Formats: - HTML - YAML - JSON - 2026-10-11T06:25:59.995260
  • artin_reps • Show schema
    {'BadPrimes': [2, 3], 'Baselabel': '2.2916.18t16.f', 'CharacterField': 9, 'Conductor': 2916, 'Container': '18t16', 'Dets': ['1.27.18t1.a.b', '1.27.18t1.a.d', '1.27.18t1.a.e', '1.27.18t1.a.f', '1.27.18t1.a.c', '1.27.18t1.a.a'], '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], [0, 0, 0, -1], [1, 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': 1, 'HardFactors': [28, 28, 18, 11, 3, 19, 5, 18, 18, 20, 12, 13, 23, 20, 11, 13], '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], [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, -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, -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]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, 0, 0, -2], [0, 0, 0, 2], [-1], [1, 0, 0, 1], [0, 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': 2, 'HardFactors': [28, 28, 18, 11, 3, 19, 5, 18, 18, 20, 12, 13, 23, 20, 11, 13], '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], [-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, 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, -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]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, 0, 0, -2], [0, 0, 0, 2], [-1], [1, 0, 0, 1], [0, 0, 0, -1], [0], [0], [0, 0, -2, 0, 0, -2], [0, -2, 0, 0, -2], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 2], [0, 0, 2], [0, 2], [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], [0], [0], [0], [0]], 'GalOrbIndex': 3, 'HardFactors': [28, 28, 18, 11, 3, 19, 5, 18, 18, 20, 12, 13, 23, 20, 11, 13], '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], [-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, 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, 0, 1, 0, 0, 1]], [[1], [0], [0, 0, 0, 0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, 1, 0, 0, 1]], [[1], [0], [0, 0, 0, 0, 0, -1]], [[1], [0], [0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [0], [0, 0, 0, 2], [-2, 0, 0, -2], [-1], [0, 0, 0, -1], [1, 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': 4, 'HardFactors': [28, 28, 18, 11, 3, 19, 5, 18, 18, 20, 12, 13, 23, 20, 11, 13], '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], [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, 2, 0, 0, 2], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, -2], [0, 1]], [[1], [0, -2], [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, -2], [0, 0, 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, 1], [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], [0, 0, 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], [0, 0, 0, 2], [-2, 0, 0, -2], [-1], [0, 0, 0, -1], [1, 0, 0, 1], [0], [0], [0, 0, 0, 0, 2], [0, 0, -2, 0, 0, -2], [0, -2, 0, 0, -2], [0, 0, 2], [0, 2], [0, 0, 0, 0, 0, 2], [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], [0], [0], [0], [0], [0]], 'GalOrbIndex': 5, 'HardFactors': [28, 28, 18, 11, 3, 19, 5, 18, 18, 20, 12, 13, 23, 20, 11, 13], '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], [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, -2], [0, 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, -2], [0, 0, 0, 0, 1]], [[1], [0, -2], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, -2], [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], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1], [0, 0, 0, 0, 1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1], [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], [-2, 