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artin_reps • Show schema
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{'BadPrimes': [2, 19], 'Baselabel': '2.2888.12t18.f', 'CharacterField': 3, 'Conductor': 2888, 'Container': '12t18', 'Dets': ['1.152.6t1.c.b', '1.152.6t1.c.a'], 'Dim': 2, 'GalConjSigns': [0, 0], 'Galn': 12, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1], [0, -2], [2, 2], [0, 1], [-1, -1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [19, 13, 16, 3, 20, 15, 3, 15, 15, 8, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-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, 2], [-1, -1]], [[1], [-2, -2], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [-1], [1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [-1, -1]], [[1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1], [2, 2], [0, -2], [-1, -1], [0, 1], [1], [0], [0], [0], [0]], 'GalOrbIndex': 2, 'HardFactors': [19, 13, 16, 3, 20, 15, 3, 15, 15, 8, 3], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-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], [-2, -2], [0, 1]], [[1], [0, 2], [-1, -1]], [[1], [1, 1], [0, 1]], [[1], [0, -1], [-1, -1]], [[1], [-1], [1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0], [0, -1]], [[1], [0], [1, 1]], [[1], [0, 1]], [[1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 19, 23, 37, 53, 61, 233, 12703], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [139, 154, 207, -4, 72, -12, 74, -26, 16, -8, 10, -4, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [7, 13, -1, 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], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.19.2t1.a', 'Character': [[1], [-1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [-1], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.8.2t1.b', 'Character': [[1], [1], [-1], [-1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.152.2t1.a', 'Character': [[1], [-1], [-1], [1], [1], [1], [1], [1], [1], [-1], [-1], [-1], [-1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.152.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [-1, -1], [0, 1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.19.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1], [-1, 0], [1, 1], [0, -1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.a', 'Character': [[1, 0], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [0, 1], [-1, -1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.152.6t1.c', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.6t1.a', 'Character': [[1, 0], [-1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, -1], [1, 1], [0, -1], [1, 1], [-1, 0], [0, -1], [1, 1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1], [1, 0], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.19.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1], [1, 0], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2888.3t2.b', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.2888.6t3.a', 'Character': [[2], [-2], [0], [0], [2], [2], [-1], [-1], [-1], [-2], [-2], [1], [1], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.152.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [-2, -2], [0, 2], [1, 1], [0, -1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.2888.12t18.f', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, -2], [2, 2], [0, 1], [-1, -1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.152.6t5.a', 'Character': [[2, 0], [2, 0], [0, 0], [0, 0], [-2, -2], [0, 2], [0, -1], [1, 1], [-1, 0], [0, 2], [-2, -2], [0, -1], [1, 1], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '2.2888.12t18.f', 'Character': [[2, 0], [-2, 0], [0, 0], [0, 0], [0, 2], [-2, -2], [1, 1], [0, -1], [-1, 0], [2, 2], [0, -2], [-1, -1], [0, 1], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0]], 'CharacterField': 3}], 'ComplexConjugation': 4, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]}, {'Size': '1', 'Order': 2, 'Representative': [3, 11, 1, 6, 8, 4, 9, 5, 7, 12, 2, 10]}, {'Size': '3', 'Order': 2, 'Representative': [4, 10, 6, 1, 7, 3, 5, 9, 8, 2, 12, 11]}, {'Size': '3', 'Order': 2, 'Representative': [6, 12, 4, 3, 9, 1, 8, 7, 5, 11, 10, 2]}, {'Size': '1', 'Order': 3, 'Representative': [8, 6, 5, 9, 10, 7, 2, 12, 11, 3, 4, 