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artin_reps • Show schema
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{'BadPrimes': [2, 13], 'Baselabel': '2.1352.12t18.a', 'CharacterField': 3, 'Conductor': 1352, 'Container': '12t18', 'Dets': ['1.104.6t1.b.b', '1.104.6t1.b.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, 8, 14, 12, 16, 20, 7, 3, 1, 15], '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, 8, 14, 12, 16, 20, 7, 3, 1, 15], '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, 11, 13, 43, 53, 1091, 6961], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [27, 132, 130, 36, 347, -74, 202, -30, 61, -10, 13, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-2, -1, 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], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.13.2t1.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': '1.104.2t1.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': '1.8.2t1.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': '1.104.6t1.d', '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': '1.13.6t1.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': '1.13.6t1.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': '1.104.6t1.b', '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': '1.104.6t1.b', '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': '1.104.6t1.d', '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': '1.13.3t1.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': '1.13.3t1.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': '2.104.3t2.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': '2.104.6t3.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': '2.1352.6t5.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': '2.1352.12t18.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': '2.1352.6t5.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': '2.1352.12t18.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}], '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': [6, 11, 10, 9, 8, 1, 12, 5, 4, 3, 2, 7]}, {'Size': '3', 'Order': 2, 'Representative': [7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [12, 5, 4, 3, 2, 7, 6, 11, 10, 9, 8, 1]}, {'Size': '1', 'Order': 3, 'Representative': [10, 12, 8, 11, 1, 3, 4, 6, 2, 5, 7, 9]}, {'Size': '1', 'Order': 3, 'Representative': [5, 9, 6, 7, 10, 8, 11, 3, 12, 1, 4, 2]}, {'Size': '2', 'Order': 3, 'Representative': [10, 2, 8, 4, 1, 3, 7, 6, 9, 5, 11, 12]}, {'Size': '2', 'Order': 3, 'Representative': [5, 2, 6, 4, 10, 8, 7, 3, 9, 1, 11, 12]}, {'Size': '2', 'Order': 3, 'Representative': [10, 9, 8, 7, 1, 3, 11, 6, 12, 5, 4, 2]}, {'Size': '1', 'Order': 6, 'Representative': [8, 4, 1, 12, 3, 5, 2, 10, 7, 6, 9, 11]}, {'Size': '1', 'Order': 6, 'Representative': [3, 7, 5, 2, 6, 10, 9, 1, 11, 8, 12, 4]}, {'Size': '2', 'Order': 6, 'Representative': [3, 11, 5, 9, 6, 10, 12, 1, 4, 8, 2, 7]}, {'Size': '2', 'Order': 6, 'Representative': [8, 11, 1, 9, 3, 5, 12, 10, 4, 6, 2, 7]}, {'Size': '2', 'Order': 6, 'Representative': [3, 4, 5, 12, 6, 10, 2, 1, 7, 8, 9, 11]}, {'Size': '3', 'Order': 6, 'Representative': [11, 3, 12, 1, 4, 2, 5, 9, 6, 7, 10, 8]}, {'Size': '3', 'Order': 6, 'Representative': [4, 6, 2, 5, 7, 9, 10, 12, 8, 11, 1, 3]}, {'Size': '3', 'Order': 6, 