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artin_reps • Show schema
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{'BadPrimes': [2, 5], 'Baselabel': '1.80.4t1.b', 'CharacterField': 4, 'Conductor': 80, 'Container': '4t1', 'Dets': ['80.59', '80.19'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [5, 5], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [2, 5], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [50, 0, 20, 0, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.80.4t1.b', 'Character': [[1, 0], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.8.2t1.a', 'Character': [[1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '1.80.4t1.b', 'Character': [[1, 0], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4]}, {'Size': '1', 'Order': 2, 'Representative': [4, 3, 2, 1]}, {'Size': '1', 'Order': 4, 'Representative': [3, 1, 4, 2]}, {'Size': '1', 'Order': 4, 'Representative': [2, 4, 1, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['200', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-200', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [4]}], 'Frobs': [1, 4, 3, 2, 4, 3, 2, 3, 2, 4, 2, 4, 2, 3, 1, 4, 4, 4, 4, 1, 1, 2, 4, 2, 2, 3, 2, 3, 4, 2, 1, 3, 1, 4, 3, 1, 3, 4, 2, 3, 3, 3, 2, 2, 4, 1, 3, 1, 4, 3, 1, 2, 1, 4, 2, 2, 4, 2, 4, 2, 3, 4, 4, 1, 1, 3, 4, 2, 3, 4, 2, 1, 1, 4, 4, 1, 3, 3, 1, 2, 3, 3, 2, 2, 1, 3, 1, 1, 4, 1, 4, 2, 2, 4, 3, 2, 4, 2, 3, 4, 4, 3, 4, 2, 4, 2, 3, 2, 1, 2, 1, 4, 1, 4, 1, 1, 4, 2, 3, 3, 3, 2, 4, 3, 3, 4, 3, 2, 2, 3, 3, 2, 2, 4, 2, 1, 4, 4, 3, 2, 4, 3, 2, 3, 4, 1, 4, 1, 4, 1, 3, 1, 4, 2, 3, 2, 1, 1, 1, 4, 4, 1, 2, 4, 2, 2, 2, 4], 'G-Gens': [[3, 1, 4, 2], [4, 3, 2, 1]], 'G-Name': 'C4', 'Polynomial': [50, 0, 20, 0, 1], 'QpRts': [['-45432263'], ['-54186622'], ['54186622'], ['45432263']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 47, 'QpRts-prec': 5, 'Size': 4, 'TransitiveDegree': 4}