-
artin_reps • Show schema
Hide schema
{'BadPrimes': [17], 'Baselabel': '1.17.8t1.a', 'CharacterField': 8, 'Conductor': 17, 'Container': '8t1', 'Dets': ['17.8', '17.2', '17.9', '17.15'], 'Dim': 1, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 8, 'GaloisConjugates': [{'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, 1], [0, 0, 0, 1], [0, -1], [0, 0, 0, -1]], 'GalOrbIndex': 1, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, 1], [0, 1], [0, 0, 0, -1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, 1], [0, 0, -1], [0, -1], [0, 0, 0, -1], [0, 1], [0, 0, 0, 1]], 'GalOrbIndex': 3, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, -1]], [[1], [0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, 1]], [[1], [0, -1]], [[1], [0, 0, 0, -1]], [[1]]]}, {'Sign': 0, 'Character': [[1], [-1], [0, 0, -1], [0, 0, 1], [0, 0, 0, -1], [0, -1], [0, 0, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [9, 7], 'LocalFactors': [[[1], [-1]], [[1], [1]], [[1], [0, 0, 1]], [[1], [0, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [0, 1]], [[1], [0, 0, 0, -1]], [[1], [0, -1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '8T1', 'Galt': 1, 'HardPrimes': [17, 31], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [1, 4, -10, -10, 15, 6, -7, -1, 1], 'NumBadPrimes': 1, 'Proj_GAP': [1, 1], 'Proj_Polynomial': [0, 1], 'Proj_nTj': [1, 1]}
-
artin_field_data • Show schema
Hide schema
{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.17.8t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [0, 0, -1, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, -1, 0, 0], [0, 0, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '1.17.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [0, -1], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.17.8t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, -1], [0, -1, 0, 0]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '1.17.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 3, 'Baselabel': '1.17.8t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 1, 0], [0, 0, -1, 0], [0, -1, 0, 0], [0, 0, 0, -1], [0, 1, 0, 0], [0, 0, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '1.17.4t1.a', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, -1], [0, 1], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 4, 'Baselabel': '1.17.8t1.a', 'Character': [[1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, -1], [0, -1, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0]], 'CharacterField': 8}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [2, 1, 7, 5, 4, 8, 3, 6]}, {'Size': '1', 'Order': 4, 'Representative': [3, 7, 2, 8, 6, 4, 1, 5]}, {'Size': '1', 'Order': 4, 'Representative': [7, 3, 1, 6, 8, 5, 2, 4]}, {'Size': '1', 'Order': 8, 'Representative': [8, 6, 5, 1, 2, 7, 4, 3]}, {'Size': '1', 'Order': 8, 'Representative': [5, 4, 6, 3, 7, 1, 8, 2]}, {'Size': '1', 'Order': 8, 'Representative': [6, 8, 4, 2, 1, 3, 5, 7]}, {'Size': '1', 'Order': 8, 'Representative': [4, 5, 8, 7, 3, 2, 6, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4', '1'], 'ConjugacyClass': 3}, {'RootOf': ['13', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['-116', '1'], 'ConjugacyClass': 5}, {'RootOf': ['88', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-643', '1'], 'ConjugacyClass': 7}, {'RootOf': ['37', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [8]}], 'Frobs': [4, 7, 5, 8, 6, 2, 1, 4, 6, 5, 7, 7, 8, 3, 2, 4, 3, 8, 1, 7, 5, 6, 4, 2, 5, 1, 1, 5, 8, 6, 3, 5, 1, 7, 2, 4, 2, 8, 7, 7, 3, 6, 2, 6, 8, 5, 8, 4, 6, 3, 5, 1, 7, 2, 4, 3, 7, 1, 5, 3, 6, 2, 1, 5, 8, 6, 3, 7, 8, 3, 2, 4, 8, 1, 5, 3, 4, 6, 8, 1, 6, 2, 6, 3, 7, 1, 8, 4, 4, 2, 3, 7, 6, 4, 6, 8, 1, 6, 2, 7, 7, 2, 4, 3, 8, 1, 3, 4, 2, 6, 5, 1, 5, 8, 4, 5, 7, 1, 8, 2, 4, 8, 7, 7, 6, 2, 5, 5, 2, 4, 3, 5, 7, 3, 2, 2, 3, 5, 4, 8, 5, 5, 8, 6, 2, 6, 7, 8, 3, 2, 8, 7, 1, 7, 6, 8, 1, 6, 4, 6, 5, 1, 4, 4, 3, 7, 5, 6], 'G-Gens': [[8, 6, 5, 1, 2, 7, 4, 3], [3, 7, 2, 8, 6, 4, 1, 5], [2, 1, 7, 5, 4, 8, 3, 6]], 'G-Name': 'C8', 'Polynomial': [1, 4, -10, -10, 15, 6, -7, -1, 1], 'QpRts': [['339272929'], ['443617057'], ['107125985'], ['-168679434'], ['-339091377'], ['-279750341'], ['-43358595'], ['-59136223']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 67, 'QpRts-prec': 5, 'Size': 8, 'TransitiveDegree': 8}