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artin_reps • Show schema
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{'BadPrimes': [5, 19], 'Baselabel': '2.475.8t8.a', 'CharacterField': 8, 'Conductor': 475, 'Container': '8t8', 'Dets': ['1.19.2t1.a.a', '1.19.2t1.a.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [0], [0, -1, 0, -1], [0, 1, 0, 1]], 'GalOrbIndex': 1, 'HardFactors': [7, 7, 8, 9, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0, 1, 0, 1], [-1]], [[1], [0, -1, 0, -1], [-1]], [[1]], [[1], [-1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0], [0, 1, 0, 1], [0, -1, 0, -1]], 'GalOrbIndex': 2, 'HardFactors': [7, 7, 8, 9, 1], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [1]], [[1], [0], [1]], [[1], [0, -1, 0, -1], [-1]], [[1], [0, 1, 0, 1], [-1]], [[1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '8T8', 'Galt': 8, 'HardPrimes': [2, 3, 5, 19, 131], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, -6, -7, 5, 1, 0, 2, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [8, 3], 'Proj_Polynomial': [-1, -1, 2, -2, 1], 'Proj_nTj': [4, 3]}
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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], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.19.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.95.2t1.a', 'Character': [[1], [1], [-1], [1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.95.4t3.c', 'Character': [[2], [2], [0], [-2], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.475.8t8.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.475.8t8.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [7, 3, 2, 5, 4, 8, 1, 6]}, {'Size': '4', 'Order': 2, 'Representative': [1, 8, 6, 5, 4, 3, 7, 2]}, {'Size': '2', 'Order': 4, 'Representative': [5, 6, 8, 1, 7, 3, 4, 2]}, {'Size': '4', 'Order': 4, 'Representative': [2, 7, 1, 6, 8, 5, 3, 4]}, {'Size': '2', 'Order': 8, 'Representative': [8, 7, 1, 3, 2, 4, 6, 5]}, {'Size': '2', 'Order': 8, 'Representative': [6, 1, 7, 2, 3, 5, 8, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-3', '1'], 'ConjugacyClass': 4}, {'RootOf': ['171', '0', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['15', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-15', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [7, 7, 1, 5, 4, 6, 5, 1, 5, 3, 3, 6, 3, 5, 5, 7, 3, 4, 7, 3, 5, 3, 5, 3, 6, 4, 6, 7, 3, 6, 6, 1, 5, 4, 4, 3, 5, 5, 6, 6, 3, 3, 2, 7, 5, 1, 3, 7, 7, 4, 5, 2, 3, 2, 6, 5, 3, 4, 5, 3, 5, 7, 7, 4, 5, 7, 3, 7, 5, 1, 5, 4, 5, 7, 3, 6, 2, 5, 3, 3, 2, 3, 3, 6, 3, 5, 3, 5, 1, 5, 5, 4, 7, 2, 4, 5, 3, 3, 7, 4, 6, 5, 7, 3, 4, 5, 5, 5, 3, 3, 7, 5, 5, 4, 4, 3, 5, 5, 5, 3, 3, 6, 6, 7, 4, 4, 1, 4, 5, 5, 1, 7, 3, 5, 4, 4, 6, 6, 6, 1, 3, 1, 5, 6, 3, 3, 5, 6, 2, 7, 6, 4, 5, 7, 7, 3, 2, 1, 5, 3, 5, 7, 5, 3, 7, 6, 3, 5], 'G-Gens': [[7, 3, 2, 5, 4, 8, 1, 6], [5, 6, 8, 1, 7, 3, 4, 2], [1, 8, 6, 5, 4, 3, 7, 2], [2, 7, 1, 6, 8, 5, 3, 4]], 'G-Name': 'SD16', 'Polynomial': [1, -6, -7, 5, 1, 0, 2, -2, 1], 'QpRts': [['80791284449'], ['-63947048418'], ['83445124409'], ['14883726687'], ['-109684636572'], ['-116800650899'], ['14009625437'], ['97302574909']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 199, 'QpRts-prec': 5, 'Size': 16, 'TransitiveDegree': 8}