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artin_reps • Show schema
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{'BadPrimes': [2, 13, 17], 'Baselabel': '2.3536.4t3.m', 'CharacterField': 1, 'Conductor': 3536, 'Container': '4t3', 'Dets': ['1.221.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1], 'Galn': 4, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [6, 7, 8], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0], [1]], [[1]], [[1], [1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '4T3', 'Galt': 3, 'HardPrimes': [2, 13, 17], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [17, 0, -9, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [4, 2], 'Proj_Polynomial': [1, 0, -15, 0, 1], 'Proj_nTj': [4, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.17.2t1.a', 'Character': [[1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.221.2t1.a', 'Character': [[1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3536.4t3.m', 'Character': [[2], [-2], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4]}, {'Size': '1', 'Order': 2, 'Representative': [4, 3, 2, 1]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 4, 3]}, {'Size': '2', 'Order': 2, 'Representative': [4, 2, 3, 1]}, {'Size': '2', 'Order': 4, 'Representative': [3, 1, 4, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-54', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-2448', '0', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4]}], 'Frobs': [3, 4, 5, 5, 5, 3, 1, 3, 4, 4, 5, 5, 5, 1, 3, 2, 3, 4, 3, 5, 5, 4, 3, 3, 5, 1, 2, 4, 5, 4, 2, 4, 3, 4, 3, 3, 2, 5, 5, 4, 2, 4, 1, 5, 5, 4, 4, 3, 5, 3, 4, 3, 5, 2, 2, 2, 4, 3, 4, 3, 4, 3, 3, 4, 4, 5, 3, 4, 4, 3, 3, 3, 4, 1, 5, 3, 2, 5, 5, 3, 4, 3, 5, 1, 4, 1, 5, 3, 3, 3, 1, 5, 5, 1, 5, 4, 3, 4, 1, 5, 4, 3, 2, 2, 4, 3, 3, 3, 2, 4, 4, 3, 5, 5, 3, 4, 5, 2, 4, 1, 3, 4, 4, 5, 5, 1, 5, 4, 1, 3, 3, 5, 4, 1, 3, 3, 3, 5, 1, 4, 5, 5, 4, 5, 2, 5, 5, 4, 1, 3, 5, 4, 1, 4, 4, 4, 1, 5, 1, 5, 5, 1, 3, 2, 3, 5, 4, 4], 'G-Gens': [[2, 1, 4, 3], [1, 3, 2, 4]], 'G-Name': 'D8', 'Polynomial': [17, 0, -9, 0, 1], 'QpRts': [['10257783'], ['-41572136'], ['41572136'], ['-10257783']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 43, 'QpRts-prec': 5, 'Size': 8, 'TransitiveDegree': 4}