'Representative': [2, 10, 7, 6, 9, 11, 8, 4, 1, 12, 3, 5]}, {'Size': '3', 'Order': 6, 'Representative': [9, 1, 11, 8, 12, 4, 3, 7, 5, 2, 6, 10]}], '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': ['430', '28', '1'], 'ConjugacyClass': 7}, {'RootOf': ['196', '28', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['28', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-428', '-101', '-10', '1'], 'ConjugacyClass': 3}, {'RootOf': ['-7792', '-118', '32', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['251', '30', '1'], 'ConjugacyClass': 12}, {'RootOf': ['4', '4', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['94', '1'], 'ConjugacyClass': 5}, {'RootOf': ['68', '1'], 'ConjugacyClass': 6}, {'RootOf': ['11657', '162', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-24', '1'], 'ConjugacyClass': 10}, {'RootOf': ['2', '1'], 'ConjugacyClass': 11}, {'RootOf': ['147', '-22', '1'], 'ConjugacyClass': 14}, {'RootOf': ['13768', '-101', '-10', '1'], 'ConjugacyClass': 15}, {'RootOf': ['-3704', '172', '-10', '1'], 'ConjugacyClass': 16}, {'RootOf': ['9784', '558', '32', '1'], 'ConjugacyClass': 17}, {'RootOf': ['6352', '532', '32', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [16, 8, 14, 12, 16, 18, 7, 15, 18, 18, 2, 13, 16, 7, 14, 4, 15, 17, 16, 12, 3, 4, 3, 16, 15, 18, 4, 5, 14, 6, 18, 9, 15, 7, 10, 14, 4, 15, 11, 17, 8, 4, 17, 16, 13, 17, 8, 13, 15, 14, 9, 14, 15, 6, 8, 18, 17, 13, 17, 3, 5, 12, 3, 4, 9, 2, 15, 9, 7, 13, 16, 2, 18, 17, 16, 12, 4, 10, 16, 15, 8, 14, 13, 7, 18, 9, 15, 16, 12, 2, 1, 13, 10, 8, 3, 17, 11, 9, 5, 14, 9, 13, 7, 8, 9, 3, 16, 3, 4, 8, 17, 11, 15, 3, 12, 6, 15, 18, 18, 6, 11, 8, 4, 15, 16, 4, 10, 17, 4, 14, 16, 13, 18, 18, 15, 16, 12, 15, 17, 8, 3, 13, 17, 3, 18, 10, 14, 1, 1, 14, 12, 8, 9, 18, 8, 4, 17, 15, 1, 14, 16, 7, 14, 7, 16, 14, 18, 17], 'G-Gens': [[6, 11, 10, 9, 8, 1, 12, 5, 4, 3, 2, 7], [10, 2, 8, 4, 1, 3, 7, 6, 9, 5, 11, 12], [11, 3, 12, 1, 4, 2, 5, 9, 6, 7, 10, 8], [1, 9, 3, 7, 5, 6, 11, 8, 12, 10, 4, 2]], 'G-Name': 'C6*S3', 'Polynomial': [27, 132, 130, 36, 347, -74, 202, -30, 61, -10, 13, -2, 1], 'QpRts': [['1130697728', '-2635522711', '-8461667358', '2800489371', '3163018575', '-1218183533'], ['4034837429', '-480892595', '6183632727', '-6346535086', '3743597919', '2248589950'], ['4522187778', '7449287305', '-1200786504', '-4222260021', '2807294264', '1423199462'], ['1603940149', '-3164116525', '8453346059', '-5226778518', '4790449489', '1474432973'], ['-4619114271', '-8311981418', '-4351137548', '-5229045184', '-5021846470', '6623554090'], ['6130563502', '7060692303', '3134977571', '6833641926', '-4885192432', '-8105637046'], ['-7480333020', '6785412849', '-4676174790', '-2030156211', '-2644506940', '-6473793486'], ['-6178987574', '7847767932', '-265017587', '4656026695', '1075796616', '-3959732271'], ['-4080699363', '-6223908506', '5431620856', '5174688921', '-235885181', '6477007746'], ['-3460085768', '-4946479791', '-6835544854', '-762831265', '-363727830', '-5068299674'], ['3948501257', '-4710875445', '-1112384550', '-6535241234', '76613176', '4662289630'], ['4448492155', '1330616602', '3699135978', '-6095562435', '-2505611186', '1916572159']], 'QpRts-minpoly': [2, 6, 17, 17, 0, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 8, 'Size': 36, 'TransitiveDegree': 12}