-
artin_reps • Show schema
Hide schema
{'BadPrimes': [2, 7], 'Baselabel': '2.392.4t3.b', 'CharacterField': 1, 'Conductor': 392, 'Container': '4t3', 'Dets': ['1.8.2t1.b.a'], 'Dim': 2, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[2], [-2], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [6, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0], [-1]], [[1], [0], [1]], [[1], [-1]], [[1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T4', 'Galt': 4, 'HardPrimes': [2, 7], 'Hide': 1, 'Indicator': 1, 'Is_Even': False, 'NFGal': [2, -12, 23, -2, 1, 8, -3, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [4, 2], 'Proj_Polynomial': [2, -8, 9, -2, 1], 'Proj_nTj': [4, 2]}
-
artin_field_data • Show schema
Hide schema
{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.2t1.a', 'Character': [[1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.56.2t1.a', 'Character': [[1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.392.4t3.b', 'Character': [[2], [-2], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '1', 'Order': 2, 'Representative': [5, 4, 7, 2, 1, 8, 3, 6]}, {'Size': '2', 'Order': 2, 'Representative': [2, 1, 8, 5, 4, 7, 6, 3]}, {'Size': '2', 'Order': 2, 'Representative': [3, 6, 1, 8, 7, 2, 5, 4]}, {'Size': '2', 'Order': 4, 'Representative': [6, 3, 4, 7, 8, 5, 2, 1]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['12', '1'], 'ConjugacyClass': 2}, {'RootOf': ['86', '-20', '1'], 'ConjugacyClass': 3}, {'RootOf': ['72', '-6', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [4, 4]}], 'Frobs': [1, 5, 3, 4, 2, 3, 5, 5, 4, 4, 3, 4, 5, 2, 3, 4, 5, 3, 1, 4, 5, 4, 5, 5, 5, 3, 3, 1, 4, 2, 4, 5, 2, 5, 4, 4, 3, 2, 3, 3, 1, 3, 4, 2, 4, 3, 1, 3, 5, 3, 2, 4, 5, 5, 5, 4, 3, 3, 4, 2, 5, 3, 5, 3, 5, 4, 2, 1, 2, 3, 5, 4, 3, 4, 2, 3, 4, 3, 1, 5, 5, 4, 4, 5, 3, 1, 1, 2, 3, 4, 5, 3, 4, 1, 1, 3, 3, 5, 5, 4, 2, 4, 5, 1, 2, 5, 5, 5, 4, 5, 3, 4, 1, 5, 4, 1, 5, 3, 4, 2, 3, 2, 3, 1, 5, 4, 4, 3, 3, 3, 2, 4, 4, 4, 5, 5, 3, 5, 3, 2, 5, 4, 4, 1, 3, 3, 3, 5, 5, 4, 4, 5, 1, 3, 1, 4, 4, 5, 5, 3, 2, 1, 4, 5, 2, 3, 4, 3], 'G-Gens': [[2, 1, 8, 5, 4, 7, 6, 3], [3, 6, 1, 8, 7, 2, 5, 4]], 'G-Name': 'D8', 'Polynomial': [2, -12, 23, -2, 1, 8, -3, -2, 1], 'QpRts': [['34049804'], ['-138294094'], ['-286444018'], ['370306144'], ['40099663'], ['-117911929'], ['-292493877'], ['390688309']], 'QpRts-minpoly': [-1, 1], 'QpRts-p': 67, 'QpRts-prec': 5, 'Size': 8, 'TransitiveDegree': 8}