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artin_reps • Show schema
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{'BadPrimes': [79], 'Baselabel': '2.79.5t2.a', 'CharacterField': 5, 'Conductor': 79, 'Container': '5t2', 'Dets': ['1.79.2t1.a.a', '1.79.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [1, 1], 'Galn': 5, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [0], [0, 0, 1, 1], [-1, 0, -1, -1]], 'GalOrbIndex': 1, 'HardFactors': [3, 5], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1, -1], [1]], [[1], [1, 0, 1, 1], [1]], [[1], [-1]]]}, {'Sign': 1, 'Character': [[2], [0], [-1, 0, -1, -1], [0, 0, 1, 1]], 'GalOrbIndex': 2, 'HardFactors': [3, 5], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [1, 0, 1, 1], [1]], [[1], [0, 0, -1, -1], [1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [1, 1], 'GaloisLabel': '5T2', 'Galt': 2, 'HardPrimes': [2, 79], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, 3, -2, 1, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [10, 1], 'Proj_Polynomial': [-1, 3, -2, 1, -1, 1], 'Proj_nTj': [5, 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.79.2t1.a', 'Character': [[1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.79.5t2.a', 'Character': [[2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 1], [-1, 0, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '2.79.5t2.a', 'Character': [[2, 0, 0, 0], [0, 0, 0, 0], [-1, 0, -1, -1], [0, 0, 1, 1]], 'CharacterField': 5}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5]}, {'Size': '5', 'Order': 2, 'Representative': [3, 5, 1, 4, 2]}, {'Size': '2', 'Order': 5, 'Representative': [5, 3, 1, 2, 4]}, {'Size': '2', 'Order': 5, 'Representative': [4, 1, 5, 3, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2]}, {'Data': [2, 3, 4, 5, 1], 'Classes': [{'RootOf': ['-79', '1'], 'ConjugacyClass': 4}, {'RootOf': ['79', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'ALT', 'CycleType': [5]}], 'Frobs': [3, 2, 4, 2, 3, 3, 2, 4, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 1, 1, 3, 4, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 3, 3, 2, 1, 3, 2, 2, 2, 2, 2, 1, 2, 2, 2, 4, 3, 2, 3, 3, 4, 2, 4, 4, 3, 2, 2, 2, 3, 1, 2, 4, 4, 2, 2, 2, 3, 2, 2, 3, 3, 1, 2, 2, 2, 4, 4, 4, 4, 2, 2, 3, 2, 2, 3, 1, 3, 2, 3, 2, 2, 2, 3, 1, 3, 4, 1, 4, 3, 2, 2, 4, 4, 2, 2, 2, 3, 2, 2, 4, 4, 2, 3, 2, 2, 2, 1, 4, 2, 2, 2, 3, 1, 4, 2, 3, 3, 1, 4, 2, 4, 4, 2, 3, 1, 3, 2, 2, 2, 4, 2, 4, 2, 1, 3, 2, 2, 4, 1, 4, 3, 2, 2, 1, 2, 3, 1, 3, 2, 2, 2, 4], 'G-Gens': [[3, 5, 1, 4, 2], [2, 1, 3, 5, 4]], 'G-Name': 'D10', 'Polynomial': [-1, 3, -2, 1, -1, 1], 'QpRts': [['-585', '-5611'], ['5021', '0'], ['5957', '2636'], ['6948', '-2636'], ['-533', '5611']], 'QpRts-minpoly': [3, 6, 1], 'QpRts-p': 7, 'QpRts-prec': 5, 'Size': 10, 'TransitiveDegree': 5}