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artin_reps • Show schema
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{'BadPrimes': [8647], 'Baselabel': '6.646541456023.20t30.a', 'CharacterField': 1, 'Conductor': 646541456023, 'Container': '20t30', 'Dets': ['1.8647.2t1.a.a'], 'Dim': 6, 'GalConjSigns': [1], 'Galn': 5, 'GaloisConjugates': [{'Sign': 1, 'Character': [[6], [0], [-2], [0], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [8], 'LocalFactors': [[[1], [-6], [15], [-20], [15], [-6], [1]], [[1], [0], [-3], [0], [3], [0], [-1]], [[1], [2], [-1], [-4], [-1], [2], [1]], [[1], [0], [0], [-2], [0], [0], [1]], [[1], [0], [1], [0], [-1], [0], [-1]], [[1], [-1], [0], [0], [0], [-1], [1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '5T5', 'Galt': 5, 'HardPrimes': [8647], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, 2, -2, -3, 0, 1], 'NumBadPrimes': 1, 'Proj_GAP': [120, 34], 'Proj_Polynomial': [1, 2, -2, -3, 0, 1], 'Proj_nTj': [5, 5]}
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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': '1.8647.2t1.a', 'Character': [[1], [-1], [1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.646541456023.10t12.a', 'Character': [[4], [-2], [0], [1], [0], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.8647.5t5.a', 'Character': [[4], [2], [0], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.74770609.10t13.a', 'Character': [[5], [1], [1], [-1], [-1], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.646541456023.6t14.a', 'Character': [[5], [-1], [1], [-1], [1], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.646541456023.20t30.a', 'Character': [[6], [0], [-2], [0], [0], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5]}, {'Size': '10', 'Order': 2, 'Representative': [2, 1, 3, 4, 5]}, {'Size': '15', 'Order': 2, 'Representative': [2, 1, 4, 3, 5]}, {'Size': '20', 'Order': 3, 'Representative': [2, 3, 1, 4, 5]}, {'Size': '30', 'Order': 4, 'Representative': [2, 3, 4, 1, 5]}, {'Size': '24', 'Order': 5, 'Representative': [2, 3, 4, 5, 1]}, {'Size': '20', 'Order': 6, 'Representative': [2, 3, 1, 5, 4]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 4]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [2, 3]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [5]}], 'Frobs': [6, 7, 5, 7, 7, 5, 7, 3, 6, 6, 6, 4, 6, 5, 4, 2, 6, 6, 5, 4, 5, 2, 6, 7, 5, 5, 7, 7, 4, 2, 5, 7, 6, 5, 6, 5, 6, 3, 5, 5, 6, 5, 2, 5, 7, 5, 6, 4, 5, 3, 6, 6, 6, 5, 5, 4, 7, 6, 7, 6, 5, 4, 6, 7, 4, 5, 3, 6, 5, 4, 2, 6, 3, 4, 3, 6, 5, 4, 4, 5, 4, 5, 2, 6, 4, 4, 7, 3, 7, 5, 5, 5, 6, 5, 4, 7, 4, 6, 5, 6, 5, 6, 1, 3, 7, 3, 7, 6, 3, 6, 6, 4, 4, 2, 5, 3, 4, 4, 7, 2, 5, 7, 5, 7, 2, 2, 7, 6, 7, 5, 7, 4, 5, 7, 7, 4, 4, 3, 7, 4, 5, 6, 3, 5, 7, 2, 7, 4, 5, 7, 4, 5, 6, 5, 7, 6, 5, 5, 6, 4, 5, 5, 5, 4, 7, 3, 5, 6], 'G-Gens': [[2, 1, 3, 4, 5], [2, 3, 4, 5, 1]], 'G-Name': 'S5', 'Polynomial': [1, 2, -2, -3, 0, 1], 'QpRts': [['7504255455742'], ['23644236994010'], ['1976716293362'], ['-15419975465936'], ['-17705233277178']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 563, 'QpRts-prec': 5, 'Size': 120, 'TransitiveDegree': 5}