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artin_reps • Show schema
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{'BadPrimes': [2, 3, 5], 'Baselabel': '2.1200.6t3.c', 'CharacterField': 1, 'Conductor': 1200, 'Container': '6t3', 'Dets': ['1.3.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [-1], [1]], 'GalOrbIndex': 1, 'HardFactors': [7, 8, 7, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [1], [1]], [[1], [-1], [1]], [[1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T3', 'Galt': 3, 'HardPrimes': [2, 3, 5, 37], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [2, -8, 16, -6, 2, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-3, -3, -1, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.12.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.4.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.300.3t2.a', 'Character': [[2], [2], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.1200.6t3.c', 'Character': [[2], [-2], [0], [0], [-1], [1]], 'CharacterField': 1}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [4, 5, 6, 1, 2, 3]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 3, 5, 4, 6]}, {'Size': '3', 'Order': 2, 'Representative': [4, 3, 2, 1, 6, 5]}, {'Size': '2', 'Order': 3, 'Representative': [2, 6, 4, 5, 3, 1]}, {'Size': '2', 'Order': 6, 'Representative': [3, 4, 2, 6, 1, 5]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['14', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-736', '48', '12', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [3, 2, 3, 6, 4, 5, 3, 6, 4, 3, 6, 1, 3, 6, 4, 3, 4, 5, 6, 4, 1, 2, 4, 3, 5, 3, 2, 4, 5, 3, 2, 4, 3, 2, 3, 6, 5, 6, 4, 3, 4, 5, 4, 5, 3, 6, 6, 6, 4, 5, 3, 4, 5, 4, 3, 4, 3, 2, 5, 3, 6, 3, 6, 4, 5, 3, 2, 5, 4, 1, 3, 4, 6, 5, 6, 4, 3, 5, 3, 5, 4, 1, 4, 5, 6, 4, 3, 1, 3, 2, 4, 4, 6, 4, 6, 4, 3, 3, 6, 5, 2, 3, 4, 3, 6, 5, 4, 3, 4, 5, 2, 1, 3, 6, 6, 3, 2, 4, 3, 4, 1, 1, 3, 4, 2, 3, 5, 4, 6, 1, 2, 4, 2, 5, 3, 5, 3, 6, 3, 3, 6, 3, 6, 4, 1, 4, 5, 3, 2, 4, 5, 3, 6, 4, 2, 4, 6, 3, 5, 3, 4, 3, 2, 4, 3, 4, 6, 1], 'G-Gens': [[2, 1, 3, 5, 4, 6], [1, 6, 5, 4, 3, 2], [3, 4, 2, 6, 1, 5]], 'G-Name': 'D12', 'Polynomial': [2, -8, 16, -6, 2, -2, 1], 'QpRts': [['-204068', '-5630669'], ['-6663640', '5630669'], ['2084685', '0'], ['-3673054', '-353221'], ['1978482', '353221'], ['6477597', '0']], 'QpRts-minpoly': [3, 16, 1], 'QpRts-p': 17, 'QpRts-prec': 6, 'Size': 12, 'TransitiveDegree': 6}