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Views: 418346############################################################################# ## #A imf13.grp GAP group library Volkmar Felsch ## ## #Y Copyright (C) 1995, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains, for each Z-class representative of the irreducible ## maximal finite integral matrix groups of dimension 13, ## ## [1] a quadratic form (as lower triangle of the Gram matrix), ## [2] a list of matrix generators. ## ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 13. ## IMFList[13].matrices := [ [ # Z-class [13][01] [[1], [0,1], [0,0,1], [0,0,0,1], [0,0,0,0,1], [0,0,0,0,0,1], [0,0,0,0,0,0,1], [0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,1]], [[[0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1]], [[1,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0]]]], [ # Z-class [13][02] [[2], [0,2], [1,0,2], [0,1,0,2], [0,0,1,0,2], [0,0,0,1,0,2], [0,0,0,0,1,0,2], [0,0,0,0,0,1,0,2], [0,0,0,0,0,0,1,0,2], [0,0,0,0,0,0,0,1,0,2], [0,0,0,0,0,0,0,0,1,0,2], [1,0,0,0,0,0,0,0,0,1,0,2], [0,1,0,0,0,0,0,0,0,0,1,0,2]], [[[0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,1,0,-1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,-1,0,1,0,0,0], [0,0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,-1,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0,0], [0,-1,0,1,0,0,0,0,0,0,0,0,1], [-1,0,0,1,0,-1,0,1,0,-1,0,1,0]], [[-1,0,1,0,-1,-1,1,1,-1,-1,1,1,0], [0,1,1,0,-1,0,1,0,-1,0,1,0,-1], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,1,1,-1,-1,1,1,0,-1,0,1,0,-1], [0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,0,0,0,1,0,-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,-1,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,-1,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,1,0,0,0,0,0], [0,1,0,0,-1,0,1,0,-1,0,1,0,-1]]]], [ # Z-class [13][03] [[13], [-11,13], [9,-11,13], [-7,9,-11,13], [5,-7,9,-11,13], [-3,5,-7,9,-11,13], [1,-3,5,-7,9,-11,13], [1,1,-3,5,-7,9,-11,13], [-3,1,1,-3,5,-7,9,-11,13], [5,-3,1,1,-3,5,-7,9,-11,13], [-7,5,-3,1,1,-3,5,-7,9,-11,13], [9,-7,5,-3,1,1,-3,5,-7,9,-11,13], [-11,9,-7,5,-3,1,1,-3,5,-7,9,-11,13]], [[[1,1,1,1,1,1,1,1,1,1,1,1,1], [-1,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1], [1,0,0,0,0,1,1,1,1,1,1,1,1], [-1,0,0,0,0,0,0,-1,-1,-1,-1,-1,-1], [1,0,0,0,0,0,0,0,0,1,1,1,1], [-1,0,0,0,0,0,0,0,0,0,0,-1,-1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,-1,-1,-1,0,0], [0,0,0,0,0,0,1,1,1,1,1,0,0], [0,0,0,0,-1,-1,-1,-1,-1,-1,-1,0,0], [0,0,1,1,1,1,1,1,1,1,1,0,0], [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0,0]], [[0,-1,0,0,0,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0], [0,0,0,0,0,0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,0,0,0,0,0,-1], [-1,0,0,0,0,0,0,0,0,0,0,0,0]]]], [ # Z-class [13][04] [[13], [-1,13], [-1,-1,13], [-1,-1,-1,13], [-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,13], [-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,13]], [[[0,-1,0,0,0,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0], [0,0,0,0,0,0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,0,0,0,0,0,-1], [1,1,1,1,1,1,1,1,1,1,1,1,1]], [[1,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0], [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]]]], [ # Z-class [13][05] [[2], [1,2], [1,1,2], [1,1,1,2], [1,1,1,1,2], [1,1,1,1,1,2], [1,1,1,1,1,1,2], [1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,2]], [[[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,-1], [0,0,0,0,0,0,0,0,0,0,-1,1,0], [0,0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,0,0,0,0,-1,0,0,1,0], [0,0,0,0,0,0,0,-1,0,0,0,1,0], [0,0,0,0,0,0,-1,0,0,0,0,1,0], [0,0,0,0,0,-1,0,0,0,0,0,1,0], [0,0,0,0,-1,0,0,0,0,0,0,1,0], [0,0,0,-1,0,0,0,0,0,0,0,1,0], [0,0,-1,0,0,0,0,0,0,0,0,1,0], [0,-1,0,0,0,0,0,0,0,0,0,1,0], [-1,0,0,0,0,0,0,0,0,0,0,1,0]], [[-1,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,1,-1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,-1,1,0], [0,0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,0,0,0,0,-1,0,0,1,0], [0,0,0,0,0,0,0,-1,0,0,0,1,0], [0,0,0,0,0,0,-1,0,0,0,0,1,0], [0,0,0,0,0,-1,0,0,0,0,0,1,0], [0,0,0,0,-1,0,0,0,0,0,0,1,0], [0,0,0,-1,0,0,0,0,0,0,0,1,0], [0,0,-1,0,0,0,0,0,0,0,0,1,0], [0,-1,0,0,0,0,0,0,0,0,0,1,0]]]], [ # Z-class [13][06] [[12], [5,12], [-2,5,12], [-2,-2,5,12], [-2,-2,-2,5,12], [-2,-2,-2,-2,5,12], [-2,-2,-2,-2,-2,5,12], [-2,-2,-2,-2,-2,-2,5,12], [-2,-2,-2,-2,-2,-2,-2,5,12], [-2,-2,-2,-2,-2,-2,-2,-2,5,12], [-2,-2,-2,-2,-2,-2,-2,-2,-2,5,12], [-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,5,12], [5,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,5,12]], [[[0,-1,0,-1,0,-1,0,-1,0,-1,0,-1,0], [0,-1,0,-1,0,-1,0,-1,0,-1,0,0,-1], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0], [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]], [[1,0,1,0,1,0,1,0,1,0,0,1,0], [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,-1], [0,0,0,0,0,0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,0,-1,1,-1,0,0], [0,0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,0,-1,1,-1,0,0,0,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0], [0,0,0,0,-1,1,-1,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,-1,1,-1,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,1,0,1,0,1,0,1,0,1]]]], [ # Z-class [13][07] [[7], [5,7], [3,5,7], [1,3,5,7], [-1,1,3,5,7], [-3,-1,1,3,5,7], [-5,-3,-1,1,3,5,7], [-5,-5,-3,-1,1,3,5,7], [-3,-5,-5,-3,-1,1,3,5,7], [-1,-3,-5,-5,-3,-1,1,3,5,7], [1,-1,-3,-5,-5,-3,-1,1,3,5,7], [3,1,-1,-3,-5,-5,-3,-1,1,3,5,7], [5,3,1,-1,-3,-5,-5,-3,-1,1,3,5,7]], [[[0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,-1,1,0,0,0,0,-1,0], [0,0,0,0,-1,0,1,0,0,0,-1,-1,1], [0,0,0,-1,0,0,1,0,0,-1,-1,0,1], [0,0,-1,0,0,0,1,0,-1,-1,0,0,1], [0,-1,0,0,0,0,1,-1,-1,0,0,0,1], [-1,0,0,0,0,0,0,-1,0,0,0,0,1]], [[-1,-1,-1,0,1,1,0,-1,-1,0,0,1,1], [0,-1,-1,0,1,1,1,-1,-1,0,0,1,1], [0,0,-1,-1,1,1,1,0,-1,-1,0,1,1], [0,0,0,-1,0,1,1,0,0,-1,-1,1,1], [0,0,0,0,-1,1,1,0,0,-1,0,0,1], [0,0,1,0,-1,1,0,0,0,0,0,0,0], [0,1,1,0,-1,0,0,0,1,0,0,0,-1], [0,1,1,0,-1,-1,0,0,1,0,0,-1,-1], [-1,1,1,1,-1,-1,-1,0,1,1,0,-1,-1], [-1,0,1,1,0,-1,-1,-1,1,1,1,-1,-1], [-1,0,0,1,1,-1,-1,-1,0,1,1,0,-1], [-1,0,0,0,1,-1,0,-1,0,1,0,0,0], [-1,0,-1,0,1,0,0,-1,0,0,0,0,1]]]], [ # Z-class [13][08] [[5], [3,5], [2,3,5], [1,2,3,5], [-1,1,2,3,5], [-3,-1,1,2,3,5], [-3,-3,-1,1,2,3,5], [-3,-3,-3,-1,1,2,3,5], [-3,-3,-3,-3,-1,1,2,3,5], [-1,-3,-3,-3,-3,-1,1,2,3,5], [1,-1,-3,-3,-3,-3,-1,1,2,3,5], [2,1,-1,-3,-3,-3,-3,-1,1,2,3,5], [3,2,1,-1,-3,-3,-3,-3,-1,1,2,3,5]], [[[0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,1,0,-1,0,0,1,0,-1,1,0], [0,0,0,1,0,0,0,-1,0,1,0,1,-1], [0,0,-1,1,0,0,0,-1,0,0,0,1,-1], [0,0,0,1,0,0,0,0,0,0,0,1,-1], [0,0,0,1,-1,0,0,0,0,0,0,0,-1], [0,0,-1,0,0,1,0,0,-1,0,0,0,0], [0,0,0,0,0,0,-1,1,0,0,0,-1,0], [0,0,0,0,0,0,0,1,0,0,0,-1,1], [0,0,0,-1,0,0,0,1,-1,0,0,-1,1], [0,1,0,-1,0,0,0,1,0,0,0,-1,1], [-1,0,1,0,0,-1,0,1,0,0,0,0,1]], [[-1,-1,0,0,0,0,0,1,-1,-1,0,1,1], [0,0,0,-1,0,1,0,1,-1,0,0,0,1], [0,0,-1,0,0,1,0,0,0,0,0,0,1], [-1,1,0,0,0,0,0,0,0,1,0,0,0], [0,1,0,0,0,0,-1,0,1,1,0,-1,0], [0,1,0,0,0,0,0,-1,1,1,0,-1,0], [0,1,0,0,0,-1,0,-1,1,1,0,-1,-1], [0,1,1,0,-1,-1,0,0,1,0,0,-1,-1], [1,0,0,0,0,-1,0,0,1,0,-1,-1,0], [0,0,0,0,0,-1,1,0,0,-1,0,0,0], [0,-1,1,0,0,-1,0,1,0,-1,0,0,0], [0,-1,0,0,0,0,0,1,-1,-1,0,0,1], [0,-1,0,0,0,0,1,1,-1,-1,0,1,1]]]], [ # Z-class [13][09] [[3], [1,3], [-1,1,3], [-1,-1,1,3], [0,-1,-1,1,3], [0,0,-1,-1,1,3], [0,0,0,-1,-1,1,3], [0,0,0,0,-1,-1,1,3], [0,0,0,0,0,-1,-1,1,3], [0,0,0,0,0,0,-1,-1,1,3], [-1,0,0,0,0,0,0,-1,-1,1,3], [-1,-1,0,0,0,0,0,0,-1,-1,1,3], [1,-1,-1,0,0,0,0,0,0,-1,-1,1,3]], [[[-1,0,0,-1,1,-1,0,0,-1,0,0,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,1,-1,1,0], [0,0,0,0,0,0,0,0,0,0,-1,1,-1], [0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0], [0,0,1,-1,1,0,0,1,0,0,1,-1,1], [-1,1,0,0,1,-1,1,0,0,1,0,0,1], [0,0,0,1,0,0,0,0,0,0,0,0,0], [1,-1,0,1,-1,1,0,-1,1,-1,0,0,-1], [1,-1,0,0,-1,0,0,-1,1,-1,0,0,-1], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,-1,1,0,0,0], [-1,1,-1,0,1,-1,1,0,-1,1,-1,0,0]], [[1,0,0,0,0,0,0,0,0,0,0,0,0], [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,-1], [1,-1,0,1,-1,1,0,0,1,-1,1,0,-1], [1,-1,1,0,0,1,0,0,1,-1,1,0,0], [0,0,0,0,0,0,0,-1,1,-1,0,0,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,-1,1,-1,0,0,0,0], [0,0,0,0,0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,-1,1,-1,0,0,0,0,0], [-1,1,0,0,1,-1,1,0,0,1,0,0,1], [-1,1,-1,0,1,-1,1,0,0,1,-1,1,0], [0,0,-1,0,0,0,0,0,0,0,0,0,0]]]], [ # Z-class [13][10] [[4], [2,4], [1,2,4], [-1,1,2,4], [-1,-1,1,2,4], [-1,-1,-1,1,2,4], [0,-1,-1,-1,1,2,4], [0,0,-1,-1,-1,1,2,4], [-1,0,0,-1,-1,-1,1,2,4], [-1,-1,0,0,-1,-1,-1,1,2,4], [-1,-1,-1,0,0,-1,-1,-1,1,2,4], [1,-1,-1,-1,0,0,-1,-1,-1,1,2,4], [2,1,-1,-1,-1,0,0,-1,-1,-1,1,2,4]], [[[0,-1,0,1,0,0,-1,0,1,0,-1,0,1], [-1,0,0,0,0,0,0,0,0,1,-1,0,1], [0,0,0,0,0,0,0,0,0,1,0,-1,1], [0,0,0,-1,1,0,0,0,0,1,0,-1,1], [0,0,0,0,1,-1,0,1,0,0,0,0,1], [0,0,0,0,0,0,0,0,1,-1,0,1,0], [0,0,-1,1,0,-1,0,0,1,-1,-1,1,0], [0,1,-1,0,0,0,0,-1,1,0,-1,1,-1], [0,1,-1,0,0,0,0,0,0,0,0,0,-1], [1,0,0,-1,0,1,-1,0,0,0,1,-1,-1], [0,0,0,-1,1,0,-1,1,-1,0,1,-1,0], [0,-1,1,0,0,0,-1,1,0,-1,1,0,0], [-1,-1,1,0,0,0,-1,1,0,-1,0,0,1]], [[-1,-1,1,0,0,-1,0,1,0,-1,0,0,1], [-1,0,0,0,0,-1,0,1,0,-1,0,1,0], [-1,0,0,0,0,-1,0,1,-1,0,0,0,0], [-1,1,0,0,-1,0,1,0,-1,0,0,1,-1], [0,0,0,0,-1,1,0,-1,0,0,0,0,-1], [0,1,0,-1,0,1,0,-1,0,0,0,0,-1], [1,0,0,-1,0,1,0,-1,0,0,1,-1,-1], [1,0,0,0,0,0,0,0,0,-1,1,0,-1], [1,0,0,0,0,0,0,0,0,0,1,0,-1], [0,0,1,0,0,0,0,1,-1,0,1,0,0], [0,0,1,0,-1,1,0,0,0,0,1,0,0], [-1,0,1,0,0,0,0,0,0,0,0,0,1], [-1,0,1,-1,0,0,0,0,0,0,0,0,1]]]], [ # Z-class [13][11] [[4], [2,4], [2,2,4], [1,2,2,4], [0,1,2,2,4], [0,0,1,2,2,4], [-1,0,0,1,2,2,4], [-1,-1,0,0,1,2,2,4], [0,-1,-1,0,0,1,2,2,4], [0,0,-1,-1,0,0,1,2,2,4], [1,0,0,-1,-1,0,0,1,2,2,4], [2,1,0,0,-1,-1,0,0,1,2,2,4], [2,2,1,0,0,-1,-1,0,0,1,2,2,4]], [[[0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,-1,1], [0,0,0,0,0,0,0,0,0,0,-1,0,1], [0,0,0,0,1,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,-1,0,0,0,0], [0,1,0,-1,1,0,-1,1,0,-1,0,1,-1], [1,0,-1,0,1,-1,0,1,-1,-1,1,0,-1], [0,1,-1,-1,1,0,-1,1,0,-1,0,1,-1], [1,0,-1,0,1,-1,0,1,-1,0,1,0,-1], [0,0,0,-1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,1,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0,0,0,0,1], [-1,0,0,0,0,0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,0,0,0,0,0,-1,0,1,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0], [0,0,0,0,0,0,0,0,0,-1,1,0,0], [1,-1,0,1,0,-1,1,0,-1,0,1,-1,0], [0,0,0,1,0,-1,0,0,0,0,1,-1,0], [0,-1,1,1,-1,0,1,-1,0,1,0,-1,1], [0,-1,0,1,0,0,0,-1,0,1,0,-1,1], [0,-1,0,1,-1,0,1,-1,0,1,0,-1,1], [0,-1,0,1,0,0,0,-1,0,1,0,0,0], [0,0,-1,1,0,0,0,0,0,0,0,0,0], [-1,0,0,0,0,1,0,-1,0,0,0,1,0], [0,0,-1,0,1,0,0,0,0,-1,0,1,0]]]], [ # Z-class [13][12] [[15], [-5,15], [-5,-5,15], [3,-5,-5,15], [-1,3,-5,-5,15], [7,-1,3,-5,-5,15], [-5,7,-1,3,-5,-5,15], [-5,-5,7,-1,3,-5,-5,15], [7,-5,-5,7,-1,3,-5,-5,15], [-1,7,-5,-5,7,-1,3,-5,-5,15], [3,-1,7,-5,-5,7,-1,3,-5,-5,15], [-5,3,-1,7,-5,-5,7,-1,3,-5,-5,15], [-5,-5,3,-1,7,-5,-5,7,-1,3,-5,-5,15]], [[[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,-1], [1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,1,1,0,0,-1,-1,0,0,0,0], [-1,0,-1,0,-1,0,0,1,1,1,1,0,0], [0,0,0,0,0,0,0,0,0,-1,-1,-1,0], [0,0,1,0,1,0,0,0,0,0,0,0,-1], [0,-1,-1,0,0,0,0,0,0,1,1,1,0], [0,1,1,1,0,0,0,0,0,0,-1,-1,0], [-1,0,0,0,0,0,0,0,1,0,1,0,0], [0,-1,-1,-1,0,0,0,0,0,0,0,0,0], [0,0,1,1,1,1,0,0,-1,0,-1,0,-1], [0,0,0,0,-1,-1,0,0,1,1,1,0,0]], [[-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0], [0,0,1,1,1,0,-1,-1,-1,0,0,0,-1], [1,1,0,0,0,0,1,0,0,-1,0,0,1], [0,-1,-1,-1,0,1,1,1,0,0,-1,0,0], [-1,0,0,0,0,-1,-1,0,1,1,1,0,-1], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [1,0,1,0,1,0,0,-1,-1,-1,-1,0,0], [0,1,0,0,0,0,1,1,1,0,0,-1,0], [0,-1,-1,-1,-1,0,0,1,0,1,0,1,0], [-1,0,1,1,1,0,-1,-1,0,0,0,0,-1], [0,0,0,0,0,0,1,0,0,-1,0,-1,0], [1,0,0,0,0,0,0,0,-1,0,-1,0,0], [0,1,0,0,0,0,0,1,1,0,0,0,0]]]], [ # Z-class [13][13] [[13], [-3,13], [-7,-3,13], [5,-7,-3,13], [1,5,-7,-3,13], [-7,1,5,-7,-3,13], [5,-7,1,5,-7,-3,13], [5,5,-7,1,5,-7,-3,13], [-7,5,5,-7,1,5,-7,-3,13], [1,-7,5,5,-7,1,5,-7,-3,13], [5,1,-7,5,5,-7,1,5,-7,-3,13], [-7,5,1,-7,5,5,-7,1,5,-7,-3,13], [-3,-7,5,1,-7,5,5,-7,1,5,-7,-3,13]], [[[0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0], [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], [0,1,