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Views: 418346############################################################################# ## #A imf1to9.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 dimensions 1 to 9, ## ## [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 representative of ## the irreducible maximal finite integral matrix groups of dimension 1. ## IMFList[1].matrices := [ [ # Z-class [01][01] [[1]], [[[-1]]]] ]; MakeImmutable( IMFList[1].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 2. ## IMFList[2].matrices := [ [ # Z-class [02][01] [[1], [0,1]], [[[0,1], [1,0]], [[-1,0], [0,1]]]], [ # Z-class [02][02] [[2], [-1,2]], [[[0,-1], [1,1]], [[0,1], [1,0]]]] ]; MakeImmutable( IMFList[2].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 3. ## IMFList[3].matrices := [ [ # Z-class [03][01] [[1], [0,1], [0,0,1]], [[[1,0,0], [0,0,1], [0,1,0]], [[0,0,-1], [1,0,0], [0,1,0]]]], [ # Z-class [03][02] [[3], [-1,3], [-1,-1,3]], [[[0,1,0], [1,0,0], [0,0,1]], [[-1,0,0], [0,0,-1], [1,1,1]]]], [ # Z-class [03][03] [[2], [1,2], [1,1,2]], [[[0,1,0], [1,0,0], [0,0,1]], [[-1,1,0], [0,1,-1], [0,1,0]]]] ]; MakeImmutable( IMFList[3].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 4. ## IMFList[4].matrices := [ [ # Z-class [04][01] [[1], [0,1], [0,0,1], [0,0,0,1]], [[[0,1,0,0], [1,0,0,0], [0,0,1,0], [0,0,0,1]], [[-1,0,0,0], [0,0,1,0], [0,0,0,1], [0,1,0,0]]]], [ # Z-class [04][02] [[2], [1,2], [0,1,2], [0,1,0,2]], [[[-1,1,-1,-1], [-1,0,0,0], [0,-1,1,0], [0,-1,0,1]], [[0,1,-1,-1], [0,0,0,-1], [-1,1,0,-1], [0,-1,0,0]]]], [ # Z-class [04][03] [[2], [-1,2], [0,0,2], [0,0,-1,2]], [[[0,1,0,0], [1,0,0,0], [0,0,1,0], [0,0,0,1]], [[0,-1,0,0], [1,1,0,0], [0,0,1,0], [0,0,0,1]], [[0,0,1,0], [0,0,0,1], [1,0,0,0], [0,1,0,0]]]], [ # Z-class [04][04] [[4], [-2,4], [-2,1,4], [1,-2,-2,4]], [[[0,1,0,0], [1,0,0,0], [0,0,0,1], [0,0,1,0]], [[0,-1,0,0], [1,1,0,0], [0,0,0,-1], [0,0,1,1]], [[1,0,0,0], [0,0,1,0], [0,1,0,0], [0,0,0,1]]]], [ # Z-class [04][05] [[2], [1,2], [1,1,2], [1,1,1,2]], [[[0,0,0,1], [-1,0,0,1], [0,-1,0,1], [0,0,-1,1]], [[0,1,0,0], [1,0,0,0], [0,0,1,0], [0,0,0,1]]]], [ # Z-class [04][06] [[4], [-1,4], [-1,-1,4], [-1,-1,-1,4]], [[[1,1,1,1], [-1,0,0,0], [0,-1,0,0], [0,0,-1,0]], [[0,1,0,0], [1,0,0,0], [0,0,1,0], [0,0,0,1]]]] ]; MakeImmutable( IMFList[4].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 5. ## IMFList[5].matrices := [ [ # Z-class [05][01] [[1], [0,1], [0,0,1], [0,0,0,1], [0,0,0,0,1]], [[[-1,0,0,0,0], [0,1,0,0,0], [0,0,0,1,0], [0,0,0,0,1], [0,0,1,0,0]], [[0,1,0,0,0], [0,0,1,0,0], [0,0,0,1,0], [1,0,0,0,0], [0,0,0,0,1]]]], [ # Z-class [05][02] [[2], [1,2], [0,1,2], [0,0,1,2], [0,0,1,0,2]], [[[-1,2,-2,1,1], [0,1,-1,1,1], [0,0,0,1,0], [0,0,1,0,-1], [0,0,-1,1,0]], [[0,1,0,0,0], [0,0,1,0,0], [1,-1,1,0,0], [1,-1,1,0,-1], [1,-1,1,-1,0]]]], [ # Z-class [05][03] [[4], [0,4], [0,0,4], [0,0,0,4], [2,2,2,2,5]], [[[-1,0,0,0,0], [0,1,0,0,0], [0,0,0,1,0], [-1,-1,-1,-1,2], [-1,0,0,0,1]], [[0,1,0,0,0], [0,0,1,0,0], [0,0,0,1,0], [1,0,0,0,0], [0,0,0,0,1]]]], [ # Z-class [05][04] [[5], [-1,5], [-1,-1,5], [-1,-1,-1,5], [-1,-1,-1,-1,5]], [[[0,1,0,0,0], [1,0,0,0,0], [0,0,1,0,0], [0,0,0,1,0], [0,0,0,0,1]], [[-1,0,0,0,0], [0,0,-1,0,0], [0,0,0,-1,0], [0,0,0,0,-1], [1,1,1,1,1]]]], [ # Z-class [05][05] [[2], [1,2], [1,1,2], [1,1,1,2], [1,1,1,1,2]], [[[0,1,0,0,0], [1,0,0,0,0], [0,0,1,0,0], [0,0,0,1,0], [0,0,0,0,1]], [[-1,1,0,0,0], [0,1,-1,0,0], [0,1,0,-1,0], [0,1,0,0,-1], [0,1,0,0,0]]]], [ # Z-class [05][06] [[4], [1,4], [-2,1,4], [-2,-2,1,4], [-2,1,1,1,4]], [[[1,0,0,0,0], [1,-1,1,-1,1], [0,0,1,0,0], [0,0,0,1,0], [0,0,0,0,1]], [[-1,1,-1,1,-1], [0,0,-1,0,0], [0,0,0,-1,0], [1,0,1,0,0], [1,0,0,0,1]]]], [ # Z-class [05][07] [[3], [1,3], [-1,1,3], [-1,-1,1,3], [-1,1,1,1,3]], [[[1,0,0,0,0], [0,1,0,1,-1], [0,0,1,0,0], [0,0,0,0,1], [0,0,0,1,0]], [[0,-1,0,-1,1], [0,0,-1,0,0], [1,0,0,0,0], [0,1,0,0,0], [0,1,-1,1,0]]]] ]; MakeImmutable( IMFList[5].