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artin_reps • Show schema
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{'BadPrimes': [3], 'Baselabel': '2.729.18t16.a', 'CharacterField': 9, 'Conductor': 729, 'Container': '18t16', 'Dets': ['1.27.18t1.a.e', '1.27.18t1.a.f', '1.27.18t1.a.d', '1.27.18t1.a.b', '1.27.18t1.a.a', '1.27.18t1.a.c'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 18, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [0], [0, 0, 0, 2], [-2, 0, 0, -2], [-1], [1, 0, 0, 1], [0, 0, 0, -1], [0], [0], [0, -2, 0, 0, -2], [0, 0, 0, 0, 0, 2], [0, 2], [0, 0, -2, 0, 0, -2], [0, 0, 0, 0, 2], [0, 0, 2], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, -1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, -1], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [26, 28, 25, 19, 7, 27, 20, 5, 17, 19, 26, 16, 11, 18], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, -2], [-1, 0, 0, -1]], [[1], [2, 0, 0, 2], [0, 0, 0, 1]], [[1], [1], [1]], [[1], [-1, 0, 0, -1], [0, 0, 0, 1]], [[1], [0, 0, 0, 1], [-1, 0, 0, -1]], [[1], [0], [1, 0, 0, 1]], [[1], [0], [0, 0, 0, -1]], 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2, 'HardFactors': [26, 28, 25, 19, 7, 27, 20, 5, 17, 19, 26, 16, 11, 18], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [2, 0, 0, 2], [0, 0, 0, 1]], [[1], [0, 0, 0, -2], [-1, 0, 0, -1]], [[1], [1], [1]], [[1], [0, 0, 0, 1], [-1, 0, 0, -1]], [[1], [-1, 0, 0, -1], [0, 0, 0, 1]], [[1], [0], [0, 0, 0, -1]], [[1], [0], [1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -2], [0, 1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, -2], [0, 0, 0, 0, 1]], [[1], [0, 2, 0, 0, 2], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 2, 0, 0, 2], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, -2], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1], [0, 1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 1], [0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, 0, 0, 0, -1]], [[1], [0], [0, 1, 0, 0, 1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, 0, 0, 0, -1]], [[1], [0], [0, 0, 1, 0, 0, 1]], [[1]]]}, 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[0, 0, 0, -1]], [[1], [0], [1, 0, 0, 1]], [[1], [0, 0, 2, 0, 0, 2], [0, -1, 0, 0, -1]], [[1], [0, 2, 0, 0, 2], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -2], [0, 1]], [[1], [0, 0, 0, 0, -2], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, -2], [0, 0, 0, 0, 1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1], [0, 1]], [[1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 1], [0, 0, 0, 0, 1]], [[1], [0, 1], [0, 0, 1]], [[1], [0], [0, 1, 0, 0, 1]], [[1], [0], [0, 0, 1, 0, 0, 1]], [[1], [0], [0, 0, 0, 0, -1]], [[1], [0], [0, 0, 0, 0, 0, -1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, 0, 0, -2], [0, 0, 0, 2], [-1], [0, 0, 0, -1], [1, 0, 0, 1], [0], [0], [0, 0, 2], [0, 0, 0, 0, 2], [0, 0, -2, 0, 0, -2], [0, 2], [0, 0, 0, 0, 0, 2], [0, -2, 0, 0, -2], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 5, 'HardFactors': [26, 28, 25, 19, 7, 27, 20, 5, 17, 19, 26, 16, 11, 18], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [2, 0, 0, 2], [0, 0, 0, 1]], [[1], [0, 0, 0, -2], [-1, 0, 0, -1]], [[1], [1], [1]], [[1], [0, 0, 0, 1], [-1, 0, 0, -1]], [[1], [-1, 0, 0, -1], [0, 0, 0, 1]], [[1], [0], [0, 0, 0, -1]], [[1], [0], [1, 0, 0, 1]], [[1], [0, 0, -2], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -2], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 2, 0, 0, 2], [0, -1, 0, 0, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, -2], [0, 1]], [[1], [0, 2, 0, 0, 2], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1], [0, 1]], [[1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1]], [[1], [0], [0, 0, 0, 0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, 1, 0, 0, 1]], [[1], [0], [0, 1, 0, 0, 1]], [[1], [0], [0, 0, 0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [0, 0, 0, 2], [-2, 0, 0, -2], [-1], [1, 0, 0, 1], [0, 0, 0, -1], [0], [0], [0, 2], [0, 0, 