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artin_reps • Show schema
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{'BadPrimes': [23], 'Baselabel': '1.23.22t1.a', 'CharacterField': 11, 'Conductor': 23, 'Container': '22t1', 'Dets': ['23.10', '23.15', '23.11', '23.5', '23.19', '23.17', '23.14', '23.21', '23.20', '23.7'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'Galn': 22, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-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], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -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], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, -1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 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8, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, -1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 1]], [[1], [0, 0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [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, 0, 1], [0, 1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 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0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1], [0, 0, 1], [0, 1], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -1], [0, 0, 0, -1], [0, 0, -1], [0, -1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [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, -1], [0, 0, 0, 0, 0, 0, -1]], 'GalOrbIndex': 10, 'HardFactors': [5, 4, 14, 18, 12, 23], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, 0, -1]], [[1], [0, 0, 0, 0, -1]], [[1], [0, 0, 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, 0, 1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 0, 1]], [[1], [0, 0, 0, 0, 0, 0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'GaloisLabel': '22T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 7, 13, 23], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
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artin_field_data • Show schema
Hide schema
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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, 1, 0, 0, 0], [0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 1], [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, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0]], 'CharacterField': 11}, {'GalConj': 8, 'Baselabel': '1.23.22t1.a', 'Character': [[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, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 1, 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, 1], [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, 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, -1, 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, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0]], 'CharacterField': 11}, {'GalConj': 9, 'Baselabel': '1.23.11t1.a', 'Character': [[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, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 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, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 9, 'Baselabel': '1.23.22t1.a', 'Character': [[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, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, -1, 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, -1], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 10, 'Baselabel': '1.23.11t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [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, 1, 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, 1, 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, 1, 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, 1, 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], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [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, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0]], 'CharacterField': 11}, {'GalConj': 10, 'Baselabel': '1.23.22t1.a', 'Character': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1], [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, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 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6, 10, 5, 21, 2, 3, 15, 19, 4, 22, 13, 12, 9, 20, 1, 7, 14, 18]}, {'Size': '1', 'Order': 11, 'Representative': [2, 13, 7, 1, 22, 18, 14, 5, 15, 20, 16, 17, 19, 10, 12, 4, 11, 8, 9, 21, 6, 3]}, {'Size': '1', 'Order': 11, 'Representative': [15, 12, 21, 9, 10, 3, 6, 14, 16, 8, 13, 1, 17, 18, 4, 19, 2, 7, 11, 5, 22, 20]}, {'Size': '1', 'Order': 11, 'Representative': [16, 4, 5, 11, 18, 20, 22, 6, 13, 7, 12, 9, 1, 3, 19, 17, 15, 21, 2, 14, 10, 8]}, {'Size': '1', 'Order': 11, 'Representative': [13, 19, 14, 2, 3, 8, 10, 22, 12, 21, 4, 11, 9, 20, 17, 1, 16, 5, 15, 6, 18, 7]}, {'Size': '1', 'Order': 11, 'Representative': [12, 17, 6, 15, 20, 7, 18, 10, 4, 5, 19, 2, 11, 8, 1, 9, 13, 14, 16, 22, 3, 21]}, {'Size': '1', 'Order': 11, 'Representative': [4, 1, 22, 16, 8, 21, 3, 18, 19, 14, 17, 15, 2, 7, 9, 11, 12, 6, 13, 10, 20, 5]}, {'Size': '1', 'Order': 11, 'Representative': [19, 9, 10, 13, 7, 5, 20, 3, 17, 6, 1, 16, 15, 21, 11, 2, 4, 22, 12, 18, 8, 14]}, {'Size': '1', 'Order': 11, 'Representative': [17, 11, 18, 12, 21, 14, 8, 20, 1, 22, 9, 13, 16, 5, 2, 15, 19, 10, 4, 3, 7, 6]}, {'Size': '1', 'Order': 22, 'Representative': [18, 8, 11, 6, 12, 19, 16, 15, 3, 1, 20, 14, 5, 4, 7, 21, 10, 9, 22, 2, 13, 17]}, {'Size': '1', 'Order': 22, 'Representative': [3, 7, 2, 22, 4, 17, 13, 16, 20, 9, 8, 6, 14, 19, 21, 5, 18, 11, 10, 15, 12, 1]}, {'Size': '1', 'Order': 22, 'Representative': [20, 21, 15, 10, 19, 1, 12, 13, 8, 11, 7, 22, 6, 17, 5, 14, 3, 2, 18, 16, 4, 9]}, {'Size': '1', 'Order': 22, 'Representative': [8, 5, 16, 18, 17, 9, 4, 12, 7, 2, 21, 10, 22, 1, 14, 6, 20, 15, 3, 13, 19, 11]}, {'Size': '1', 'Order': 22, 'Representative': [7, 14, 13, 3, 1, 11, 19, 4, 21, 15, 5, 18, 10, 9, 6, 22, 8, 16, 20, 12, 17, 2]}, {'Size': '1', 'Order': 22, 'Representative': [5, 22, 4, 8, 11, 15, 1, 17, 14, 13, 6, 20, 3, 2, 10, 18, 21, 12, 7, 19, 9, 16]}, {'Size': '1', 'Order': 22, 'Representative': [14, 10, 19, 7, 2, 16, 9, 1, 6, 12, 22, 8, 20, 15, 18, 3, 5, 4, 21, 17, 11, 13]}, {'Size': '1', 'Order': 22, 'Representative': [6, 18, 17, 21, 15, 13, 11, 9, 22, 4, 10, 7, 8, 16, 3, 20, 14, 19, 5, 1, 2, 12]}, {'Size': '1', 'Order': 22, 'Representative': [22, 3, 1, 5, 16, 12, 2, 11, 10, 19, 18, 21, 7, 13, 20, 8, 6, 17, 14, 9, 15, 4]}, {'Size': '1', 'Order': 22, 'Representative': [10, 20, 9, 14, 13, 4, 15, 2, 18, 17, 3, 5, 21, 12, 8, 7, 22, 1, 6, 11, 16, 19]}], '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, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-356', '1'], 'ConjugacyClass': 3}, {'RootOf': ['35', '1'], 'ConjugacyClass': 4}, {'RootOf': ['-34', '1'], 'ConjugacyClass': 5}, {'RootOf': ['173', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-126', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-80', '1'], 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