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0]], [[1,1,1,1,1,1,1,0,0,0,0,0,0], [0,0,0,0,-1,-1,0,0,0,0,0,1,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0], [0,0,0,0,1,1,1,0,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,-1,0,0,0,0,0,1], [0,0,0,0,1,1,1,1,1,1,1,0,0], [0,0,0,0,0,0,1,0,0,0,-1,0,-1], [0,0,0,0,-1,-1,-1,-1,0,-1,0,0,0], [0,0,0,1,1,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,1,1,0,0,0,0,0], [0,-1,0,-1,-1,-1,-1,0,0,0,0,0,0], [-1,0,0,0,1,0,0,0,0,0,0,-1,0]]]], [ # Z-class [13][14] [[5], [-1,5], [-1,-1,5], [-1,-1,-1,5], [1,-1,-1,-1,5], [-1,1,-1,-1,-1,5], [1,-1,1,-1,-1,-1,5], [1,1,-1,1,-1,-1,-1,5], [-1,1,1,-1,1,-1,-1,-1,5], [1,-1,1,1,-1,1,-1,-1,-1,5], [-1,1,-1,1,1,-1,1,-1,-1,-1,5], [-1,-1,1,-1,1,1,-1,1,-1,-1,-1,5], [-1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,5]], [[[-1,0,-1,-1,0,-1,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,1,0], [0,-1,0,0,0,1,0,0,0,-1,0,-1,-1], [0,1,0,0,0,-1,0,-1,-1,0,-1,0,0], [1,0,1,0,0,0,-1,0,0,0,1,0,1], [-1,0,0,0,1,0,1,1,0,1,0,0,0], [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,-1,-1,0,-1,0,0,0,1,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [1,1,0,1,0,0,0,-1,0,0,0,1,0], [0,0,1,0,1,1,0,1,0,0,0,-1,0]], [[1,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [0,-1,0,0,0,1,0,0,0,-1,0,-1,-1], [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,-1,0,0,0,1,0,1,1,0,1], [0,0,0,1,0,1,1,0,1,0,0,0,-1], [0,0,0,0,0,0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0], [0,-1,0,-1,-1,0,-1,0,0,0,1,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0]]]], [ # Z-class [13][15] [[4], [-2,4], [0,-2,4], [1,0,-2,4], [0,1,0,-2,4], [-1,0,1,0,-2,4], [1,-1,0,1,0,-2,4], [1,1,-1,0,1,0,-2,4], [-1,1,1,-1,0,1,0,-2,4], [0,-1,1,1,-1,0,1,0,-2,4], [1,0,-1,1,1,-1,0,1,0,-2,4], [0,1,0,-1,1,1,-1,0,1,0,-2,4], [-2,0,1,0,-1,1,1,-1,0,1,0,-2,4]], [[[0,-1,-1,1,1,0,-1,0,1,0,-1,0,1], [0,1,1,-1,-1,0,0,-1,-1,0,1,0,-1], [0,0,0,0,0,1,1,1,0,0,0,0,0], [1,0,0,1,1,-1,-2,-1,0,0,-1,0,1], [-1,0,1,0,-1,0,1,0,-1,-1,1,1,0], [0,-1,-1,-1,0,0,0,1,1,1,0,0,0], [0,0,1,2,1,0,0,0,0,-1,-1,0,0], [1,0,-1,-1,0,0,-1,-1,0,0,0,0,1], [-1,0,1,0,-1,0,1,1,0,0,0,0,-1], [1,1,0,0,1,1,0,-1,-1,0,0,0,0], [0,-1,0,1,0,-1,-1,0,0,-1,-1,0,1], [-1,0,0,-1,0,1,1,0,0,1,1,0,-1], [1,0,0,0,0,0,0,0,0,0,0,0,0]], [[1,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0], [1,0,-1,0,1,0,-1,-1,0,0,-1,-1,0], [0,1,0,-1,-1,1,1,0,0,1,1,0,-1], [-1,-1,0,0,0,-1,0,1,1,0,0,0,0], [0,1,1,0,0,1,1,-1,-2,-1,0,0,-1], [1,0,-1,-1,-1,-1,-1,0,1,1,1,1,1], [-1,0,1,1,1,1,1,1,0,-1,-1,-1,-1], [1,1,0,-1,0,0,-1,-2,-1,1,1,0,0], [0,-1,-1,0,0,0,0,1,1,0,-1,0,0], [0,1,0,-1,0,1,1,0,0,1,1,-1,-1], [-1,0,1,0,-1,-1,0,0,-1,-1,0,1,0]]]], [ # Z-class [13][16] [[13], [-7,13], [1,-7,13], [1,1,-7,13], [-1,1,1,-7,13], [3,-1,1,1,-7,13], [-1,3,-1,1,1,-7,13], [-1,-1,3,-1,1,1,-7,13], [3,-1,-1,3,-1,1,1,-7,13], [-1,3,-1,-1,3,-1,1,1,-7,13], [1,-1,3,-1,-1,3,-1,1,1,-7,13], [1,1,-1,3,-1,-1,3,-1,1,1,-7,13], [-7,1,1,-1,3,-1,-1,3,-1,1,1,-7,13]], [[[2,2,1,0,-1,-2,-3,-2,-1,0,1,2,2], [-1,0,1,2,2,2,2,1,0,-1,-2,-3,-2], [1,0,-1,-1,-1,-1,-1,-1,-1,0,1,2,2], [1,1,1,0,0,0,0,0,0,0,0,0,0], [-2,-2,-2,-1,-1,0,1,2,2,2,1,0,-1], [2,2,2,1,0,-1,-2,-3,-2,-1,0,1,2], [0,0,0,1,1,1,1,1,0,-1,-1,-1,-1], [-1,-1,-1,-1,0,1,1,1,1,1,0,0,0], [2,1,0,-1,-2,-3,-2,-1,0,1,2,2,2], [-1,0,1,2,2,2,1,0,-1,-1,-2,-2,-2], [0,0,0,0,0,0,0,0,0,0,1,1,1], [2,2,1,0,-1,-1,-1,-1,-1,-1,-1,0,1], [-2,-3,-2,-1,0,1,2,2,2,2,1,0,-1]], [[1,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0], [-1,-1,-1,0,1,1,1,1,1,0,-1,-1,-1], [1,1,1,1,0,-1,-1,-1,-1,0,1,1,1], [-1,-1,-1,-1,0,1,1,1,1,0,0,0,-1], [0,0,0,0,0,0,0,0,0,1,0,0,0], [1,0,-1,-2,-2,-2,-1,0,1,1,2,2,2], [-1,0,1,2,2,2,1,1,0,-1,-2,-2,-2], [0,0,0,0,0,0,1,0,0,0,0,0,0], [-1,-1,-1,-1,0,0,0,1,1,1,1,0,-1], [1,1,1,1,1,1,0,-1,-1,-1,-1,0,1], [-1,-1,-1,-1,-1,-1,0,1,1,1,1,1,0]]]], [ # Z-class [13][17] [[6], [1,6], [2,1,6], [2,2,1,6], [-2,2,2,1,6], [1,-2,2,2,1,6], [-2,1,-2,2,2,1,6], [-2,-2,1,-2,2,2,1,6], [1,-2,-2,1,-2,2,2,1,6], [-2,1,-2,-2,1,-2,2,2,1,6], [2,-2,1,-2,-2,1,-2,2,2,1,6], [2,2,-2,1,-2,-2,1,-2,2,2,1,6], [1,2,2,-2,1,-2,-2,1,-2,2,2,1,6]], [[[0,0,-1,0,1,0,-1,0,0,0,0,0,0], [0,0,0,0,1,-1,0,0,1,-1,0,0,0], [-1,1,0,0,0,0,-1,0,1,0,0,0,0], [0,0,0,0,1,-1,0,0,0,0,1,0,-1], [0,0,1,0,0,-1,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,-1,1,0,0,-1,1,0,0,0,0,0,0], [0,0,1,0,-1,0,0,0,0,1,-1,0,0], [0,-1,0,1,0,0,0,0,-1,1,0,0,0], [0,-1,1,0,0,0,0,0,0,0,-1,1,0], [0,0,0,0,0,1,-1,0,0,1,-1,0,0], [0,-1,0,0,1,0,0,-1,0,0,0,0,0], [0,0,0,0,0,0,-1,0,1,0,-1,0,0]], [[1,0,0,0,0,0,0,1,0,0,-1,0,0], [0,0,0,0,0,0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,0,0,0,-1,0,0], [0,0,1,-1,0,0,0,0,1,0,-1,0,0], [-1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,1,0,0,0,0,-1,1,0], [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], [1,0,0,-1,0,0,1,0,0,0,0,0,0], [0,1,-1,0,0,0,0,0,0,0,1,-1,0], [1,0,-1,0,1,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,1,0,-1,0], [0,0,-1,1,0,0,0,0,0,0,0,-1,1]]]] ]; MakeImmutable( IMFList[13].matrices );