2], [0, 0, 0, 0, 2], [0, 0, 0, 0, 0, 2], [0, -2, 0, 0, -2], [0, 0, -2, 0, 0, -2], [0, -1], [0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 6, 'HardFactors': [26, 28, 25, 19, 7, 27, 20, 5, 17, 19, 26, 16, 11, 18], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, 0, -2], [-1, 0, 0, -1]], [[1], [2, 0, 0, 2], [0, 0, 0, 1]], [[1], [1], [1]], [[1], [-1, 0, 0, -1], [0, 0, 0, 1]], [[1], [0, 0, 0, 1], [-1, 0, 0, -1]], [[1], [0], [1, 0, 0, 1]], [[1], [0], [0, 0, 0, -1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, -2], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, -2], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -2], [0, 1]], [[1], [0, 2, 0, 0, 2], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 2, 0, 0, 2], [0, -1, 0, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1], [0, 1]], [[1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, 0, 0, 0, -1]], [[1], [0], [0, 0, 0, 0, -1]], [[1], [0], [0, 0, 1, 0, 0, 1]], [[1], [0], [0, 1, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '18T16', 'Galt': 16, 'HardPrimes': [2, 3, 5, 13, 19, 23, 43, 109, 157, 337, 677, 1627, 19219, 1170853], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 0, 0, 27, 0, 0, -53, 0, 0, 36, 0, 0, -9, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-3, 0, 0, 1], 'Proj_nTj': [3, 2]}
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artin_field_data • Show schema
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{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.27.18t1.a', 'Character': [[1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, 0, 0, -1, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, -1, 0, 0], [1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 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'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]}, {'Size': '3', 'Order': 2, 'Representative': [8, 7, 4, 3, 6, 5, 2, 1, 16, 15, 18, 17, 14, 13, 10, 9, 12, 11]}, {'Size': '1', 'Order': 3, 'Representative': [7, 14, 9, 16, 17, 12, 13, 2, 15, 4, 5, 18, 1, 8, 3, 10, 11, 6]}, {'Size': '1', 'Order': 3, 'Representative': [13, 8, 15, 10, 11, 18, 1, 14, 3, 16, 17, 6, 7, 2, 9, 4, 5, 12]}, {'Size': '2', 'Order': 3, 'Representative': [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6]}, {'Size': '2', 'Order': 3, 'Representative': [7, 2, 9, 4, 5, 12, 13, 8, 15, 10, 11, 18, 1, 14, 3, 16, 17, 6]}, {'Size': '2', 'Order': 3, 'Representative': [13, 2, 15, 4, 5, 18, 1, 8, 3, 10, 11, 6, 7, 14, 9, 16, 17, 12]}, {'Size': '3', 'Order': 6, 'Representative': [2, 13, 16, 9, 12, 17, 14, 7, 10, 3, 6, 11, 8, 1, 4, 15, 18, 5]}, {'Size': '3', 'Order': 6, 'Representative': [14, 1, 10, 15, 18, 11, 8, 13, 4, 9, 12, 5, 2, 7, 16, 3, 6, 17]}, {'Size': '1', 'Order': 9, 'Representative': [15, 4, 12, 17, 2, 7, 3, 10, 18, 5, 8, 13, 9, 16, 6, 11, 14, 1]}, {'Size': '1', 'Order': 9, 'Representative': [6, 17, 13, 14, 4, 3, 12, 5, 1, 2, 10, 9, 18, 11, 7, 8, 16, 15]}, {'Size': '1', 'Order': 9, 'Representative': [3, 16, 18, 11, 14, 13, 9, 4, 6, 17, 2, 1, 15, 10, 12, 5, 8, 7]}, {'Size': '1', 'Order': 9, 'Representative': [12, 11, 1, 8, 16, 9, 18, 17, 7, 14, 4, 15, 6, 5, 13, 2, 10, 3]}, {'Size': '1', 'Order': 9, 'Representative': [9, 10, 6, 5, 8, 1, 15, 16, 12, 11, 14, 7, 3, 4, 18, 17, 2, 13]}, {'Size': '1', 'Order': 9, 'Representative': [18, 5, 7, 2, 10, 15, 6, 11, 13, 8, 16, 3, 12, 17, 1, 14, 4, 9]}, {'Size': '2', 'Order': 9, 'Representative': [3, 10, 18, 5, 8, 13, 9, 16, 6, 11, 14, 1, 15, 4, 12, 17, 2, 7]}, {'Size': '2', 'Order': 9, 'Representative': [18, 11, 7, 8, 16, 15, 6, 17, 13, 14, 4, 3, 12, 5, 1, 2, 10, 9]}, {'Size': '2', 'Order': 9, 'Representative': [9, 4, 6, 17, 2, 1, 15, 10, 12, 5, 8, 7, 3, 16, 18, 11, 14, 13]}, {'Size': '2', 'Order': 9, 'Representative': [6, 5, 13, 2, 10, 3, 12, 11, 1, 8, 16, 9, 18, 17, 7, 14, 4, 15]}, {'Size': '2', 'Order': 9, 'Representative': [15, 16, 12, 11, 14, 7, 3, 4, 18, 17, 2, 13, 9, 10, 6, 5, 8, 1]}, {'Size': '2', 'Order': 9, 'Representative': [12, 17, 1, 14, 4, 9, 18, 5, 7, 2, 