0, 0, -2], [0, 0, 0, 2], [-1], [1, 0, 0, 1], [0, 0, 0, -1], [0], [0], [0, 0, 0, 0, 0, 2], [0, 2], [0, 0, 2], [0, -2, 0, 0, -2], [0, 0, -2, 0, 0, -2], [0, 0, 0, 0, 2], [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], [0], [0], [0], [0]], 'GalOrbIndex': 6, 'HardFactors': [28, 28, 18, 11, 3, 19, 5, 18, 18, 20, 12, 13, 23, 20, 11, 13], '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], [-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, 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, 0, 0, 0, 0, -1]], [[1], [0], [0, 1, 0, 0, 1]], [[1], [0], [0, 0, 1, 0, 0, 1]], [[1], [0], [0, -1]], [[1], [0], [0, 0, -1]], [[1], [0], [0, 0, 0, 0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0], 'GaloisLabel': '18T16', 'Galt': 16, 'HardPrimes': [2, 3, 7, 13, 19, 31, 109, 277, 601, 1051, 1951, 2083, 9209, 16927, 238639, 729679], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [64, 0, 0, -288, 0, 0, 576, 0, 0, -424, 0, 0, 108, 0, 0, 0, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-12, 0, 0, 1], 'Proj_nTj': [3, 2]}
  • artin_field_data • Show schema
    {'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], [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], [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], [1, 1], [0, -1], [1, 1], [0, -1], [1, 1], [0, -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], [-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], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 1], [-1, -1], [0, 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], [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, 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11, 4, 1, 6, 9, 2, 5, 16, 13, 18, 3, 14, 17, 10, 7]}, {'Size': '1', 'Order': 9, 'Representative': [16, 1, 18, 14, 15, 11, 4, 7, 6, 2, 3, 17, 10, 13, 12, 8, 9, 5]}, {'Size': '1', 'Order': 9, 'Representative': [8, 16, 5, 13, 12, 3, 14, 4, 11, 1, 18, 9, 2, 10, 17, 7, 6, 15]}, {'Size': '1', 'Order': 9, 'Representative': [4, 7, 12, 2, 9, 5, 10, 13, 18, 8, 15, 11, 16, 1, 6, 14, 3, 17]}, {'Size': '1', 'Order': 9, 'Representative': [14, 4, 17, 1, 6, 15, 2, 10, 5, 7, 12, 3, 8, 16, 11, 13, 18, 9]}, {'Size': '1', 'Order': 9, 'Representative': [10, 13, 6, 8, 3, 17, 16, 1, 12, 14, 9, 5, 4, 7, 18, 2, 15, 11]}, {'Size': '1', 'Order': 9, 'Representative': [2, 10, 11, 7, 18, 9, 8, 16, 17, 13, 6, 15, 14, 4, 5, 1, 12, 3]}, {'Size': '2', 'Order': 9, 'Representative': [4, 7, 6, 2, 3, 17, 10, 13, 12, 8, 9, 5, 16, 1, 18, 14, 15, 11]}, {'Size': '2', 'Order': 9, 'Representative': [2, 10, 17, 7, 6, 15, 8, 16, 5, 13, 12, 3, 14, 4, 11, 1, 18, 9]}, {'Size': '2', 'Order': 9, 'Representative': [10, 13, 18, 8, 15, 11, 16, 1, 6, 14, 3, 17, 4, 7, 12, 2, 9, 5]}, {'Size': '2', 'Order': 9, 'Representative': [8, 16, 11, 13, 18, 9, 14, 4, 17, 1, 6, 15, 2, 10, 5, 7, 12, 3]}, {'Size': '2', 'Order': 9, 'Representative': [16, 1, 12, 14, 9, 5, 4, 7, 18, 2, 15, 11, 10, 13, 6, 8, 3, 17]}, {'Size': '2', 'Order': 9, 'Representative': [14, 4, 5, 1, 12, 3, 2, 10, 11, 7, 18, 9, 8, 16, 17, 13, 6, 15]}, {'Size': '3', 'Order': 18, 'Representative': [9, 17, 4, 18, 13, 8, 3, 11, 16, 12, 7, 2, 15, 5, 10, 6, 1, 14]}, {'Size': '3', 'Order': 18, 'Representative': [11, 6, 13, 15, 2, 4, 5, 18, 7, 9, 14, 16, 17, 12, 1, 3, 8, 10]}, {'Size': '3', 'Order': 18, 'Representative': [3, 11, 10, 12, 1, 14, 15, 5, 4, 6, 13, 8, 9, 17, 16, 18, 7, 2]}, {'Size': '3', 'Order': 18, 'Representative': [5, 18, 1, 9, 8, 10, 17, 12, 13, 3, 2, 4, 11, 6, 7, 15, 14, 