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 6. ## IMFList[6].matrices := [ [ # Z-class [06][01] [[1], [0,1], [0,0,1], [0,0,0,1], [0,0,0,0,1], [0,0,0,0,0,1]], [[[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[-1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1], [0,1,0,0,0,0]]]], [ # Z-class [06][02] [[2], [1,2], [0,1,2], [0,0,1,2], [0,0,0,1,2], [0,0,0,1,0,2]], [[[1,0,0,0,0,0], [1,-1,2,-2,1,1], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[-1,1,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,1,-1,1,0,-1], [0,-1,1,-1,1,0]]]], [ # Z-class [06][03] [[2], [0,2], [0,0,2], [0,0,0,2], [0,0,0,0,2], [1,1,1,1,1,3]], [[[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[-1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [-1,-1,-1,-1,-1,2], [-1,0,0,0,0,1]]]], [ # Z-class [06][04] [[2], [1,2], [1,1,2], [0,0,0,2], [0,0,0,1,2], [0,0,0,1,1,2]], [[[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[-1,1,0,0,0,0], [0,1,-1,0,0,0], [0,1,0,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1], [1,0,0,0,0,0], [0,1,0,0,0,0], [0,0,1,0,0,0]]]], [ # Z-class [06][05] [[3], [-1,3], [-1,-1,3], [0,0,0,3], [0,0,0,-1,3], [0,0,0,-1,-1,3]], [[[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[-1,0,0,0,0,0], [0,0,-1,0,0,0], [1,1,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1], [1,0,0,0,0,0], [0,1,0,0,0,0], [0,0,1,0,0,0]]]], [ # Z-class [06][06] [[3], [1,3], [1,1,3], [1,1,1,3], [1,1,1,1,3], [1,1,-1,-1,1,3]], [[[1,0,-1,-1,1,-1], [0,0,0,-1,0,0], [0,1,-1,-1,1,-1], [0,0,-1,0,0,0], [1,1,-1,-1,0,-1], [1,0,0,-1,0,-1]], [[1,0,0,0,0,0], [0,1,0,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [1,1,-1,-1,1,-2], [1,1,-1,-1,0,-1]]]], [ # Z-class [06][07] [[2], [-1,2], [0,0,2], [0,0,-1,2], [0,0,0,0,2], [0,0,0,0,-1,2]], [[[0,-1,0,0,0,0], [1,1,0,0,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1], [0,0,1,0,0,0], [0,0,0,1,0,0]], [[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]], [[0,0,0,0,-1,0], [0,0,0,0,0,-1], [-1,0,0,0,0,0], [0,-1,0,0,0,0], [0,0,-1,0,0,0], [0,0,0,-1,0,0]]]], [ # Z-class [06][08] [[2], [0,2], [-1,0,2], [0,-1,-1,2], [0,0,0,-1,2], [0,0,0,0,-1,2]], [[[0,0,1,0,0,0], [1,1,1,1,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1], [-1,0,-1,-1,-1,-1]], [[0,0,-1,0,0,0], [1,1,1,1,0,0], [0,0,0,-1,0,0], [0,-1,0,0,0,0], [-1,0,-1,-1,-1,0], [0,0,0,0,0,-1]]]], [ # Z-class [06][09] [[4], [1,4], [-2,1,4], [-2,-2,1,4], [1,-2,-2,1,4], [1,1,-2,-2,1,4]], [[[-1,0,-1,0,0,0], [-1,0,0,-1,0,0], [0,0,0,-1,0,-1], [0,1,0,0,1,-1], [0,0,0,1,0,0], [0,0,0,1,-1,1]], [[1,-1,1,1,-1,1], [1,-1,0,0,-1,0], [0,0,0,-1,0,0], [0,1,0,0,1,0], [0,1,0,1,0,0], [0,0,0,0,0,-1]]]], [ # Z-class [06][10] [[4], [2,4], [2,2,4], [-2,-1,-1,4], [-1,-2,-1,2,4], [-1,-1,-2,2,2,4]], [[[0,0,0,-1,0,0], [0,0,0,0,-1,0], [0,0,0,0,0,-1], [1,0,0,1,0,0], [0,1,0,0,1,0], [0,0,1,0,0,1]], [[0,0,0,1,-1,0], [0,0,0,0,-1,1], [0,0,0,0,-1,0], [1,-1,0,0,0,0], [0,-1,1,0,0,0], [0,-1,0,0,0,0]], [[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,0,1,0], [0,0,0,1,0,0], [0,0,0,0,0,1]]]], [ # Z-class [06][11] [[6], [-2,6], [-2,-2,6], [-3,1,1,6], [1,-3,1,-2,6], [1,1,-3,-2,-2,6]], [[[0,0,0,-1,0,0], [0,0,0,0,-1,0], [0,0,0,0,0,-1], [1,0,0,1,0,0], [0,1,0,0,1,0], [0,0,1,0,0,1]], [[0,0,0,1,0,0], [0,0,0,0,0,1], [0,0,0,-1,-1,-1], [1,0,0,0,0,0], [0,0,1,0,0,0], [-1,-1,-1,0,0,0]], [[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,0,1,0], [0,0,0,1,0,0], [0,0,0,0,0,1]]]], [ # Z-class [06][12] [[6], [-1,6], [-1,-1,6], [-1,-1,-1,6], [-1,-1,-1,-1,6], [-1,-1,-1,-1,-1,6]], [[[0,-1,0,0,0,0], [0,0,-1,0,0,0], [0,0,0,-1,0,0], [0,0,0,0,-1,0], [0,0,0,0,0,-1], [1,1,1,1,1,1]], [[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]]]], [ # Z-class [06][13] [[2], [1,2], [1,1,2], [1,1,1,2], [1,1,1,1,2], [1,1,1,1,1,2]], [[[1,-1,0,0,0,0], [1,0,-1,0,0,0], [1,0,0,-1,0,0], [1,0,0,0,-1,0], [1,0,0,0,0,-1], [1,0,0,0,0,0]], [[0,1,0,0,0,0], [1,0,0,0,0,0], [0,0,1,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,0,0,0,0,1]]]], [ # Z-class [06][14] [[4], [-1,4], [-2,-1,4], [1,-2,-1,4], [1,1,-2,-1,4], [-2,1,1,-2,-1,4]], [[[0,-1,-1,-1,0,0], [1,1,1,0,0,0], [-1,0,0,0,0,-1], [0,0,0,1,1,1], [0,0,-1,-1,-1,0], [0,0,1,0,0,0]], [[0,0,0,0,0,-1], [0,-1,0,-1,0,0], [0,0,0,1,0,1], [0,1,1,1,1,0], [0,0,0,-1,-1,-1], [1,0,0,0,0,1]]]], [ # Z-class [06][15] [[3], [-1,3], [-1,-1,3], [1,-1,0,3], [1,0,-1,-1,3], [0,1,-1,1,-1,3]], [[[0,0,0,-1,0,0], [0,0,0,0,-1,0], [-1,0,0,1,1,0], [0,0,0,0,0,-1], [0,-1,0,-1,0,1], [0,0,-1,0,-1,-1]], [[-1,0,0,0,0,0], [0,0,0,1,0,0], [0,0,0,0,1,0], [0,1,0,0,0,0], [0,0,1,0,0,0], [0,0,0,0,0,1]]]], [ # Z-class [06][16] [[4], [1,4], [2,1,4], [2,2,1,4], [1,2,2,1,4], [0,1,-1,-1,1,4]], [[[0,-1,0,0,0,0], [0,0,-1,0,0,0], [0,0,0,-1,0,0], [0,0,0,0,-1,0], [-1,0,0,0,0,0], [0,0,-1,0,1,-1]], [[-1,0,1,0,0,0], [0,-1,0,0,1,0], [0,0,1,0,0,0], [-1,-1,1,1,0,1], [0,0,0,0,1,0], [0,0,-1,0,1,-1]]]], [ # Z-class [06][17] [[5], [1,5], [-1,1,5], [-1,-1,1,5], [1,-1,-1,1,5], [2,2,2,2,2,5]], [[[0,-1,0,0,0,0], [0,0,-1,0,0,0], [0,0,0,-1,0,0], [0,0,0,0,-1,0], [-1,0,0,0,0,0], [0,0,0,0,0,-1]], [[0,0,0,0,0,1], [0,-1,0,-1,0,1], [1,0,1,0,0,-1], [1,0,0,1,0,-1], [0,0,-1,0,-1,1], [1,0,0,0,0,0]]]] ]; MakeImmutable( IMFList[6].