-
artin_reps • Show schema
Hide schema
{'BadPrimes': [5, 7, 17], 'Baselabel': '3.2975.6t11.a', 'CharacterField': 1, 'Conductor': 2975, 'Container': '6t11', 'Dets': ['1.119.2t1.a.a'], 'Dim': 3, 'GalConjSigns': [1], 'Galn': 6, 'GaloisConjugates': [{'Sign': 1, 'Character': [[3], [-3], [1], [-1], [1], [-1], [0], [1], [-1], [0]], 'GalOrbIndex': 1, 'HardFactors': [11, 12, 13], 'LocalFactors': [[[1], [-3], [3], [-1]], [[1], [3], [3], [1]], [[1], [-1], [-1], [1]], [[1], [1], [-1], [-1]], [[1], [-1], [-1], [1]], [[1], [1], [-1], [-1]], [[1], [0], [0], [-1]], [[1], [-1], [1], [-1]], [[1], [1], [1], [1]], [[1], [0], [0], [1]], [[1], [1]], [[1], [2], [1]], [[1], [0], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '6T11', 'Galt': 11, 'HardPrimes': [5, 7, 17], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-1, -1, 1, -1, -1, -1, 1], 'NumBadPrimes': 3, 'Proj_GAP': [24, 12], 'Proj_Polynomial': [-1, 4, 5, -1, 1], 'Proj_nTj': [4, 5]}
-
artin_field_data • Show schema
Hide schema
{'ArtinReps': [{'GalConj': 1, 'Baselabel': '1.1.1t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.119.2t1.a', 'Character': [[1], [-1], [-1], [1], [-1], [1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.7.2t1.a', 'Character': [[1], [1], [1], [1], [-1], [-1], [1], [-1], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.17.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [-1], [1], [-1], [1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.50575.6t3.d', 'Character': [[2], [-2], [-2], [2], [0], [0], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.175.3t2.b', 'Character': [[2], [2], [2], [2], [0], [0], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.50575.4t5.a', 'Character': [[3], [3], [-1], [-1], [1], [1], [0], [-1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2975.6t11.a', 'Character': [[3], [-3], [1], [-1], [1], [-1], [0], [1], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.20825.6t11.a', 'Character': [[3], [-3], [1], [-1], [-1], [1], [0], [-1], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.354025.6t8.b', 'Character': [[3], [3], [-1], [-1], [-1], [-1], [0], [1], [1], [0]], 'CharacterField': 1}], 'ComplexConjugation': 5, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6]}, {'Size': '1', 'Order': 2, 'Representative': [6, 5, 4, 3, 2, 1]}, {'Size': '3', 'Order': 2, 'Representative': [6, 2, 3, 4, 5, 1]}, {'Size': '3', 'Order': 2, 'Representative': [6, 5, 3, 4, 2, 1]}, {'Size': '6', 'Order': 2, 'Representative': [1, 3, 2, 5, 4, 6]}, {'Size': '6', 'Order': 2, 'Representative': [6, 3, 2, 5, 4, 1]}, {'Size': '8', 'Order': 3, 'Representative': [2, 3, 1, 6, 4, 5]}, {'Size': '6', 'Order': 4, 'Representative': [5, 1, 3, 4, 6, 2]}, {'Size': '6', 'Order': 4, 'Representative': [6, 4, 2, 5, 3, 1]}, {'Size': '8', 'Order': 6, 'Representative': [5, 3, 1, 6, 4, 2]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-45', '0', '-5', '1'], 'ConjugacyClass': 4}, {'RootOf': ['2135', '555', '-305', '-13', '37', '-11', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1304', '1980', '1108', '295', '42', '5', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [2, 4]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [3, 3]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [6]}], 'Frobs': [7, 8, 6, 6, 10, 9, 8, 9, 10, 10, 8, 10, 6, 7, 5, 4, 9, 6, 7, 10, 8, 10, 9, 5, 8, 9, 9, 3, 10, 10, 7, 6, 4, 6, 7, 7, 5, 3, 6, 8, 4, 8, 4, 10, 10, 6, 3, 5, 6, 9, 10, 4, 6, 5, 5, 7, 8, 9, 3, 7, 8, 9, 5, 8, 8, 10, 7, 3, 10, 5, 9, 7, 6, 7, 10, 5, 7, 6, 10, 5, 6, 7, 2, 9, 8, 4, 10, 7, 5, 4, 9, 8, 10, 7, 3, 8, 5, 8, 5, 10, 10, 7, 9, 7, 10, 9, 9, 5, 7, 8, 6, 7, 10, 6, 7, 10, 8, 9, 2, 4, 5, 2, 8, 10, 6, 4, 3, 8, 5, 5, 7, 3, 3, 7, 5, 5, 5, 6, 5, 10, 6, 3, 10, 10, 5, 8, 6, 8, 9, 7, 3, 8, 7, 8, 3, 10, 7, 8, 9, 6, 2, 7, 4, 5, 7, 8, 10, 6], 'G-Gens': [[6, 2, 3, 4, 5, 1], [2, 1, 3, 4, 6, 5], [2, 3, 1, 6, 4, 5]], 'G-Name': 'C2*S4', 'Polynomial': [-1, -1, 1, -1, -1, -1, 1], 'QpRts': [['-54543891137', '-180886657342'], ['-86380218635', '0'], ['-20614238155', '180886657342'], ['-239599577720', '-21114328434'], ['197215844301', '0'], ['203922081347', '21114328434']], 'QpRts-minpoly': [5, 45, 1], 'QpRts-p': 47, 'QpRts-prec': 7, 'Size': 48, 'TransitiveDegree': 6}