, -2, -1, 0, 3, 4, -5, -1, 2, 1, 0, -3, -2, -3, 1, -3, 10, -1, 0, 0, -3, -1, -2, 2, 2, 0, -5, 1, 2, 0, -3, 2, 1, -3, 0, 0, 0, -1, 0, 3, 1, 0, 1, 3, -1, 6, 1, 3, 0, -3, 0, 0, -3, 0, 0, 2, -1, 0, 1, 1, -1, 2, -1, -1, 0, -1, 2, 1, 1, 1, 2, 0, 0, 1, 6, 0, 0, 0, 0, 1, 1, -1, -2, 0, 1, 1, 1, 0, 0, 0, 0, -2, 2, -2, 1, 2, 0, -1, 0, 1, 0, 3, 0, 6, -2, -2, -2, 0, -1, 0, -2, 1, 1, 0, 1, 1, -1, -3, 0, 2, -2, -1, 1, 1, 2, 3, -1, 2, -3, 0, 0, -2, 8, 0, 4, -3, 0, 0, 2, -3, -2, -2, 1, 0, -3, 0, 3, 2, 2, 3, -1, -3, 0, 2, -1, -1, -1, -3, 0, -2, 0, 8, -2, 1, 1, 1, 2, -3, 0, 2, -1, -2, -1, -1, -1, 0, -3, -2, 1, 0, 0, 2, 0, 1, -2, 0, 0, -2, 4, -2, 6, -2, 1, -3, 1, -1, 0, 0, 3, 1, 2, 3, 0, 1, -1, 1, 0, -3, -1, 0, 2, 0, 2, 0, 1, 0, -3, 1, -2, 6, 0, 0, -1, 1, 2, 0, -4, -4, -2, 4, -2, -1, 2, 0, 0, -3, -3, -1, -2, -2, 2, -3, 1, -1, 0, 1, 1, 0, 8, -4, -2, -1, 1, 3, 1, 4, 2, -2, 1, 1, 1, 2, -1, 2, 2, 0, 0, 1, 0, 0, -1, 0, 0, 1, -3, 0, -4, 6, 0, 1, -2, -3, -3, 0, -3, -4, 5, 2, -2, 1, -2, -1, 0, 2, -2, 1, -5, 0, -2, -2, 2, 2, 1, -1, -2, 0, 8, -2, -2, 1, 1, 0, 3, 1, -2, -2, 1, 1, 1, 2, -1, -3, 1, 2, 1, 2, 0, 1, -3, -3, -1, 1, -1, 1, -2, 6, 1, -1, -2, -3, 0, 4, -2, -2, 0, 0, 3, -2, -2, -1, 1, -1, 2, -1, 1, 1, -2, 0, 0, 2, 1, -2, -2, 1, 6, 1, 0, -3, -3, 1, 1, 0, 2, 1, -1, -2, -2, -1, -1, -2, 0, 0, 1, 0, -2, 2, 0, 0, 3, -3, 1, -1, 1, 6, 2, -4, -5, -2, 1, -2, -1, -3, 0, 2, 1, 2, -2, -1, -3, 1, 1, 1, 1, -1, 3, -4, 1, -3, 1, -2, 0, 2, 10 ]:CheckPositive:=false) ];