16]}, {'Size': '3', 'Order': 18, 'Representative': [15, 5, 16, 6, 7, 2, 9, 17, 10, 18, 1, 14, 3, 11, 4, 12, 13, 8]}, {'Size': '3', 'Order': 18, 'Representative': [17, 12, 7, 3, 14, 16, 11, 6, 1, 15, 8, 10, 5, 18, 13, 9, 2, 4]}], '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': ['2916', '54', '1'], 'ConjugacyClass': 6}, {'RootOf': ['2916', '-54', '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': ['-54', '1'], 'ConjugacyClass': 3}, {'RootOf': ['54', '1'], 'ConjugacyClass': 4}, {'RootOf': ['0', '0', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [2, 5, -2, -7, 1]}, 'Classes': [{'RootOf': ['-6377292', '0', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['42978924', '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': ['4856328', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-596700', '1'], 'ConjugacyClass': 11}, {'RootOf': ['-2493072', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-2396412', '1'], 'ConjugacyClass': 13}, {'RootOf': ['-2363256', '1'], 'ConjugacyClass': 14}, {'RootOf': ['2993112', '1'], 'ConjugacyClass': 15}, {'RootOf': ['23583921643584', '-4856328', '1'], 'ConjugacyClass': 16}, {'RootOf': ['356050890000', '596700', '1'], 'ConjugacyClass': 17}, {'RootOf': ['6215407997184', '2493072', '1'], 'ConjugacyClass': 18}, {'RootOf': ['5742790473744', '2396412', '1'], 'ConjugacyClass': 19}, {'RootOf': ['5584978921536', '2363256', '1'], 'ConjugacyClass': 20}, {'RootOf': ['8958719444544', '-2993112', '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': ['-16966070595099433764', '0', '0', '1'], 'ConjugacyClass': 22}, {'RootOf': ['-27312328075836711168', '0', '0', '1'], 'ConjugacyClass': 23}, {'RootOf': ['14302832884507337364', '0', '0', '1'], 'ConjugacyClass': 24}, {'RootOf': ['80358472645417001268', '0', '0', '1'], 'ConjugacyClass': 25}, {'RootOf': ['2873796732000000', '0', '0', '1'], 'ConjugacyClass': 26}, {'RootOf': ['-2216181044088562500', '0', '0', '1'], 'ConjugacyClass': 27}], 'Algorithm': 'RES', 'CycleType': [18]}], 'Frobs': [23, 1, 24, 18, 25, 11, 8, 3, 22, 23, 19, 7, 26, 16, 27, 2, 24, 18, 17, 8, 6, 14, 23, 9, 10, 27, 21, 2, 5, 24, 6, 22, 23, 19, 26, 16, 21, 5, 24, 25, 8, 6, 23, 19, 9, 4, 15, 18, 25, 17, 8, 22, 20, 9, 26, 27, 2, 5, 18, 25, 17, 22, 4, 26, 16, 27, 12, 17, 22, 20, 23, 9, 16, 15, 5, 24, 25, 6, 22, 19, 26, 16, 2, 5, 12, 25, 8, 20, 23, 13, 9, 27, 1, 24, 11, 8, 22, 9, 7, 5, 18, 8, 22, 23, 19, 7, 27, 2, 24, 18, 17, 6, 22, 20, 7, 27, 15, 2, 24, 25, 17, 14, 23, 9, 16, 2, 12, 8, 14, 19, 7, 26, 21, 5, 24, 11, 8, 19, 26, 2, 5, 25, 11, 8, 3, 23, 16, 27, 21, 2, 17, 8, 3, 22, 10, 27, 1, 25, 6, 22, 23, 9, 21, 2, 24, 25, 6, 14], 'G-Gens': [[9, 17, 4, 18, 13, 8, 3, 11, 16, 12, 7, 2, 15, 5, 10, 6, 1, 14], [16, 1, 18, 14, 15, 11, 4, 7, 6, 2, 3, 17, 10, 13, 12, 8, 9, 5], [1, 2, 9, 4, 11, 12, 7, 8, 15, 10, 17, 18, 13, 14, 3, 16, 5, 6], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6]], 'G-Name': 'C9*S3', 'Polynomial': [64, 0, 0, -288, 0, 0, 576, 0, 0, -424, 0, 0, 108, 0, 0, 0, 0, 0, 1], 'QpRts': [['220501893707288380817215798508', '-115838857280803819353041007204', '-2986623925054310397061562646', '228715894588465370879677682485', '139927808880879480158237473447', '-171489951525823669907288260396', '-245258939428499305527397745526', '175705541632031805447700086905', '-118434020258362890151912955660'], ['-211761002640436364486246061291', '-119738582854102908009751113169', '-238303531466570519048446477525', '-90666359335629076887123833683', 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