10, 15, 6, 11, 13, 8, 16, 3]}, {'Size': '3', 'Order': 18, 'Representative': [10, 3, 17, 12, 7, 2, 4, 15, 11, 6, 1, 14, 16, 9, 5, 18, 13, 8]}, {'Size': '3', 'Order': 18, 'Representative': [17, 18, 8, 1, 9, 16, 11, 12, 2, 13, 3, 10, 5, 6, 14, 7, 15, 4]}, {'Size': '3', 'Order': 18, 'Representative': [16, 15, 5, 6, 1, 8, 10, 9, 17, 18, 13, 2, 4, 3, 11, 12, 7, 14]}, {'Size': '3', 'Order': 18, 'Representative': [5, 12, 14, 13, 3, 4, 17, 6, 8, 7, 15, 16, 11, 18, 2, 1, 9, 10]}, {'Size': '3', 'Order': 18, 'Representative': [4, 9, 11, 18, 13, 14, 16, 3, 5, 12, 7, 8, 10, 15, 17, 6, 1, 2]}, {'Size': '3', 'Order': 18, 'Representative': [11, 6, 2, 7, 15, 10, 5, 18, 14, 1, 9, 4, 17, 12, 8, 13, 3, 16]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['729', '-27', '1'], 'ConjugacyClass': 6}, {'RootOf': ['0', '0', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['0', '1'], 'ConjugacyClass': 3}, {'RootOf': ['27', '1'], 'ConjugacyClass': 4}, {'RootOf': ['729', '27', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['2250423', '0', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['177147', '0', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['9063', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-34866', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-29952', '1'], 'ConjugacyClass': 12}, {'RootOf': ['56205', '1'], 'ConjugacyClass': 13}, {'RootOf': ['20889', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-21339', '1'], 'ConjugacyClass': 15}, {'RootOf': ['82137969', '-9063', '1'], 'ConjugacyClass': 16}, {'RootOf': ['1215637956', '34866', '1'], 'ConjugacyClass': 17}, {'RootOf': ['897122304', '29952', '1'], 'ConjugacyClass': 18}, {'RootOf': ['3159002025', '-56205', '1'], 'ConjugacyClass': 19}, {'RootOf': ['436350321', '-20889', '1'], 'ConjugacyClass': 20}, {'RootOf': ['455352921', '21339', '1'], 'ConjugacyClass': 21}], 'Algorithm': 'RES', 'CycleType': [9, 9]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-11913778728', '0', '0', '1'], 'ConjugacyClass': 22}, {'RootOf': ['142489429479000', '0', '0', '1'], 'ConjugacyClass': 23}, {'RootOf': ['17772902526024', '0', '0', '1'], 'ConjugacyClass': 24}, {'RootOf': ['-2298991622625', '0', '0', '1'], 'ConjugacyClass': 25}, {'RootOf': ['-13503034326528', '0', '0', '1'], 'ConjugacyClass': 26}, {'RootOf': ['-59468668624125', '0', '0', '1'], 'ConjugacyClass': 27}], 'Algorithm': 'RES', 'CycleType': [18]}], 'Frobs': [26, 1, 25, 16, 24, 19, 9, 7, 27, 26, 21, 6, 23, 20, 22, 2, 25, 10, 13, 9, 3, 18, 26, 8, 20, 22, 11, 2, 5, 25, 7, 27, 26, 21, 23, 14, 17, 5, 25, 24, 9, 7, 26, 15, 8, 6, 17, 16, 24, 19, 9, 27, 18, 8, 23, 22, 2, 1, 16, 24, 19, 27, 4, 23, 20, 22, 16, 19, 27, 18, 26, 8, 14, 17, 5, 25, 24, 7, 27, 21, 23, 20, 2, 5, 10, 24, 9, 18, 26, 21, 8, 22, 5, 25, 13, 9, 27, 8, 4, 5, 10, 9, 27, 26, 21, 4, 22, 2, 25, 16, 19, 3, 27, 12, 6, 22, 11, 2, 25, 24, 13, 18, 26, 8, 20, 2, 16, 9, 12, 21, 6, 23, 17, 1, 25, 19, 9, 15, 23, 2, 5, 24, 19, 9, 7, 26, 14, 22, 17, 2, 19, 9, 7, 27, 20, 22, 1, 24, 7, 27, 26, 8, 11, 2, 25, 24, 3, 12], 'G-Gens': [[8, 7, 4, 3, 6, 5, 2, 1, 16, 15, 18, 17, 14, 13, 10, 9, 12, 11], [15, 4, 12, 17, 2, 7, 3, 10, 18, 5, 8, 13, 9, 16, 6, 11, 14, 1], [7, 2, 9, 4, 5, 12, 13, 8, 15, 10, 11, 18, 1, 14, 3, 16, 17, 6], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C9*S3', 'Polynomial': [1, 0, 0, 0, 0, 0, 27, 0, 0, -53, 0, 0, 36, 0, 0, -9, 0, 0, 1], 'QpRts': [['-9337741367829706114925', '-5347731305115805484215', '-9448460784616709018838', '-330278415913826854439', '-1586950838499349408133', '8842417307121212260853', '-5194337644117859225310', '2104756673356912947494', '-8883046019369169667596'], ['8266330288455542055926', '3693418745167950341385', '10717017087760624562029', '3794617586888139405140', '-7140798973051176577416', '1795783875236263034185', '-1180846689261958397631', '7473975906220926752022', '-5887905386145462120585'], ['2754649246083455309130', '-9330408809352378876330', '-8568665982079879717148', 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