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artin_reps • Show schema
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{'BadPrimes': [5, 7, 11], 'Baselabel': '2.385.6t5.a', 'CharacterField': 3, 'Conductor': 385, 'Container': '6t5', 'Dets': ['1.385.6t1.a.a', '1.385.6t1.a.b'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 9, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [6, 10, 11, 12, 7, 4, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [0, -2], [-1, -1]], [[1], [2, 2], [0, 1]], [[1], [-1, -1], [0, 1]], [[1], [0, 1], [-1, -1]], [[1], [1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0, -1]], [[1], [-1]], [[1], [1, 1]]]}, {'Sign': 0, 'Character': [[2], [0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [6, 10, 11, 12, 7, 4, 7], 'LocalFactors': [[[1], [-2], [1]], [[1], [0], [-1]], [[1], [2, 2], [0, 1]], [[1], [0, -2], [-1, -1]], [[1], [0, 1], [-1, -1]], [[1], [-1, -1], [0, 1]], [[1], [1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [1, 1]], [[1], [-1]], [[1], [0, -1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '9T4', 'Galt': 4, 'HardPrimes': [2, 5, 7, 11, 13, 17, 43], 'Hide': 1, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, -7, 10, -14, 14, -4, 7, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-7, 7, 0, 1], 'Proj_nTj': [3, 2]}
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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], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.55.2t1.a', 'Character': [[1], [-1], [1], [1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.385.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.385.6t1.a', 'Character': [[1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.7.3t1.a', 'Character': [[1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2695.3t2.a', 'Character': [[2], [0], [2], [2], [-1], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.385.6t5.a', 'Character': [[2, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.385.6t5.a', 'Character': [[2, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 2, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '3', 'Order': 2, 'Representative': [8, 3, 2, 4, 5, 6, 9, 1, 7]}, {'Size': '1', 'Order': 3, 'Representative': [9, 8, 1, 6, 4, 5, 2, 7, 3]}, {'Size': '1', 'Order': 3, 'Representative': [3, 7, 9, 5, 6, 4, 8, 2, 1]}, {'Size': '2', 'Order': 3, 'Representative': [6, 9, 4, 8, 2, 7, 1, 3, 5]}, {'Size': '2', 'Order': 3, 'Representative': [7, 5, 8, 3, 9, 1, 6, 4, 2]}, {'Size': '2', 'Order': 3, 'Representative': [8, 6, 2, 9, 1, 3, 4, 5, 7]}, {'Size': '3', 'Order': 6, 'Representative': [2, 9, 7, 5, 6, 4, 1, 3, 8]}, {'Size': '3', 'Order': 6, 'Representative': [7, 1, 8, 6, 4, 5, 3, 9, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-3', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-6', '1'], 'ConjugacyClass': 4}, {'RootOf': ['64', '6', '1'], 'ConjugacyClass': 5}, {'RootOf': ['16', '3', '1'], 'ConjugacyClass': 6}, {'RootOf': ['256', '12', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['56', '28', '0', '1'], 'ConjugacyClass': 8}, {'RootOf': ['7', '7', '0', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 6]}], 'Frobs': [6, 8, 3, 1, 4, 7, 4, 9, 9, 2, 5, 9, 2, 7, 9, 8, 5, 9, 8, 7, 5, 9, 7, 6, 2, 8, 9, 3, 8, 2, 1, 9, 8, 2, 9, 8, 8, 9, 1, 6, 5, 7, 6, 4, 7, 5, 2, 2, 5, 6, 3, 2, 8, 1, 9, 5, 4, 9, 5, 2, 4, 7, 7, 5, 9, 9, 6, 7, 5, 2, 8, 9, 8, 6, 7, 9, 5, 9, 6, 8, 7, 1, 8, 2, 9, 9, 7, 6, 2, 2, 9, 8, 8, 2, 6, 7, 6, 5, 6, 9, 7, 4, 5, 9, 8, 8, 2, 6, 5, 2, 6, 5, 2, 4, 7, 4, 2, 8, 9, 2, 4, 7, 3, 8, 3, 2, 6, 3, 2, 3, 8, 7, 6, 2, 9, 2, 8, 5, 2, 8, 2, 9, 8, 1, 5, 1, 1, 5, 3, 9, 6, 7, 2, 6, 8, 7, 9, 3, 7, 8, 9, 1, 7, 6, 8, 8, 4, 5], 'G-Gens': [[1, 6, 3, 7, 8, 2, 4, 5, 9], [2, 9, 7, 5, 6, 4, 1, 3, 8], [5, 2, 6, 9, 1, 3, 7, 8, 4]], 'G-Name': 'C3*S3', 'Polynomial': [1, 0, -7, 10, -14, 14, -4, 7, 0, 1], 'QpRts': [['14361194', '19864396', '-20603363'], ['-15590378', '-29645175', '19681475'], ['-12341863', '13684747', '6430732'], ['15483892', '18035513', '11612919'], ['29136370', '25478834', '-9521981'], ['27932241', '15960428', '-26112207'], ['-271209', '-31207740', '-15890536'], ['19250953', '17405287', '30125344'], ['-15212683', '13172227', '4277617']], 'QpRts-minpoly': [11, 2, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 7, 'Size': 18, 'TransitiveDegree': 9}