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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #A imf28.grp GAP group library Volkmar Felsch ## ## #Y Copyright (C) 1995, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains, for each Q-class representative of the irreducible ## maximal finite integral matrix groups of dimension 28, ## ## [1] a quadratic form (as lower triangle of the Gram matrix), ## [2] a list of matrix generators. ## ############################################################################# ## ## Quadratic form and matrix generators for the Q-class representatives of ## the irreducible maximal finite integral matrix groups of dimension 28. ## IMFList[28].matrices := [ [ # Q-class [28][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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], 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[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]]], [ # Q-class [28][02] [[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], [0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], 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[-1,1,1,-1,-1,0,1,1,0,-1,0,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0,0,0,1], [2,1,-1,1,-1,-1,0,1,2,-3,-1,0,-1,2,-2,-3,-1,2,2,-1,-1,1,-1,1,1,0,-1,1], [-2,-1,1,-1,-1,1,1,1,0,0,1,1,-1,-1,1,1,0,1,0,0,0,0,0,0,-1,-1,1,0], [1,0,0,1,-2,-1,1,1,1,-2,0,0,-1,1,-1,-1,-1,2,2,-1,-1,0,-1,1,0,0,0,0], [0,0,0,0,-1,-1,1,1,1,-1,0,1,0,1,-1,0,0,2,1,-2,-1,-1,-1,1,-1,0,1,0], [0,0,0,0,-1,0,0,1,1,-1,0,0,-1,0,0,-1,0,1,1,0,0,1,0,0,0,-1,0,0], [-1,-1,0,0,-1,0,1,1,0,0,1,1,-1,0,1,1,0,1,0,-1,0,-1,0,1,-1,-1,1,0], [-1,-1,1,0,-1,1,1,0,-1,1,0,0,0,0,1,1,0,0,-1,0,0,-1,0,0,0,-1,1,0], [-1,0,1,0,-1,-1,1,1,0,0,0,0,1,0,0,1,0,1,0,-1,-1,-1,0,0,-1,0,0,1], [-2,-1,1,0,-1,0,1,1,0,0,1,0,-1,-1,1,1,0,1,0,0,0,0,0,0,-1,-1,1,0], [1,0,-1,1,0,0,-1,0,0,0,0,-1,-1,0,0,-1,0,0,0,1,1,0,0,0,1,0,-1,0]]]], [ # Q-class [28][16] [[6], [3,6], [2,3,6], [2,3,2,6], [2,3,2,2,6], [2,1,2,2,2,6], [0,3,2,2,2,2,6], [1,2,3,3,1,3,3,6], [2,3,2,2,2,2,2,3,6], [2,3,2,2,2,2,2,3,2,6], [1,1,1,1,3,3,1,1,1,1,6], [3,3,1,3,1,1,1,1,1,1,0,6], [2,3,2,2,2,2,2,3,2,2,1,3,6], [0,1,0,0,2,0,2,1,2,0,1,1,2,6], [1,2,1,1,3,1,1,0,1,1,1,1,1,1,6], [1,2,1,1,3,3,1,2,1,1,3,1,1,1,2,6], [2,1,2,2,2,2,-2,1,2,2,3,1,2,0,1,1,6], [3,2,1,3,1,1,1,2,1,1,1,3,3,1,-2,0,1,6], [2,1,0,2,2,0,0,1,2,0,1,1,2,2,3,1,2,1,6], [3,1,1,1,3,3,1,1,1,1,2,2,1,1,1,3,1,1,1,6], [1,1,3,1,1,1,1,1,1,-1,2,2,1,1,1,1,1,1,1,2,6], [1,2,1,1,1,1,3,2,1,1,1,1,3,1,0,0,-1,2,1,1,1,6], [1,2,3,1,1,1,1,2,1,1,1,1,1,1,2,2,1,0,1,1,3,2,6], [2,3,2,2,2,0,2,1,2,0,1,3,2