1]}, {'Size': '1', 'Order': 3, 'Representative': [12, 7, 10, 11, 3, 2, 6, 1, 4, 5, 9, 8]}, {'Size': '2', 'Order': 3, 'Representative': [1, 6, 3, 9, 5, 7, 2, 8, 11, 10, 4, 12]}, {'Size': '2', 'Order': 3, 'Representative': [1, 7, 3, 11, 5, 2, 6, 8, 4, 10, 9, 12]}, {'Size': '2', 'Order': 3, 'Representative': [12, 6, 10, 9, 3, 7, 2, 1, 11, 5, 4, 8]}, {'Size': '1', 'Order': 6, 'Representative': [10, 9, 12, 2, 1, 11, 4, 3, 6, 8, 7, 5]}, {'Size': '1', 'Order': 6, 'Representative': [5, 4, 8, 7, 12, 9, 11, 10, 2, 1, 6, 3]}, {'Size': '2', 'Order': 6, 'Representative': [3, 4, 1, 7, 8, 9, 11, 5, 2, 12, 6, 10]}, {'Size': '2', 'Order': 6, 'Representative': [3, 9, 1, 2, 8, 11, 4, 5, 6, 12, 7, 10]}, {'Size': '2', 'Order': 6, 'Representative': [5, 9, 8, 2, 12, 11, 4, 10, 6, 1, 7, 3]}, {'Size': '3', 'Order': 6, 'Representative': [2, 8, 11, 10, 4, 12, 1, 6, 3, 9, 5, 7]}, {'Size': '3', 'Order': 6, 'Representative': [7, 1, 9, 5, 11, 8, 12, 2, 10, 4, 3, 6]}, {'Size': '3', 'Order': 6, 'Representative': [9, 10, 7, 1, 2, 3, 5, 11, 8, 6, 12, 4]}, {'Size': '3', 'Order': 6, 'Representative': [4, 5, 6, 12, 7, 10, 3, 9, 1, 2, 8, 11]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['44', '12', '1'], 'ConjugacyClass': 7}, {'RootOf': ['162', '24', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-6', '1'], 'ConjugacyClass': 2}, {'RootOf': ['160', '-58', '4', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-13330', '-609', '4', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['177', '-26', '1'], 'ConjugacyClass': 12}, {'RootOf': ['162', '24', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-20', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-8', '1'], 'ConjugacyClass': 6}, {'RootOf': ['198', '-28', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-22', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-72', '1'], 'ConjugacyClass': 11}, {'RootOf': ['2211', '-94', '1'], 'ConjugacyClass': 14}, {'RootOf': ['62350', '4967', '124', '1'], 'ConjugacyClass': 15}, {'RootOf': ['69152', '5100', '124', '1'], 'ConjugacyClass': 16}, {'RootOf': ['-37894', '3447', '-104', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-5518', '2877', '-104', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [16, 13, 18, 3, 9, 15, 5, 8, 17, 15, 4, 4, 13, 5, 17, 15, 13, 17, 12, 16, 8, 16, 9, 10, 13, 17, 4, 2, 16, 14, 15, 8, 7, 7, 18, 4, 18, 9, 15, 16, 14, 15, 3, 11, 3, 17, 11, 16, 14, 3, 8, 3, 12, 7, 12, 18, 16, 18, 3, 12, 8, 4, 13, 3, 7, 15, 14, 13, 8, 3, 9, 18, 17, 4, 2, 16, 17, 18, 13, 12, 1, 16, 15, 10, 16, 7, 14, 9, 18, 3, 9, 17, 4, 5, 8, 17, 15, 14, 10, 17, 10, 17, 14, 2, 9, 9, 5, 7, 15, 14, 4, 18, 7, 1, 17, 13, 8, 3, 3, 10, 15, 2, 4, 2, 1, 18, 17, 18, 18, 3, 8, 16, 15, 18, 9, 6, 15, 14, 4, 9, 10, 17, 17, 12, 4, 16, 18, 13, 7, 4, 16, 9, 7, 15, 13, 4, 3, 8, 7, 15, 5, 13, 18, 13, 14, 16, 16, 17], 'G-Gens': [[3, 11, 1, 6, 8, 4, 9, 5, 7, 12, 2, 10], [4, 10, 6, 1, 7, 3, 5, 9, 8, 2, 12, 11], [10, 9, 12, 2, 1, 11, 4, 3, 6, 8, 7, 5], [1, 6, 3, 9, 5, 7, 2, 8, 11, 10, 4, 12]], 'G-Name': 'C6*S3', 'Polynomial': [139, 154, 207, -4, 72, -12, 74, -26, 16, -8, 10, -4, 1], 'QpRts': [['5024336305', '-4514378091', '-498672429', '4028268488', '-1636068704', '3173934689'], ['-4153370640', '-1050832387', '2380479729', '5141069232', '-3584205911', '1003357962'], ['3259968090', '-2270484442', '-4952969316', '-636279445', '-1561216886', '-20067125'], ['-1028390727', '2224184064', '4516456760', '-2312607550', '175493873', '-770086830'], ['-4777822958', '3872501161', '4918630023', '2113244675', '-4292811896', '1909518396'], ['-870575012', '-3160702242', '2847987657', '3712422067', '-5189026161', '5159881127'], ['-3476536110', '-1339563042', '4431411466', '1871576939', '-3907514339', '419873518'], ['1469487497', '656613844', '4082144756', '-3102347360', '3801026517', '-2687152417'], ['-2522760298', '3175134770', '2069986402', '-4130688819', '3120739352', '-1526388338'], ['-586162741', '3949080952', '978959814', '-1597534095', '-2674223553', '2131935495'], ['-2548897720', '-345917132', '3073435690', '-4040634139', '5232019110', '-1724911598'], ['-393775055', '-1195637455', '-2638851806', '-1046489993', '-88710775', '3534604494']], 'QpRts-minpoly': [2, 11, 11, 10, 0, 0, 1], 'QpRts-p': 13, 'QpRts-prec': 9, 'Size': 36, 'TransitiveDegree': 12}