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 7. ## IMFList[7].matrices := [ [ # Z-class [07][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]], [[[0,1,0,0,0,0,0], [0,0,1,0,0,0,0], [0,0,0,1,0,0,0], [1,0,0,0,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0], [0,1,0,0,0,0,0], [0,0,0,1,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,0,0,0,0,1], [0,0,1,0,0,0,0]]]], [ # Z-class [07][02] [[2], [1,2], [0,1,2], [0,0,1,2], [0,0,0,1,2], [0,0,0,0,1,2], [0,0,0,0,1,0,2]], [[[0,1,0,0,0,0,0], [0,0,1,0,0,0,0], [1,-1,1,0,0,0,0], [1,-1,1,-1,2,-1,-1], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,0,0,0,0,1]], [[-1,2,-2,2,-2,1,1], [0,1,-1,2,-2,1,1], [0,0,0,1,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,1,-1,1,0,-1], [0,0,-1,1,-1,1,0]]]], [ # Z-class [07][03] [[4], [0,4], [0,0,4], [0,0,0,4], [0,0,0,0,4], [0,0,0,0,0,4], [2,2,2,2,2,2,7]], [[[0,1,0,0,0,0,0], [0,0,1,0,0,0,0], [0,0,0,1,0,0,0], [1,0,0,0,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0], [0,1,0,0,0,0,0], [0,0,0,1,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [-1,-1,-1,-1,-1,-1,2], [-1,0,0,0,0,0,1]]]], [ # Z-class [07][04] [[7], [-1,7], [-1,-1,7], [-1,-1,-1,7], [-1,-1,-1,-1,7], [-1,-1,-1,-1,-1,7], [-1,-1,-1,-1,-1,-1,7]], [[[0,1,0,0,0,0,0], [1,0,0,0,0,0,0], [0,0,1,0,0,0,0], [0,0,0,1,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0], [0,0,0,-1,0,0,0], [0,0,0,0,-1,0,0], [0,0,0,0,0,-1,0], [0,0,0,0,0,0,-1], [1,1,1,1,1,1,1]]]], [ # Z-class [07][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]], [[[0,1,0,0,0,0,0], [1,0,0,0,0,0,0], [0,0,1,0,0,0,0], [0,0,0,1,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0], [0,0,0,0,0,0,1]], [[-1,1,0,0,0,0,0], [0,1,-1,0,0,0,0], [0,1,0,-1,0,0,0], [0,1,0,0,-1,0,0], [0,1,0,0,0,-1,0], [0,1,0,0,0,0,-1], [0,1,0,0,0,0,0]]]], [ # Z-class [07][06] [[2], [0,2], [1,0,2], [0,1,1,2], [0,0,0,1,2], [0,0,0,0,1,2], [0,0,0,0,0,1,2]], [[[1,-1,-1,1,0,0,0], [0,0,0,1,0,0,0], [1,0,0,0,0,0,0], [0,0,1,0,0,0,0], [0,-1,0,1,-1,0,0], [0,0,0,0,0,-1,0], [0,0,0,0,0,0,-1]], [[-1,0,1,-1,1,-1,1], [0,1,0,-1,1,-1,1], [-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0], [0,0,0,-1,0,0,0], [0,0,0,0,-1,0,0], [0,0,0,0,0,-1,0]]]], [ # Z-class [07][07] [[3], [1,3], [1,1,3], [1,1,1,3], [1,1,1,1,3], [1,1,-1,-1,-1,3], [1,1,1,1,1,-1,3]], [[[0,0,0,0,0,0,1], [0,0,0,0,0,-1,0], [0,0,0,0,1,0,0], [1,0,0,-1,0,-1,0], [1,0,-1,0,0,-1,0], [0,1,0,0,-1,-1,0], [-1,-1,0,0,1,1,1]], [[-2,-1,1,1,1,2,1], [0,0,0,0,0,0,1], [0,0,0,0,0,-1,0], [-1,-1,0,1,0,1,1], [-1,-1,1,0,0,1,1], [0,1,0,0,0,0,0], [-1,-1,0,0,1,1,1]]]] ]; MakeImmutable( IMFList[7].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 8. ## IMFList[8].matrices := [ [ # Z-class [08][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]], [[[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [0,1,0,0,0,0,0,0]]]], [ # Z-class [08][02] [[2], [1,2], [0,1,2], [0,0,1,2], [0,0,0,1,2], [0,0,0,0,1,2], [0,0,0,0,0,1,2], [0,0,0,0,0,1,0,2]], [[[1,0,0,0,0,0,0,0], [1,-1,2,-2,2,-2,1,1], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[-1,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,1,-1,1,-1,1,0,-1], [0,-1,1,-1,1,-1,1,0]]]], [ # Z-class [08][03] [[2], [0,2], [0,0,2], [0,0,0,2], [0,0,0,0,2], [0,0,0,0,0,2], [0,0,0,0,0,0,2], [1,1,1,1,1,1,1,4]], [[[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [-1,-1,-1,-1,-1,-1,-1,2], [-1,0,0,0,0,0,0,1]]]], [ # Z-class [08][04] [[2], [1,2], [0,1,2], [0,1,0,2], [0,0,0,0,2], [0,0,0,0,1,2], [0,0,0,0,0,1,2], [0,0,0,0,0,1,0,2]], [[[-1,1,-1,-1,0,0,0,0], [-1,0,0,0,0,0,0,0], [0,-1,1,0,0,0,0,0], [0,-1,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,1,-1,-1,0,0,0,0], [0,0,0,-1,0,0,0,0], [-1,1,0,-1,0,0,0,0], [0,-1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]]]], [ # Z-class [08][05] [[2], [0,2], [-1,0,2], [0,-1,-1,2], [0,0,0,-1,2], [0,0,0,0,-1,2], [0,0,0,0,0,-1,2], [0,0,0,0,0,0,-1,2]], [[[-1,-1,-1,-1,0,0,0,0], [0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,1,0,1,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[-1,0,-1,-1,-1,-1,-1,-1], [0,1,0,1,1,1,1,1], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0]]]], [ # Z-class [08][06] [[4], [2,4], [0,2,4], [0,2,0,4], [-2,-1,0,0,4], [-1,-2,-1,-1,2,4], [0,-1,-2,0,0,2,4], [0,-1,0,-2,0,2,0,4]], [[[0,0,0,0,0,-1,1,1], [0,0,0,0,0,0,0,1], [0,0,0,0,1,-1,0,1], [0,0,0,0,0,1,0,0], [0,1,-1,-1,0,1,-1,-1], [0,0,0,-1,0,0,0,-1], [-1,1,0,-1,-1,1,0,-1], [0,-1,0,0,0,-1,0,0]], [[0,0,0,0,-1,1,-1,-1], [0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,1,0], [0,0,0,0,0,-1,0,1], [-1,1,-1,-1,0,0,0,0], [-1,0,0,0,0,0,0,0], [0,-1,1,0,0,0,0,0], [0,-1,0,1,0,0,0,0]], [[-1,1,-1,-1,0,0,0,0], [-1,0,0,0,0,0,0,0], [0,-1,1,0,0,0,0,0], [0,-1,0,1,0,0,0,0], [0,0,0,0,-1,1,-1,-1], [0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,1,0], [0,0,0,0,0,-1,0,1]]]], [ # Z-class [08][07] [[2], [-1,2], [0,0,2], [0,0,-1,2], [0,0,0,0,2], [0,0,0,0,-1,2], [0,0,0,0,0,0,2], [0,0,0,0,0,0,-1,2]], [[[0,-1,0,0,0,0,0,0], [1,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]], [[0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]]]], [ # Z-class [08][08] [[4], [-2,4], [0,0,4], [0,0,-2,4], [-2,1,-1,-1,4], [1,-2,2,-1,-2,4], [1,-2,-1,2,-2,1,4], [1,1,-1,-1,1,-2,-2,4]], [[[-1,0,0,0,0,1,1,1], [0,-1,0,0,-1,-1,-1,0], [0,0,-1,0,0,0,0,0], [0,0,0,-1,0,0,0,0], [0,0,0,0,-1,-1,-1,-1], [0,0,0,0,1,0,1,0], [0,0,0,0,1,1,0,0], [0,0,0,0,-1,0,0,0]], [[0,0,1,0,0,-1,0,0], [0,0,0,1,0,1,0,1], [-1,0,0,0,0,0,1,1], [0,-1,0,0,0,0,-1,0], [1,1,0,0,1,1,1,0], [-1,0,0,0,0,0,0,0], [0,-1,0,0,0,-1,-1,-1], [1,1,0,0,0,0,0,0]], [[1,0,0,0,0,0,-1,-1], [0,1,0,0,0,0,1,0], [0,0,1,0,0,0,1,1], [0,0,0,1,0,0,-1,0], [0,0,0,0,1,0,1,0], [0,0,0,0,0,1,0,1], [0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,-1]]]], [ # Z-class [08][09] [[6], [0,6], [0,0,6], [0,3,0,6], [0,0,-3,0,6], [3,0,0,0,0,6], [3,-3,0,-3,3,3,8], [0,0,3,-3,0,3,4,8]], [[[-1,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0], [0,0,0,-1,0,0,0,0], [0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,0,0], [-1,1,0,0,-1,0,1,-1], [0,0,-1,1,-1,-1,1,0]], [[0,-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,-1,0,0], [0,0,0,-1,0,0,0,0], [0,0,0,0,-1,-1,1,0], [0,1,0,-1,-1,0,1,-1]], [[1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [-1,1,0,0,-1,0,2,-1], [0,0,0,1,0,0,0,0], [0,0,1,-1,1,1,-1,-1], [0,0,0,0,0,1,0,0], [0,0,1,-1,0,1,0,-1], [-1,1,0,-1,-1,1,1,-1]]]], [ # Z-class [08][10] [[4], [-2,4], [-2,1,4], [1,-2,-2,4], [0,0,0,0,4], [0,0,0,0,-2,4], [0,0,0,0,-2,1,4], [0,0,0,0,1,-2,-2,4]], [[[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,-1,0,0,0,0,0,0], [1,1,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0], [0,0,1,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]]]], [ # Z-class [08][11] [[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]], [[[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[1,-1,0,0,0,0,0,0], [1,0,-1,0,0,0,0,0], [1,0,0,-1,0,0,0,0], [1,0,0,0,-1,0,0,0], [1,0,0,0,0,-1,0,0], [1,0,0,0,0,0,-1,0], [1,0,0,0,0,0,0,-1], [1,0,0,0,0,0,0,0]]]], [ # Z-class [08][12] [[8], [-1,8], [-1,-1,8], [-1,-1,-1,8], [-1,-1,-1,-1,8], [-1,-1,-1,-1,-1,8], [-1,-1,-1,-1,-1,-1,8], [-1,-1,-1,-1,-1,-1,-1,8]], [[[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0], [0,0,0,-1,0,0,0,0], [0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,-1], [1,1,1,1,1,1,1,1]]]], [ # Z-class [08][13] [[8], [-4,8], [-4,2,8], [2,-4,-4,8], [-4,2,2,-1,8], [2,-4,-1,2,-4,8], [2,-1,-4,2,-4,2,8], [-1,2,2,-4,2,-4,-4,8]], [[[0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,-1,0], [0,0,0,0,0,0,0,-1], [1,0,0,0,1,0,0,0], [0,1,0,0,0,1,0,0], [0,0,1,0,0,0,1,0], [0,0,0,1,0,0,0,1]], [[0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]], [[1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[1,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,1,0,0,0,0,0,0], [0,0,0,0,0,1,0,0], [0,0,1,0,0,0,0,0], [0,0,0,0,0,0,1,0], [0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,1]]]], [ # Z-class [08][14] [[2], [1,2], [1,1,2], [1,1,1,2], [0,0,0,0,2], [0,0,0,0,1,2], [0,0,0,0,1,1,2], [0,0,0,0,1,1,1,2]], [[[0,0,0,1,0,0,0,0], [-1,0,0,1,0,0,0,0], [0,-1,0,1,0,0,0,0], [0,0,-1,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]]]], [ # Z-class [08][15] [[4], [-1,4], [-1,-1,4], [-1,-1,-1,4], [0,0,0,0,4], [0,0,0,0,-1,4], [0,0,0,0,-1,-1,4], [0,0,0,0,-1,-1,-1,4]], [[[1,1,1,1,0,0,0,0], [-1,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]]]], [ # Z-class [08][16] [[4], [-2,4], [1,-1,4], [1,0,-1,4], [-1,-1,1,1,4], [-2,1,-2,1,1,4], [0,1,-2,2,-1,2,4], [2,-1,0,1,-2,0,1,4]], [[[0,0,0,0,0,0,0,1], [0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0], [0,1,0,0,1,-1,0,1], [0,1,0,0,0,0,0,0], [1,1,0,-1,1,0,0,0], [0,0,1,0,0,0,0,0], [1,0,0,0,0,0,0,0]], [[-1,-1,0,0,0,-1,1,0], [0,0,0,0,0,1,-1,0], [0,0,0,-1,0,0,1,0], [0,-1,1,1,-1,1,0,-1], [1,0,1,0,-1,1,0,-1], [0,0,1,1,-1,1,-1,0], [0,0,0,0,1,0,0,1], [-1,-1,0,1,-1,0,0,0]], [[1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,1,-1,1,-1,0], [0,-1,1,1,-2,1,0,-1]]]], [ # Z-class [08][17] [[8], [3,8], [3,3,8], [3,3,3,8], [-3,2,2,2,8], [-3,2,2,2,3,8], [-2,-2,-2,-2,2,2,8], [-2,-2,-2,3,2,2,3,8]], [[[0,0,0,0,1,0,0,0], [1,-1,0,0,1,0,0,0], [1,0,-1,0,1,0,0,0], [1,0,0,-1,1,0,0,0], [1,0,0,-1,0,0,0,1], [2,-1,-1,-1,1,1,-1,0], [1,0,0,-1,0,1,-1,1], [1,0,0,-1,0,1,0,0]], [[0,0,0,0,-1,0,0,0], [-1,1,0,0,-1,0,0,0], [-1,0,1,0,-1,0,0,0], [-1,0,0,1,-1,0,0,0], [-1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]], [[1,-1,0,0,1,0,0,0], [0,-1,0,0,0,0,0,0], [-1,0,1,1,-1,-1,1,0], [1,-1,0,0,0,1,0,0], [0,0,0,0,-1,0,0,0], [-1,0,0,1,-1,0,0,0], [0,0,0,0,0,0,-1,0], [1,0,0,-1,0,1,-1,1]]]], [ # Z-class [08][18] [[8], [-2,8], [-2,-2,8], [-2,-2,-2,8], [-4,1,1,1,8], [1,-4,1,1,-2,8], [1,1,-4,1,-2,-2,8], [1,1,1,-4,-2,-2,-2,8]], [[[0,0,0,0,1,1,1,1], [0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,-1,0], [-1,-1,-1,-1,-1,-1,-1,-1], [1,0,0,0,1,0,0,0], [0,1,0,0,0,1,0,0], [0,0,1,0,0,0,1,0]], [[0,0,0,0,1,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1], [1,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0]], [[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]]]], [ # Z-class [08][19] [[4], [2,4], [2,2,4], [2,2,2,4], [-2,-1,-1,-1,4], [-1,-2,-1,-1,2,4], [-1,-1,-2,-1,2,2,4], [-1,-1,-1,-2,2,2,2,4]], [[[0,0,0,-1,0,0,0,-1], [1,0,0,-1,1,0,0,-1], [0,1,0,-1,0,1,0,-1], [0,0,1,-1,0,0,1,-1], [0,0,0,1,0,0,0,0], [-1,0,0,1,0,0,0,0], [0,-1,0,1,0,0,0,0], [0,0,-1,1,0,0,0,0]], [[0,0,0,0,-1,0,0,0], [0,0,0,0,0,-1,0,0], [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,-1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0], [0,0,0,-1,0,0,0,0]], [[0,1,0,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1]]]], [ # Z-class [08][20] [[4], [0,4], [0,0,4], [1,1,-1,4], [0,0,0,1,4], [1,-1,1,1,-1,4], [-1,-1,-1,0,1,1,4], [1,1,1,-1,1,0,1,4]], [[[0,-1,0,1,-1,-1,0,1], [0,0,0,-1,0,0,0,0], [-1,0,-1,0,0,1,-1,1], [0,0,0,0,0,-1,0,0], [0,0,0,0,0,0,-1,0], [0,0,-1,0,0,0,0,0], [0,0,0,0,0,0,0,-1], [0,0,0,0,-1,0,0,0]], [[0,0,0,0,0,0,0,-1], [-1,-1,0,1,0,0,-1,1], [0,0,1,1,-1,-1,1,0], [0,0,0,0,0,0,-1,0], [0,0,0,0,0,-1,0,0], [0,0,0,0,-1,0,0,0], [0,0,0,-1,0,0,0,0], [-1,0,0,0,0,0,0,0]]]], [ # Z-class [08][21] [[3], [1,3], [0,0,3], [0,0,-1,3], [0,1,-1,0,3], [-1,0,1,0,-1,3], [-1,0,0,-1,1,1,3], [1,0,1,0,1,0,1,3]], [[[-1,1,-1,-1,-1,0,-1,1], [0,0,-1,-1,0,1,-1,1], [-1,0,0,0,0,0,-1,1], [0,0,-1,0,0,0,0,0], [1,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0], [1,-1,1,0,1,0,0,-1], [0,0,0,0,0,0,-1,0]], [[-1,1,-1,-1,-1,0,-1,1], [0,1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0], [0,0,0,0,0,1,0,0], [0,0,1,0,1,0,0,-1], [0,0,0,1,0,0,0,0], [0,0,1,1,0,-1,1,-1], [0,0,0,0,0,0,0,-1]]]], [ # Z-class [08][22] [[6], [-2,6], [2,-2,6], [3,-1,3,6], [3,1,1,1,6], [-1,3,1,1,0,6], [1,3,-1,2,3,3,6], [0,0,2,3,1,3,3,6]], [[[0,0,-1,0,1,1,-1,0], [0,1,1,0,0,-1,0,0], [0,0,0,0,0,1,0,0], [0,0,-1,1,1,1,-1,0], [-1,0,0,0,1,0,0,0], [0,0,1,0,0,0,1,-1], [-1,0,0,1,1,0,0,-1], [-1,-1,0,1,1,1,0,-1]], [[0,0,-1,1,0,0,-1,0], [-1,0,1,0,0,-1,1,0], [0,0,-1,0,0,0,0,0], [0,0,-1,1,0,0,0,0], [-1,0,0,1,0,0,0,-1], [-1,-1,0,0,0,0,1,0], [-1,0,0,1,0,0,0,0], [0,0,0,0,-1,0,1,0]], [[1,0,0,-1,0,0,0,1], [0,0,0,0,0,1,0,-1], [1,1,1,-1,-1,-1,0,1], [1,1,0,0,0,0,-1,1], [0,0,1,-1,0,0,1,0], [0,0,0,0,0,1,-1,0], [0,0,0,0,0,1,0,0], [0,1,0,0,0,0,-1,1]]]], [ # Z-class [08][23] [[8], [-4,8], [-1,2,8], [2,-4,-4,8], [2,-1,-4,2,8], [-4,2,2,-1,-4,8], [-1,-1,2,-1,2,-1,8], [2,-1,-1,-1,-1,2,-4,8]], [[[0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0], [1,1,-1,0,-1,0,1,0], [0,0,1,0,1,0,-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], [0,0,0,0,0,1,0,0]], [[-1,-1,1,0,1,0,-1,0], [0,0,-1,0,-1,0,1,0], [0,0,0,0,0,0,0,-1], [0,0,0,0,0,0,-1,0], [-1,0,0,0,0,-1,0,1], [1,0,-1,-1,0,1,0,-1], [0,0,0,0,0,-1,0,0], [0,0,0,0,1,1,0,0]]]], [ # Z-class [08][24] [[6], [-1,6], [0,-1,6], [1,0,3,6], [-1,-2,3,1,6], [1,1,2,1,3,6], [-1,2,-2,1,-1,2,6], [0,2,3,2,2,3,1,6]], [[[0,1,0,0,1,-1,0,0], [0,0,-1,0,0,1,-1,0], [0,0,-1,1,0,0,0,0], [-1,0,-1,1,-1,1,-1,0], [0,0,0,0,0,0,1,0], [0,0,-1,0,0,0,0,1], [-1,-1,-1,0,-1,1,-1,1], [0,0,-1,0,0,0,0,0]], [[1,0,1,-1,0,-1,1,0], [0,0,-1,0,0,1,-1,0], [0,0,1,0,0,0,0,-1], [0,-1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0], [0,0,1,-1,0,0,0,0], [-1,-1,-1,0,-1,1,-1,1], [0,0,0,0,0,0,-1,0]], [[1,0,0,0,0,0,0,0], [0,1,1,0,0,0,0,-1], [0,0,0,0,0,0,0,1], [0,0,0,0,0,1,0,0], [-1,-1,-1,1,-1,1,-1,1], [0,0,0,1,0,0,0,0], [0,0,1,0,0,0,1,-1], [0,0,1,0,0,0,0,0]]]], [ # Z-class [08][25] [[4], [2,4], [2,1,4], [-1,0,-1,4], [0,-1,2,0,4], [1,1,0,2,1,4], [0,1,2,1,1,1,4], [-1,-1,1,0,1,1,2,4]], [[[1,-1,0,0,0,0,0,0], [1,0,-1,0,1,-1,0,0], [1,0,0,0,0,0,0,0], [0,0,-1,-1,0,0,1,0], [0,0,1,0,-1,0,0,0], [1,0,-1,0,0,-1,0,1], [1,1,-1,0,1,-1,0,1], [0,1,0,0,0,0,-1,1]], [[-1,0,1,0,0,1,-1,0], [-1,0,1,0,0,1,0,-1], [0,1,0,1,1,-1,-1,1], [0,0,-1,0,0,0,1,0], [0,1,0,1,0,-1,-1,1], [-1,0,1,0,-1,1,0,0], [1,1,-1,1,1,-1,0,1], [1,0,0,1,0,-1,0,1]], [[1,-1,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0], [0,-1,1,0,-1,1,0,0], [0,1,0,1,1,-1,-1,1], [0,0,0,0,0,1,0,0], [0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0]]]], [ # Z-class [08][26] [[14], [1,14], [7,-4,14], [-4,7,-5,14], [4,-4,5,-5,14], [4,-4,5,-5,-1,14], [-5,-1,-1,4,5,-1,14], [1,5,-4,1,-1,5,5,14]], [[[0,0,1,0,0,-1,0,1], [-1,0,0,0,1,0,-1,1], [1,0,0,-1,-1,-1,1,0], [-1,0,0,0,1,0,-1,0], [1,0,0,0,0,0,0,0], [0,-1,1,0,-1,-1,0,1], [0,0,0,0,0,0,-1,0], [-1,0,1,0,0,0,-1,1]], [[1,0,0,0,0,0,0,0], [0,-1,0,1,0,0,-1,1], [0,0,1,0,0,0,0,0], [0,0,0,0,-1,0,0,0], [0,0,1,0,0,-1,0,1], [0,0,0,-1,0,0,0,0], [-1,0,1,0,0,-1,-1,1], [0,-1,0,0,0,-1,-1,1]], [[0,0,0,0,0,0,0,-1], [-1,0,0,1,1,1,-1,0], [1,0,0,0,-1,0,1,-1], [-1,0,1,1,1,0,-1,1], [1,0,-1,0,0,0,1,-1], [0,1,0,-1,-1,0,1,-1], [0,0,0,0,0,0,1,0], [-1,0,0,0,0,0,0,0]]]] ]; MakeImmutable( IMFList[8].matrices ); ############################################################################# ## ## Quadratic form and matrix generators for the Z-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 9. ## IMFList[9].matrices := [ [ # Z-class [09][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]], [[[-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], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,1,0,0,0,0,0,0]], [[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], [1,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][02] [[2], [1,2], [0,1,2], [0,0,1,2], [0,0,0,1,2], [0,0,0,0,1,2], [0,0,0,0,0,1,2], [0,0,0,0,0,0,1,2], [0,0,0,0,0,0,1,0,2]], [[[-1,2,-2,2,-2,2,-2,1,1], [0,1,-1,2,-2,2,-2,1,1], [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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,1,-1,1,-1,1,0,-1], [0,0,-1,1,-1,1,-1,1,0]], [[0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [1,-1,1,0,0,0,0,0,0], [1,-1,1,-1,2,-2,2,-1,-1], [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], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][03] [[4], [0,4], [0,0,4], [0,0,0,4], [0,0,0,0,4], [0,0,0,0,0,4], [0,0,0,0,0,0,4], [0,0,0,0,0,0,0,4], [2,2,2,2,2,2,2,2,9]], [[[-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], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [-1,-1,-1,-1,-1,-1,-1,-1,2], [-1,0,0,0,0,0,0,0,1]], [[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], [1,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][04] [[2], [1,2], [1,1,2], [0,0,0,2], [0,0,0,1,2], [0,0,0,1,1,2], [0,0,0,0,0,0,2], [0,0,0,0,0,0,1,2], [0,0,0,0,0,0,1,1,2]], [[[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[-1,1,0,0,0,0,0,0,0], [0,1,-1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[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], [0,0,0,0,0,0,1,0,0], [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], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0]], [[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][05] [[3], [-1,3], [-1,-1,3], [0,0,0,3], [0,0,0,-1,3], [0,0,0,-1,-1,3], [0,0,0,0,0,0,3], [0,0,0,0,0,0,-1,3], [0,0,0,0,0,0,-1,-1,3]], [[[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0], [1,1,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[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], [0,0,0,0,0,0,1,0,0], [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], [0,1,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0]], [[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][06] [[2], [1,2], [1,1,2], [0,0,0,2], [0,0,0,1,2], [0,0,0,1,1,2], [0,0,0,0,0,0,2], [0,0,0,0,0,0,1,2], [0,1,1,0,1,1,0,1,3]], [[[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [1,-1,0,0,0,0,0,0,1]], [[-1,1,0,0,0,0,0,0,0], [0,1,-1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [1,0,-1,0,0,0,0,0,1]], [[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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [1,-1,-1,1,-1,-1,1,-1,2], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1]], [[0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][07] [[4], [0,4], [0,0,4], [0,0,0,4], [0,0,0,0,4], [0,0,0,0,0,4], [0,0,0,0,0,0,4], [0,0,0,2,2,2,2,6], [2,2,2,0,0,2,2,1,6]], [[[1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[0,0,1,0,0,0,0,0,0], [-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], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [-1,0,0,0,0,0,0,0,1]], [[0,0,0,-1,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0], [-1,-1,-1,-1,-1,-2,-2,2,2], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [-1,0,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0], [0,0,1,0,0,1,1,0,-1], [-1,-1,-1,-1,-1,-1,-1,1,1]], [[0,0,0,-1,0,0,0,0,0], [0,0,0,0,-1,0,0,0,0], [-1,-1,-1,-1,-1,-2,-2,2,2], [-1,0,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,1,0,0,1,1,0,-1], [-1,-1,-1,-1,-1,-1,-1,1,2]]]], [ # Z-class [09][08] [[3], [-1,3], [-1,-1,3], [0,0,0,3], [0,0,0,-1,3], [0,0,0,-1,-1,3], [-1,1,1,1,-1,1,3], [1,-1,1,1,1,-1,0,3], [1,1,-1,-1,1,1,0,0,3]], [[[1,1,1,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,-1,-1,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0]], [[0,0,1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,1,0,0]], [[0,-1,-1,0,0,0,1,0,0], [0,1,1,1,0,1,-1,0,0], [0,0,0,-1,0,-1,1,0,0], [0,0,0,0,-1,-1,0,0,1], [-1,-1,0,0,0,0,0,0,1], [1,1,0,0,1,1,0,0,-1], [1,1,1,0,0,0,0,0,0], [-1,-1,-1,-1,-1,-1,1,1,1], [0,0,0,1,1,1,0,0,0]]]], [ # Z-class [09][09] [[4], [2,4], [2,2,4], [2,1,1,4], [1,2,1,2,4], [1,1,2,2,2,4], [2,1,1,2,1,1,4], [1,2,1,1,2,1,2,4], [1,1,2,-1,1,0,0,2,4]], [[[1,0,0,0,0,0,0,0,0], [1,0,0,-1,1,0,0,0,-1], [1,-1,1,-1,1,0,0,0,-1], [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], [0,0,0,0,0,0,1,0,0], [1,-1,0,-1,1,0,0,1,-1], [1,-1,0,-1,1,0,0,0,0]], [[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,0], [-1,1,-1,1,-1,1,1,-1,2], [0,1,-1,0,-1,1,1,-1,1]], [[0,0,1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,1,0,0,0,0,0], [-1,1,-1,1,-1,1,1,-1,2], [0,0,0,0,0,0,0,1,0], [1,-1,1,-1,1,-1,0,1,-1]], [[1,-1,0,0,0,0,-1,1,0], [0,0,0,0,0,0,-1,1,0], [0,0,0,1,-1,0,-1,1,0], [1,-2,2,-1,1,-1,-1,2,-2], [1,-1,1,-1,1,-1,-1,2,-2], [1,-1,1,-1,0,0,-1,2,-2], [0,-1,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,1,0], [0,1,-1,1,-1,0,0,0,1]]]], [ # Z-class [09][10] [[4], [2,4], [2,2,4], [2,1,1,4], [1,2,1,2,4], [1,1,2,2,2,4], [2,1,1,2,1,1,4], [1,2,1,1,2,1,2,4], [1,1,2,1,1,2,2,2,4]], [[[0,1,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,1,0], [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], [0,1,-1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,-1,1,0,0,0,0], [0,0,0,0,1,-1,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,-1,1,0], [0,0,0,0,0,0,0,1,-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], [0,0,0,0,0,0,1,0,0], [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], [0,0,1,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][11] [[9], [-3,9], [-3,-3,9], [-3,1,1,9], [1,-3,1,-3,9], [1,1,-3,-3,-3,9], [-3,1,1,-3,1,1,9], [1,-3,1,1,-3,1,-3,9], [1,1,-3,1,1,-3,-3,-3,9]], [[[0,1,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0], [1,1,1,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0], [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,-1], [0,0,0,0,0,0,1,1,1]], [[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], [0,1,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,1,0], [0,0,1,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][12] [[6], [-2,6], [-2,-2,6], [3,-1,-1,6], [-1,3,-1,-2,6], [-1,-1,3,-2,-2,6], [3,-1,-1,1,1,1,6], [-1,3,-1,1,1,1,2,6], [-1,-1,3,1,1,1,2,2,6]], [[[0,0,0,0,0,0,0,0,1], [0,0,1,0,0,-1,1,0,-1], [0,1,0,0,-1,0,0,0,0], [0,0,0,-1,-1,-1,0,0,1], [1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,-1,0,0,0], [0,1,-1,0,-1,0,0,-1,1]], [[-1,-1,-1,1,1,1,0,0,0], [0,1,0,0,-1,0,0,-1,1], [0,0,1,0,0,-1,0,1,-1], [0,0,0,1,1,1,0,0,0], [0,0,0,0,-1,0,0,0,0], [0,0,0,0,0,-1,0,0,0], [0,-1,-1,1,1,1,-1,0,0], [1,0,0,0,0,0,-1,0,1], [1,0,0,0,0,0,-1,1,0]], [[1,0,0,0,0,0,0,0,0], [0,0,0,-1,-1,-1,0,1,0], [0,0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,-1,0,-1,0,-1,0,1,0], [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], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][13] [[8], [4,8], [4,4,8], [0,0,0,8], [0,0,0,4,8], [0,0,0,4,4,8], [0,0,0,0,0,0,8], [0,0,0,0,0,0,4,8], [4,4,4,4,4,4,4,4,9]], [[[1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[0,0,-1,0,0,0,0,0,0], [0,1,-1,0,0,0,0,0,0], [1,0,-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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,-1,0,0,0,0,0,1]], [[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], [-1,-1,-1,-1,-1,-1,-1,-2,4], [-1,-1,-1,-1,-1,-1,-1,-1,4], [-1,-1,-1,-1,-1,-1,-2,-1,4], [0,1,-1,0,0,0,0,0,0], [-1,1,0,0,0,0,0,0,0], [-1,0,-1,-1,-1,-1,-1,-1,3]], [[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], [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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]]]], [ # Z-class [09][14] [[6], [-2,6], [-2,-2,6], [3,-1,-1,6], [-1,3,-1,-2,6], [-1,-1,3,-2,-2,6], [3,-1,-1,3,-1,-1,6], [-1,3,-1,-1,3,-1,-2,6], [-1,-1,3,-1,-1,3,-2,-2,6]], [[[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], [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], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[-1,0,0,1,0,0,0,0,0], [0,-1,0,0,1,0,0,0,0], [0,0,-1,0,0,1,0,0,0], [0,0,0,1,0,0,-1,0,0], [0,0,0,0,1,0,0,-1,0], [0,0,0,0,0,1,0,0,-1], [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]], [[0,1,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0], [0,0,0,1,0,0,0,0,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,1]], [[-1,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0], [1,1,1,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0], [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,-1], [0,0,0,0,0,0,1,1,1]]]], [ # Z-class [09][15] [[9], [-1,9], [-1,-1,9], [-1,-1,-1,9], [-1,-1,-1,-1,9], [-1,-1,-1,-1,-1,9], [-1,-1,-1,-1,-1,-1,9], [-1,-1,-1,-1,-1,-1,-1,9], [-1,-1,-1,-1,-1,-1,-1,-1,9]], [[[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[-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,-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,-1], [1,1,1,1,1,1,1,1,1]]]], [ # Z-class [09][16] [[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]], [[[0,1,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[-1,1,0,0,0,0,0,0,0], [0,1,-1,0,0,0,0,0,0], [0,1,0,-1,0,0,0,0,0], [0,1,0,0,-1,0,0,0,0], [0,1,0,0,0,-1,0,0,0], [0,1,0,0,0,0,-1,0,0], [0,1,0,0,0,0,0,-1,0], [0,1,0,0,0,0,0,0,-1], [0,1,0,0,0,0,0,0,0]]]], [ # Z-class [09][17] [[8], [3,8], [3,3,8], [3,3,3,8], [3,3,3,3,8], [3,3,3,3,3,8], [3,3,3,3,3,3,8], [3,3,3,3,3,3,3,8], [-3,-3,2,2,2,2,2,2,8]], [[[1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,-1], [0,-1,1,0,0,0,0,0,-1], [0,-1,0,1,0,0,0,0,-1], [0,-1,0,0,1,0,0,0,-1], [0,-1,0,0,0,1,0,0,-1], [0,-1,0,0,0,0,1,0,-1], [0,-1,0,0,0,0,0,1,-1], [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,-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,-1,0,0], [0,0,0,0,0,0,0,-1,0], [-3,-3,1,1,1,1,1,1,-4], [-1,0,1,0,0,0,0,0,-1]]]], [ # Z-class [09][18] [[4], [2,4], [2,2,4], [2,2,2,4], [2,2,2,2,4], [2,2,2,2,2,4], [2,2,2,2,2,2,4], [2,2,2,2,2,2,2,4], [0,0,0,2,2,2,2,2,5]], [[[-1,0,0,0,0,0,0,0,0], [-1,1,0,0,0,0,0,0,0], [-1,0,1,0,0,0,0,0,0], [-1,0,0,1,0,0,0,0,0], [-1,0,0,0,1,0,0,0,0], [-1,0,0,0,0,1,0,0,0], [-1,0,0,0,0,0,1,0,0], [-1,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,1]], [[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,-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,-1,0], [1,1,1,-1,-1,-1,-1,-1,2], [1,1,1,0,-1,-1,-1,-1,1]]]], [ # Z-class [09][19] [[12], [2,12], [2,-3,12], [-3,2,2,12], [3,3,-2,3,12], [3,3,3,-2,2,12], [-3,-3,2,2,3,3,12], [-2,3,3,3,2,-3,-2,12], [3,-2,-2,3,2,-3,3,-3,12]], [[[1,-1,-1,1,0,0,0,0,-1], [0,0,0,0,0,-1,0,0,0], [0,-1,-1,0,0,1,0,1,0], [-1,0,1,-1,1,0,-1,0,1], [0,0,0,0,0,0,-1,0,0], [0,0,-1,0,0,0,0,0,0], [-1,0,0,0,0,1,-1,0,1], [0,0,0,0,0,0,0,1,0], [-1,0,1,0,1,0,-1,-1,0]], [[1,-1,-1,1,-1,1,0,1,0], [0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,1], [0,0,0,0,1,0,0,0,0], [0,-1,-1,0,0,1,0,1,0], [-1,0,0,0,0,1,-1,0,1], [0,0,-1,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0], [1,-1,-1,1,0,0,0,0,-1]]]], [ # Z-class [09][20] [[4], [-2,4], [-1,2,4], [-1,2,0,4], [0,0,-1,-1,4], [-1,0,0,0,1,4], [1,1,0,2,0,0,4], [2,-1,1,-1,-1,1,1,4], [-1,2,1,1,-1,-1,2,0,4]], [[[0,1,0,-1,-1,0,1,-1,-1], [-1,0,-1,0,0,0,0,1,0], [0,1,-1,0,0,0,0,1,0], [-1,-1,0,0,0,0,1,0,0], [-1,0,0,0,0,-1,0,1,-1], [-1,0,0,0,1,-1,0,1,0], [-1,0,0,0,0,0,1,0,-1], [0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0]], [[0,0,0,0,0,0,1,0,0], [0,0,0,1,0,0,-1,0,0], [-1,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,-1,1,0], [0,0,-1,0,0,0,0,0,0], [0,1,-1,-1,-1,0,0,0,0], [1,0,0,1,0,1,-1,0,1], [0,0,0,0,0,0,0,0,1], [1,-1,1,1,0,1,-1,-1,1]]]] ]; MakeImmutable( IMFList[9].matrices );