,2,1,1,0,3,2,1,3,3,3,6], [2,1,2,0,0,2,0,1,2,0,1,1,2,2,1,1,2,1,2,1,3,1,3,2,6], [2,1,0,0,2,2,2,1,2,2,1,1,2,2,1,1,0,1,2,3,1,3,1,2,2,6], [0,1,2,0,2,0,2,1,0,0,1,1,2,2,1,1,0,1,2,1,3,1,1,2,2,2,6], [2,1,2,0,2,0,0,1,0,2,1,1,2,2,1,1,2,1,2,1,1,1,3,2,2,2,2,6]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [-1,1,1,-1,1,1,-1,0,-1,1,1,1,0,0,-1,-1,-2,0,2,0,0,-1,0,0,0,0,-1,0], [0,0,0,1,0,0,-1,-1,1,0,1,0,1,0,0,0,-2,0,0,0,0,0,0,-1,0,0,0,1], [1,-1,-1,0,-1,0,1,-1,1,0,-1,-1,0,0,1,1,1,1,-1,0,0,1,0,0,-1,-1,1,1], 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[-4,2,3,-1,2,0,-3,2,-1,0,4,3,0,-1,-1,-3,-5,0,3,1,-2,-2,0,-1,2,1,-2,0], [-1,0,1,1,0,-1,-1,0,0,0,2,0,1,0,0,-1,-2,0,0,1,-1,-1,0,0,1,0,0,0], [-1,1,1,-1,3,-1,0,2,-2,0,2,2,0,-1,-2,-2,-2,-1,2,0,-1,-2,0,0,2,1,-2,-1], [0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,-1,-1,0,0,0,0,-1,0,0,0,0,0,0], [-1,-1,2,0,2,-2,0,0,0,0,3,2,1,-1,-1,-1,-3,0,1,0,-2,-2,1,-1,2,1,-1,-1], [0,-1,0,1,0,0,-1,-1,1,1,1,0,1,0,0,0,-2,0,0,0,0,0,0,0,0,-1,1,0], [-2,2,1,-1,2,0,-1,2,-1,-1,2,2,-1,-1,-1,-2,-2,0,2,0,-1,-1,0,-1,1,1,-1,0], [0,0,0,1,0,-1,0,0,0,0,1,0,0,0,0,0,-1,0,0,0,0,0,0,-1,1,0,0,0], [-2,1,1,-1,2,0,-1,1,0,0,2,2,0,-1,-1,-2,-3,0,2,0,-1,-1,0,-1,2,0,-1,0]]]], [ # Q-class [28][17] [[6], [2,6], [2,2,6], [2,2,2,6], [2,2,2,2,6], [2,2,2,2,2,6], [2,2,0,2,0,2,6], [2,2,2,2,2,2,2,6], [2,2,2,2,2,0,0,2,6], [2,2,2,0,2,2,0,2,0,6], [2,2,2,2,2,2,0,2,2,0,6], [2,2,2,0,0,2,0,2,2,2,2,6], [3,1,3,1,1,1,1,1,1,3,1,1,6], [2,0,2,2,2,0,0,2,2,2,0,0,3,6], [2,2,2,2,2,2,2,2,2,2,0,2,1,2,6], [2,2,0,2,2,2,2,2,0,2,0,0,1,2,2,6], [2,2,2,2,0,2,2,2,0,2,2,2,3,2,2,2,6], [2,2,2,2,2,2,0,2,0,2,2,0,1,2,0,2,2,6], [2,2,2,2,0,2,2,2,0,2,2,2,1,0,2,2,2,2,6], [2,0,2,2,2,0,0,2,2,0,2,0,1,2,0,2,0,2,2,6], [2,0,2,2,0,2,0,2,0,2,2,2,1,2,0,0,2,2,2,2,6], [2,2,2,2,2,2,0,2,2,2,2,2,1,0,0,0,0,2,2,2,2,6], [0,0,2,2,2,2,0,2,0,2,2,0,1,2,2,2,2,2,2,2,2,0,6], [2,2,2,0,2,0,0,2,2,2,2,2,1,2,2,2,2,2,2,2,0,0,2,6], [2,2,2,2,0,0,0,0,2,2,0,2,1,2,2,0,2,2,2,0,2,2,0,2,6], [2,2,2,2,2,2,0,2,2,2,2,2,1,2,2,0,2,2,0,0,2,0,2,2,2,6], [2,0,2,0,2,2,0,2,0,2,2,2,1,2,2,2,2,2,2,2,2,0,2,2,0,2,6], [0,0,2,2,0,0,0,2,2,0,2,2,1,2,2,0,2,0,2,2,2,0,2,2,2,2,2,6]], [[[-22,-1,-10,3,2,-2,-5,10,2,-26,-5,-7,34,-20,12,9,-11,-2,0,-7,23,5,-4,17,10,6,12,-16], [4,-1,3,-2,0,-2,1,-4,2,3,-1,0,-6,2,-1,1,3,2,2,-2,-1,2,0,-2,-6,1,-3,4], [-1,0,0,0,0,-1,0,0,1,-2,-1,-1,2,-2,1,1,0,0,0,-1,2,1,0,1,0,1,1,-1], [-9,0,-4,1,0,-1,-2,4,1,-11,-2,-3,14,-8,5,4,-5,-1,0,-3,9,3,-1,7,4,3,5,-7], [-4,0,-2,1,0,0,-1,2,1,-4,-1,-2,6,-4,2,1,-2,-1,0,-1,4,1,-1,3,2,1,3,-3], [-9,0,-4,2,0,-1,-2,4,1,-10,-2,-3,14,-8,5,3,-5,-1,0,-3,9,2,-1,7,4,2,6,-7], 