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artin_reps • Show schema
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{'BadPrimes': [5, 13], 'Baselabel': '1.65.6t1.a', 'CharacterField': 3, 'Conductor': 65, 'Container': '6t1', 'Dets': ['65.4', '65.49'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 6, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [-1, -1], [0, -1], [1, 1]], 'GalOrbIndex': 1, 'HardFactors': [4, 6, 7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [1, 1]], [[1], [0, 1]], [[1], [-1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [-1, -1], [0, 1], [1, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [4, 6, 7, 7, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [1, 1]], [[1], [0, -1]], [[1], [-1, -1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '6T1', 'Galt': 1, 'HardPrimes': [2, 3, 5, 13, 47], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-1, -16, 58, 17, -18, -1, 1], 'NumBadPrimes': 2, '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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.65.2t1.a', 'Character': [[1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.65.6t1.a', 'Character': [[1, 0], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.13.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.65.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [3, 4, 1, 2, 6, 5]}, {'Size': '1', 'Order': 3, 'Representative': [2, 5, 4, 6, 1, 3]}, {'Size': '1', 'Order': 3, 'Representative': [5, 1, 6, 3, 2, 4]}, {'Size': '1', 'Order': 6, 'Representative': [4, 6, 2, 5, 3, 1]}, {'Size': '1', 'Order': 6, 'Representative': [6, 3, 5, 1, 4, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-30', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-17', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-30', '1'], 'ConjugacyClass': 5}, {'RootOf': ['48', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [6]}], 'Frobs': [4, 6, 1, 3, 6, 1, 5, 5, 6, 4, 2, 4, 6, 5, 1, 2, 5, 3, 4, 5, 1, 1, 1, 6, 3, 4, 2, 6, 2, 5, 6, 1, 3, 3, 5, 2, 2, 3, 4, 5, 4, 1, 3, 4, 4, 3, 4, 4, 3, 2, 2, 2, 5, 3, 6, 6, 3, 6, 5, 2, 6, 3, 1, 1, 2, 1, 5, 2, 5, 6, 4, 2, 6, 5, 6, 3, 1, 3, 6, 5, 4, 2, 6, 5, 4, 2, 5, 4, 5, 1, 2, 6, 3, 4, 2, 5, 6, 1, 6, 2, 2, 4, 5, 4, 1, 1, 4, 1, 1, 4, 5, 4, 3, 2, 5, 3, 3, 6, 6, 3, 6, 6, 2, 3, 6, 1, 5, 3, 2, 1, 6, 4, 4, 6, 5, 6, 3, 3, 5, 4, 2, 6, 5, 1, 4, 5, 1, 2, 1, 1, 3, 4, 2, 6, 6, 1, 3, 5, 2, 2, 4, 5, 1, 3, 4, 1, 4, 5], 'G-Gens': [[3, 4, 1, 2, 6, 5], [2, 5, 4, 6, 1, 3]], 'G-Name': 'C6', 'Polynomial': [-1, -16, 58, 17, -18, -1, 1], 'QpRts': [['365131', '5778947'], ['-8587407', '-5455148'], ['4550574', '-5778947'], ['6466130', '5455148'], ['-4626145', '8662224'], ['1831718', '-8662224']], 'QpRts-minpoly': [3, 29, 1], 'QpRts-p': 31, 'QpRts-prec': 5, 'Size': 6, 'TransitiveDegree': 6}