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artin_reps • Show schema
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{'BadPrimes': [3], 'Baselabel': '1.27.18t1.a', 'CharacterField': 9, 'Conductor': 27, 'Container': '18t1', 'Dets': ['27.5', '27.2', '27.23', '27.20', '27.14', '27.11'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0], 'Galn': 18, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, -1], [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, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1], [0, -1], [0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, 0, 1], [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, -1], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, -1], [0, 0, -1], [0, 0, 0, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, 1], [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, 1]], 'GalOrbIndex': 3, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 1], [0, 0, 1], [0, -1, 0, 0, -1], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1], [0, 0, -1], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 4, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 0, 1], [-1, 0, 0, -1], [1, 0, 0, 1], [0, 0, 0, -1], [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, -1], [0, 0, -1], [0, -1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1], [0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 5, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, -1]], [[1], [1, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, 0, 0, -1], [0, 0, 0, 1], [0, 0, 0, -1], [1, 0, 0, 1], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, -1], [0, -1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1]], 'GalOrbIndex': 6, 'HardFactors': [13, 19, 14, 9], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1, 0, 0, -1]], [[1], [0, 0, 1, 0, 0, 1]], [[1], [0, 1, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 0, -1, 0, 0, -1]], [[1], [0, -1, 0, 0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '18T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
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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]], '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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.27.9t1.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, -1, 0, 0], [0, 0, 0, 1, 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, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]], 'CharacterField': 9}, {'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, 1, 0, 0], [0, 0, 0, -1, 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, 1], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 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, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 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]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.27.18t1.a', 'Character': [[1, 0, 0, 0, 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, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1], [0, 1, 0, 0, 1, 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]], 'CharacterField': 9}, {'GalConj': 1, 'Baselabel': '1.9.3t1.a', 'Character': [[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]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.9.6t1.a', 'Character': [[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]], 'CharacterField': 3}, {'GalConj': 3, 'Baselabel': '1.27.9t1.