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[-7,0,-3,0,1,0,-2,4,0,-9,-1,-2,11,-6,4,3,-4,-1,0,-2,7,1,-1,5,4,2,3,-5], [-1,0,-1,0,0,0,-1,1,1,-3,-1,-1,3,-2,1,1,-1,0,0,-2,3,1,0,2,0,0,1,-1], [-6,-1,-2,0,1,-1,-1,2,1,-7,-1,-2,9,-5,4,3,-3,0,1,-3,7,2,-2,5,1,2,2,-4], [6,0,3,-2,-1,0,1,-3,0,6,1,1,-9,5,-2,-1,3,1,0,1,-5,0,1,-4,-4,-1,-4,5], [0,0,0,-1,0,1,0,0,0,1,1,0,-1,1,0,0,0,0,0,1,-1,-1,0,-1,1,0,-1,0], [1,0,0,0,0,0,0,-1,1,1,0,0,-1,0,0,0,0,1,0,-1,0,0,0,0,-1,-1,0,1], [-1,0,-1,0,0,0,-1,1,1,-2,-1,-1,3,-2,1,1,-1,0,0,-1,2,0,0,1,1,0,1,-1], [-7,0,-3,-1,1,-1,-2,3,1,-10,-2,-3,11,-6,4,4,-3,-1,1,-3,8,3,-1,5,3,3,3,-5], [-2,0,-1,0,0,0,-1,1,1,-2,0,-1,3,-2,1,1,-1,0,0,-1,2,0,0,1,1,0,1,-1]]]], [ # Q-class [28][18] [[6], [3,6], [3,2,6], [3,2,2,6], [2,3,3,1,6], [2,3,3,3,2,6], [1,1,3,1,3,1,6], [3,3,1,3,1,3,-2,6], [3,1,1,3,1,1,2,2,6], [3,3,1,1,1,1,0,2,2,6], [3,2,2,2,1,1,1,1,1,3,6], [1,1,1,1,1,1,0,2,0,2,3,6], [0,1,1,1,2,2,1,1,-1,1,1,3,6], [2,1,3,1,2,2,1,1,1,3,3,3,2,6], [1,3,1,1,1,1,0,2,0,2,1,0,1,1,6], [1,3,1,1,1,1,0,2,0,2,3,2,1,1,2,6], 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[-1,-3,5,-1,1,3,2,1,4,-4,-3,-4,2,-5,-5,1,2,0,3,0,2,2,-2,3,2,-1,-2,2], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-1,0,0,-1,0,0,0,0,0,-1,1,0,0,1,0,-1,0,1,0,0,0,1,0,1,1,0,-1,-1], [0,1,-2,1,0,0,1,0,-1,0,0,1,0,1,2,0,-1,-1,-1,1,0,-1,1,-2,-2,0,1,0], [-1,-4,6,-1,2,4,1,1,7,-4,-2,-6,2,-7,-7,0,3,1,4,-1,3,3,-3,4,3,-1,-4,2], [-1,-1,0,0,1,1,1,0,1,-1,0,-1,1,-1,-1,-1,0,1,0,0,1,1,-1,1,1,0,-1,0], [0,4,-5,1,-1,-1,2,-1,-5,0,0,3,-1,4,6,1,-3,-3,-2,3,-2,-2,3,-5,-4,0,4,0]]]], [ # Q-class [28][37] [[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], [1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2], [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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,-1,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,-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], [0,0,0,0,0,0,0,0,0,0,0,0,-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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,-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,-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], 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[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,-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], [0,0,0,0,0,0,0,0,0,0,0,-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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,-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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]]]] ]; MakeImmutable( IMFList[28].matrices );