| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/grp/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 18.9.2025 mit Größe 22 kB |
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Quelle imf27.grp Sprache: unbekannt |
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#############################################################################
## ## This file is part of GAP, a system for computational discrete algebra. ## This file's authors include Volkmar Felsch. ## ## Copyright of GAP belongs to its developers, whose names are too numerous ## to list here. Please refer to the COPYRIGHT file for details. ## ## SPDX-License-Identifier: GPL-2.0-or-later ## ## This file contains, for each Q-class representative of the irreducible ## maximal finite integral matrix groups of dimension 27, ## ## [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 27. ## IMFList[27].matrices := [ [ # Q-class [27][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]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]]], [ # Q-class [27][02] [[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], [0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,0,0,0,1,1,1,2], [0,0,0,0,0,0,0,0,0,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [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,-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,-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,-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,-1,0,0,0,0,0,0,1], 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[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], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [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,-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,-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,-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,-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,-1,0,0,0,0,0,0,0,1]]]], [ # Q-class [27][03] [[4], [2,4], [0,1,4], [1,2,2,4], [2,1,0,1,4], [2,1,1,2,2,4], [0,0,1,0,0,1,4], [0,1,2,1,0,0,1,4], [2,1,0,1,2,2,0,1,4], [1,1,0,1,2,1,0,0,1,4], [1,1,0,1,1,1,0,0,2,1,4], [1,1,0,2,2,1,0,0,1,2,1,4], [0,0,1,0,0,0,1,1,0,-1,0,0,4], [1,2,0,1,2,1,0,0,1,2,1,2,0,4], [0,1,2,1,0,0,2,2,0,0,0,0,1,0,4], [0,0,1,0,0,0,1,2,2,0,1,0,1,0,1,4], [0,0,1,0,0,0,1,1,0,1,0,0,2,0,1,1,4], [2,1,0,2,1,1,0,0,1,1,1,2,0,1,0,0,0,4], [1,2,2,1,0,0,1,2,0,0,0,0,1,0,2,1,1,0,4], [1,2,1,2,1,1,0,2,2,1,1,1,0,1,1,1,0,1,1,4], [1,1,0,2,1,1,0,0,2,1,2,2,0,1,0,1,0,2,0,1,4], [1,2,0,1,1,1,0,0,2,1,2,1,0,2,0,1,0,1,0,1,2,4], [2,1,0,1,1,1,0,0,1,1,2,1,0,2,0,0,0,2,0,1,1,1,4], [1,0,1,0,0,0,2,1,0,0,0,0,1,0,2,1,1,1,1,0,0,0,1,4], [0,0,1,0,1,0,2,1,0,2,0,1,1,1,2,1,2,0,1,0,0,0,0,2,4], [1,1,0,1,1,1,0,0,1,2,2,1,1,1,0,0,2,1,0,1,1,1,2,0,1,4], [0,0,1,0,0,0,2,1,1,0,1,0,1,0,2,2,1,0,1,0,1,1,0,2,2,0,4]], [[[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,-1,0,0,0,0,0,1,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,-1,1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,1,-1,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [-1,1,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,1,0,0,-1,0], [-1,1,-1,0,0,1,0,0,0,1,0,0,1,-1,0,0,0,0,0,0,0,0,1,0,0,-1,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,-1,0,1,0,-1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,-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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0], [1,-1,0,0,0,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,1,0,0,-1,0,-1,1,1], [0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,-1,1,-1,1,0], [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,-1,0], [1,-1,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [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]], [[-1,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [-1,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,1,0,0,0,-1,0,0,1,0], [-1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [-1,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [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], [-1,0,0,0,0,0,0,-1,1,0,-1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0], [1,-1,0,0,-1,0,0,0,0,0,0,0,0,1,0,0,-1,0,1,0,0,0,-1,0,0,1,0], [0,0,0,0,0,0,0,0,0,-1,0,0,-1,1,0,0,0,0,0,0,0,0,-1,1,0,1,0], [0,-1,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,-1,1,1,0,0,0,-1,0,0,1,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [-1,1,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0,1,-1,0], [0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,1,1,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [-1,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,1,1,0,-1,0,0,0,0,0,0], [0,-1,-1,1,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,-1,1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,1,0], [0,-1,0,0,0,0,0,0,0,-1,0,0,-1,1,0,0,0,0,1,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0]]]], [ # Q-class [27][04] [[6], [3,6], [1,1,6], [2,2,2,6], [3,2,0,1,6], [2,1,3,1,0,6], [1,1,3,3,0,2,6], [1,3,2,1,0,2,2,6], [1,2,2,1,0,2,3,3,6], [2,3,1,3,1,1,1,2,2,6], [2,1,2,1,0,3,2,3,2,1,6], [1,1,0,1,3,0,0,0,0,1,0,6], [2,3,1,2,1,1,1,2,3,3,1,2,6], [3,2,1,3,1,2,1,1,1,3,3,1,2,6], [3,3,3,3,2,1,2,1,1,2,1,1,2,2,6], [2,2,0,1,3,0,0,0,0,1,0,2,1,1,3,6], [2,3,0,1,3,0,0,0,0,1,0,2,1,1,2,3,6], [1,1,3,2,0,2,3,3,2,1,3,0,1,1,2,0,0,6], [0,0,1,0,3,1,2,1,2,0,1,2,0,0,0,1,1,1,6], [1,1,0,2,3,0,0,0,0,3,0,3,1,2,1,2,2,0,2,6], [0,0,1,0,2,1,1,2,1,0,2,3,0,0,0,1,1,3,3,2,6], [1,1,0,1,2,0,0,0,0,1,0,3,2,1,1,2,3,0,1,2,1,6], [1,1,0,2,2,0,0,0,0,2,0,2,1,3,1,3,2,0,1,3,1,2,6], [1,1,0,1,2,0,0,0,0,1,0,3,3,1,1,3,2,0,1,2,1,3,3,6], [3,2,1,2,1,3,1,1,1,2,2,2,3,3,2,1,1,1,0,1,0,3,1,2,6], [0,0,2,0,2,2,1,1,1,0,1,2,0,0,0,1,1,1,3,3,3,1,1,1,0,6], [0,0,1,0,1,1,3,1,2,0,1,1,0,0,0,1,2,1,3,1,2,2,1,1,0,2,6]], [[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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,-1,0,0,1,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,-1,0,0,0], [0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,-1,0,0,1,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,1,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0], [0,0,0,-1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0], [-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,-1,0,0,1,0,1], [0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1,0], [0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,0,0,0,1], [0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,1], [0,0,0,0,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,-1,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,1], [0,0,0,-1,0,0,1,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,1], [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], [0,1,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,1], [0,0,1,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,1], [0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,-1,0,0,0,0,0,0,0,0,0,1], [0,1,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,1], [0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,-1,0,0,0,0,0,0]], [[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,-1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,-1,0,0,0,0], [0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,-1,0,0,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,-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], 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[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]], [[[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,-1,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1], [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,-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,-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,-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,-1,0,0,0,0,0,0,1], 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2026-03-28