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, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 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, -1, 0, 0, -1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 3, '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, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 1, 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, 1, 0, 0, 1, 0], [0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 1, 0, 0, 1]], 'CharacterField': 9}, {'GalConj': 4, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 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, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 4, 'Baselabel': '1.27.18t1.a', 'Character': [[1, 0, 0, 0, 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, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 0, -1, 0], [0, 0, -1, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1], [0, -1, 0, 0, 0, 0]], 'CharacterField': 9}, {'GalConj': 2, 'Baselabel': '1.9.3t1.a', 'Character': [[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]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.9.6t1.a', 'Character': [[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]], 'CharacterField': 3}, {'GalConj': 5, 'Baselabel': '1.27.9t1.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, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1]], 'CharacterField': 9}, {'GalConj': 5, '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, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0], [0, 0, -1, 0, 0, -1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, -1, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, -1]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '1.27.9t1.a', 'Character': [[1, 0, 0, 0, 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, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 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, 1, 0], [0, 0, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0]], 'CharacterField': 9}, {'GalConj': 6, 'Baselabel': '1.27.18t1.a', 'Character': [[1, 0, 0, 0, 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, -1, 0, 0, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 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, -1, 0], [0, 0, 1, 0, 0, 1], [0, 1, 0, 0, 1, 0]], 'CharacterField': 9}], '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': '1', 'Order': 2, 'Representative': [12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13]}, {'Size': '1', 'Order': 3, 'Representative': [7, 14, 9, 16, 11, 18, 13, 2, 15, 4, 17, 6, 1, 8, 3, 10, 5, 12]}, {'Size': '1', 'Order': 3, 'Representative': [13, 8, 15, 10, 17, 12, 1, 14, 3, 16, 5, 18, 7, 2, 9, 4, 11, 6]}, {'Size': '1', 'Order': 6, 'Representative': [18, 5, 16, 3, 14, 1, 12, 17, 10, 15, 8, 13, 6, 11, 4, 9, 2, 7]}, {'Size': '1', 'Order': 6, 'Representative': [6, 17, 4, 15, 2, 13, 18, 11, 16, 9, 14, 7, 12, 5, 10, 3, 8, 1]}, {'Size': '1', 'Order': 9, 'Representative': [15, 18, 11, 14, 7, 10, 3, 6, 17, 2, 13, 16, 9, 12, 5, 8, 1, 4]}, {'Size': '1', 'Order': 9, 'Representative': [5, 4, 13, 12, 3, 2, 11, 10, 1, 18, 9, 8, 17, 16, 7, 6, 15, 14]}, {'Size': '1', 'Order': 9, 'Representative': [3, 12, 17, 8, 13, 4, 9, 18, 5, 14, 1, 10, 15, 6, 11, 2, 7, 16]}, {'Size': '1', 'Order': 9, 'Representative': [11, 16, 1, 6, 9, 14, 17, 4, 7, 12, 15, 2, 5, 10, 13, 18, 3, 8]}, {'Size': '1', 'Order': 9, 'Representative': [9, 6, 5, 2, 1, 16, 15, 12, 11, 8, 7, 4, 3, 18, 17, 14, 13, 10]}, {'Size': '1', 'Order': 9, 'Representative': [17, 10, 7, 18, 15, 8, 5, 16, 13, 6, 3, 14, 11, 4, 1, 12, 9, 2]}, {'Size': '1', 'Order': 18, 'Representative': [4, 7, 8, 11, 12, 15, 16, 1, 2, 5, 6, 9, 10, 13, 14, 17, 18, 3]}, {'Size': '1', 'Order': 18, 'Representative': [14, 3, 6, 13, 16, 5, 8, 15, 18, 7, 10, 17, 2, 9, 12, 1, 4, 11]}, {'Size': '1', 'Order': 18, 'Representative': [10, 1, 14, 5, 18, 9, 4, 13, 8, 17, 12, 3, 16, 7, 2, 11, 6, 15]}, {'Size': '1', 'Order': 18, 'Representative': [2, 15, 12, 7, 4, 17, 14, 9, 6, 1, 16, 11, 8, 3, 18, 13, 10, 5]}, {'Size': '1', 'Order': 18, 'Representative': [16, 13, 2, 17, 6, 3, 10, 7, 14, 11, 18, 15, 4, 1, 8, 5, 12, 9]}, {'Size': '1', 'Order': 18, 'Representative': [8, 9, 18, 1, 10, 11, 2, 3, 12, 13, 4, 5, 14, 15, 6, 7, 16, 17]}], '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': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['189', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-108', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['297', '1'], 