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artin_reps • Show schema
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{'BadPrimes': [11, 13], 'Baselabel': '1.143.4t1.a', 'CharacterField': 4, 'Conductor': 143, 'Container': '4t1', 'Dets': ['143.109', '143.21'], 'Dim': 1, 'GalConjSigns': [0, 0], 'Galn': 4, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [1, 5, 5, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, -1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, -1], [0, 1]], 'GalOrbIndex': 2, 'HardFactors': [1, 5, 5, 1], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '4T1', 'Galt': 1, 'HardPrimes': [3, 11, 13, 17], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [81, -35, -37, -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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.143.4t1.a', 'Character': [[1, 0], [-1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '1.13.2t1.a', 'Character': [[1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 2, 'Baselabel': '1.143.4t1.a', 'Character': [[1, 0], [-1, 0], [0, -1], [0, 1]], 'CharacterField': 4}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4]}, {'Size': '1', 'Order': 2, 'Representative': [2, 1, 4, 3]}, {'Size': '1', 'Order': 4, 'Representative': [4, 3, 1, 2]}, {'Size': '1', 'Order': 4, 'Representative': [3, 4, 2, 1]}], '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': [0, 0, 1]}, 'Classes': [{'RootOf': ['-35', '1'], 'ConjugacyClass': 3}, {'RootOf': ['108', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [4]}], 'Frobs': [3, 1, 4, 4, 4, 1, 1, 3, 2, 2, 4, 3, 3, 1, 3, 1, 3, 2, 4, 4, 4, 2, 3, 3, 4, 1, 2, 2, 3, 1, 1, 2, 3, 2, 3, 4, 1, 3, 4, 1, 2, 2, 1, 4, 3, 2, 2, 4, 3, 3, 1, 3, 4, 2, 2, 2, 1, 4, 1, 4, 1, 4, 4, 2, 1, 4, 4, 1, 2, 4, 4, 4, 1, 2, 4, 4, 2, 3, 3, 3, 1, 4, 3, 2, 1, 1, 3, 3, 3, 3, 2, 4, 4, 1, 4, 2, 4, 1, 2, 4, 2, 4, 1, 1, 1, 4, 4, 4, 1, 2, 2, 3, 4, 3, 3, 2, 4, 2, 1, 2, 3, 1, 2, 3, 4, 1, 3, 2, 2, 3, 4, 3, 2, 1, 4, 3, 4, 4, 2, 2, 3, 3, 2, 4, 2, 3, 4, 1, 1, 4, 3, 2, 2, 2, 2, 1, 2, 4, 2, 3, 3, 1, 3, 1, 4, 3, 1, 2], 'G-Gens': [[4, 3, 1, 2], [2, 1, 4, 3]], 'G-Name': 'C4', 'Polynomial': [81, -35, -37, -1, 1], 'QpRts': [['-65519915'], ['2467092'], ['10833992'], ['52218832']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 43, 'QpRts-prec': 5, 'Size': 4, 'TransitiveDegree': 4}