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artin_reps • Show schema
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{'BadPrimes': [3, 31], 'Baselabel': '10.4244902593608889.30t88.a', 'CharacterField': 1, 'Conductor': 4244902593608889, 'Container': '30t88', 'Dets': ['1.1.1t1.a.a'], 'Dim': 10, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[10], [-2], [1], [1], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [6, 8, 9], 'LocalFactors': [[[1], [-10], [45], [-120], [210], [-252], [210], [-120], [45], [-10], [1]], [[1], [2], [-3], [-8], [2], [12], [2], [-8], [-3], [2], [1]], [[1], [-1], [0], [-3], [3], [0], [3], [-3], [0], [-1], [1]], [[1], [-1], [0], [-3], [3], [0], [3], [-3], [0], [-1], [1]], [[1], [0], [1], [0], [-2], [0], [-2], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [1]], [[1]], [[1], [-1], [0], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T15', 'Galt': 15, 'HardPrimes': [2, 3, 31], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [-1, 0, -3, -1, 0, 0, 1], 'NumBadPrimes': 2, 'Proj_GAP': [360, 118], 'Proj_Polynomial': [-1, 0, -3, -1, 0, 0, 1], 'Proj_nTj': [6, 15]}
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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': '5.673246809.6t15.a', 'Character': [[5], [1], [2], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.700569.6t15.a', 'Character': [[5], [1], [-1], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.471655843734321.36t555.a', 'Character': [[8, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 1, 1], [0, 0, -1, -1]], 'CharacterField': 5}, {'GalConj': 2, 'Baselabel': '8.471655843734321.36t555.a', 'Character': [[8, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, -1], [1, 0, 1, 1]], 'CharacterField': 5}, {'GalConj': 1, 'Baselabel': '9.471655843734321.10t26.a', 'Character': [[9], [1], [0], [0], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.4244902593608889.30t88.a', 'Character': [[10], [-2], [1], [1], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '45', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 5, 6, 4]}, {'Size': '40', 'Order': 3, 'Representative': [2, 3, 1, 4, 5, 6]}, {'Size': '90', 'Order': 4, 'Representative': [2, 3, 4, 1, 6, 5]}, {'Size': '72', 'Order': 5, 'Representative': [2, 3, 4, 5, 1, 6]}, {'Size': '72', 'Order': 5, 'Representative': [3, 1, 4, 5, 2, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2]}, {'Data': [1, 3, 4, 5, 6, 2], 'Classes': [{'RootOf': ['-837', '1'], 'ConjugacyClass': 7}, {'RootOf': ['837', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'ALT', 'CycleType': [1, 5]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [3, 3]}], 'Frobs': [6, 5, 5, 7, 5, 7, 4, 5, 5, 6, 4, 3, 5, 6, 7, 3, 4, 5, 3, 7, 6, 3, 3, 5, 7, 2, 7, 6, 6, 6, 7, 2, 5, 2, 5, 5, 5, 3, 6, 4, 5, 7, 6, 7, 5, 7, 5, 3, 6, 2, 3, 5, 7, 6, 7, 4, 6, 5, 5, 5, 7, 6, 3, 3, 6, 7, 4, 7, 7, 7, 2, 7, 2, 4, 6, 3, 4, 3, 3, 5, 5, 7, 2, 7, 7, 2, 4, 5, 4, 4, 5, 2, 6, 4, 4, 7, 6, 5, 4, 5, 4, 2, 2, 6, 7, 4, 6, 7, 6, 2, 5, 7, 7, 6, 5, 2, 5, 6, 7, 6, 7, 5, 6, 3, 6, 5, 5, 6, 5, 7, 6, 3, 2, 6, 5, 7, 2, 7, 2, 5, 3, 2, 2, 3, 4, 7, 2, 5, 6, 3, 5, 6, 6, 6, 7, 7, 6, 5, 5, 5, 7, 2, 6, 5, 5, 7, 3, 7], 'G-Gens': [[2, 3, 1, 4, 5, 6], [2, 1, 4, 5, 6, 3]], 'G-Name': 'A6', 'Polynomial': [-1, 0, -3, -1, 0, 0, 1], 'QpRts': [['-5242887483', '0'], ['-4758128424', '3936233878'], ['4344920975', '27638568'], ['1663979879', '-27638568'], ['1691211106', '0'], ['2300903947', '-3936233878']], 'QpRts-minpoly': [2, 97, 1], 'QpRts-p': 101, 'QpRts-prec': 5, 'Size': 360, 'TransitiveDegree': 6}