'ConjugacyClass': 5}, {'RootOf': ['81', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [6, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [3, 15, -1, -4, 9, -8, 17, -2, 11, -9, -17, 7, 17, -15, 16, -16, -1]}, 'Classes': [{'RootOf': ['-117', '1'], 'ConjugacyClass': 7}, {'RootOf': ['216', '1'], 'ConjugacyClass': 8}, {'RootOf': ['72', '1'], 'ConjugacyClass': 9}, {'RootOf': ['-216', '1'], 'ConjugacyClass': 10}, {'RootOf': ['45', '1'], 'ConjugacyClass': 11}, {'RootOf': ['0', '1'], 'ConjugacyClass': 12}], 'Algorithm': 'RES', 'CycleType': [9, 9]}, {'Data': {'Powers': [1], 'Resolvent': [11, -6, 1, -4, 6, 11, -3, -4, 2, 10, 1, -6, 11, 10, -1, 7, -2]}, 'Classes': [{'RootOf': ['-18', '1'], 'ConjugacyClass': 13}, {'RootOf': ['36', '1'], 'ConjugacyClass': 14}, {'RootOf': ['90', '1'], 'ConjugacyClass': 15}, {'RootOf': ['198', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-72', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-234', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [18]}], 'Frobs': [13, 1, 14, 9, 17, 8, 5, 3, 16, 13, 10, 4, 18, 7, 15, 2, 14, 9, 8, 5, 3, 11, 13, 6, 7, 15, 12, 2, 1, 14, 3, 16, 13, 10, 18, 7, 12, 1, 14, 17, 5, 3, 13, 10, 6, 4, 12, 9, 17, 8, 5, 16, 11, 6, 18, 15, 2, 1, 9, 17, 8, 16, 4, 18, 7, 15, 9, 8, 16, 11, 13, 6, 7, 12, 1, 14, 17, 3, 16, 10, 18, 7, 2, 1, 9, 17, 5, 11, 13, 10, 6, 15, 1, 14, 8, 5, 16, 6, 4, 1, 9, 5, 16, 13, 10, 4, 15, 2, 14, 9, 8, 3, 16, 11, 4, 15, 12, 2, 14, 17, 8, 11, 13, 6, 7, 2, 9, 5, 11, 10, 4, 18, 12, 1, 14, 8, 5, 10, 18, 2, 1, 17, 8, 5, 3, 13, 7, 15, 12, 2, 8, 5, 3, 16, 7, 15, 1, 17, 3, 16, 13, 6, 12, 2, 14, 17, 3, 11], 'G-Gens': [[18, 5, 16, 3, 14, 1, 12, 17, 10, 15, 8, 13, 6, 11, 4, 9, 2, 7], [12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13], [15, 18, 11, 14, 7, 10, 3, 6, 17, 2, 13, 16, 9, 12, 5, 8, 1, 4]], 'G-Name': 'C18', 'Polynomial': [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'QpRts': [['-7316298', '-4926822', '8877292', '-4275907', '-3351119', '1811260', '2947951', '1308467', '-6067632'], ['7389513', '3172997', '-1487519', '11472886', '10021566', '-217352', '5670837', '5605212', '-11456727'], ['-10358923', '-3678047', '12513414', '-7675671', '-6467326', '-6253118', '-551634', '-13190357', '2802250'], ['-10015996', '2963956', '-2315280', '-4034698', '8985123', '3756849', '9484345', '6929009', '6295556'], ['-8450430', '6887957', '-7080380', '12857067', '-4294777', '5603233', '-9179727', '1735350', '3770266'], ['-592042', '8976805', '-8083062', '4982767', '8553265', '3641178', '-10231312', '6470107', '11198842'], ['8109745', '8901726', '-5448825', '-10609071', '4893681', '-14100736', '-11218936', '5594952', '-12637014'], ['5238587', '-12976366', '792915', '9627993', '-13551183', '6038928', '13847038', '-14165318', '6701798'], ['-13462468', '8561892', '14030907', '4982870', '11577741', '14193099', '-9715559', '7628769', '-8069609'], ['9692518', '180454', '-4185381', '-6319248', '2216963', '170715', '-13385821', '5943676', '-1085549'], ['-2635586', '8580584', '465407', '3170910', '-517850', '-8553945', '-12245299', '-13529057', '-6219992'], ['-2076511', '-1221063', '-10315696', '-4508780', '-1297463', '-8642897', '-7574914', '11090040', '-929746'], ['-793447', '-3974904', '-3428467', '-13744173', '-1542562', '12289476', '8270985', '-6903419', '-9924505'], ['-12628100', '9803369', '694604', '7528272', '3529617', '-5821576', '9111276', '8560106', '4754929'], ['-4807760', '-4883845', '2084830', '2692801', '-5110415', '-7939981', '10267193', '5561588', '5267359'], ['323478', '-3144410', '6500661', '10353946', '-11202086', '-3927564', '3901476', '-12872685', '-5210007'], ['11086016', '13160610', '6614973', '12601174', '4812627', '2950712', '-7204125', '11793707', '2449726'], ['2668553', '-7755742', '-10230393', '-473987', '-7255802', '5001719', '-10822925', '11069004', '-10269096']], 'QpRts-minpoly': [28, 29, 20, 4, 0, 0, 0, 0, 0, 1], 'QpRts-p': 31, 'QpRts-prec': 5, 'Size': 18, 'TransitiveDegree': 18}