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artin_reps • Show schema
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{'BadPrimes': [3, 11], 'Baselabel': '16.5340285714719489633060049.24t1334.a', 'CharacterField': 1, 'Conductor': 5340285714719489633060049, 'Container': '24t1334', 'Dets': ['1.1.1t1.a.a'], 'Dim': 16, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[16], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [10, 12, 10, 13, 4, 10], 'LocalFactors': [[[1], [-16], [120], [-560], [1820], [-4368], [8008], [-11440], [12870], [-11440], [8008], [-4368], [1820], [-560], [120], [-16], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [0], [-8], [0], [28], [0], [-56], [0], [70], [0], [-56], [0], [28], [0], [-8], [0], [1]], [[1], [2], [3], [-2], [-7], [-12], [-2], [8], [18], [8], [-2], [-12], [-7], [-2], [3], [2], [1]], [[1], [2], [3], [-2], [-7], [-12], [-2], [8], [18], [8], [-2], [-12], [-7], [-2], [3], [2], [1]], [[1], [-1], [0], [-5], [5], [0], [10], [-10], [0], [-10], [10], [0], [5], [-5], [0], [-1], [1]], [[1], [0], [0], [0], [-4], [0], [0], [0], [6], [0], [0], [0], [-4], [0], [0], [0], [1]], [[1], [0], [1], [0], [1], [0], [-2], [0], [-2], [0], [-2], [0], [1], [0], [1], [0], [1]], [[1], [0], [1], [0], [1], [0], [-2], [0], [-2], [0], [-2], [0], [1], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [0], [0], [1]], [[1]], [[1], [0], [-3], [0], [3], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [2, 3, 5, 11, 422857, 6880671269], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [74, -69, 141, -210, 75, 6, 12, -6, -3, 1], 'NumBadPrimes': 2, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [74, -69, 141, -210, 75, 6, 12, -6, -3, 1], 'Proj_nTj': [9, 26]}
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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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3267.3t2.b', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.3267.24t22.b', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.3267.24t22.b', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, 0], [-1, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '3.3267.4t5.c', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [0], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.9801.6t8.e', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [0], [-1], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.9801.8t23.b', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.25419964033827.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.25419964033827.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [0], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.5340285714719489633060049.24t1334.a', 'Character': [[16], [0], [0], [-2], [-2], [1], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '9', 'Order': 2, 'Representative': [5, 4, 3, 2, 1, 8, 9, 6, 7]}, {'Size': '36', 'Order': 2, 'Representative': [9, 2, 6, 5, 4, 3, 7, 8, 1]}, {'Size': '8', 'Order': 3, 'Representative': [6, 3, 4, 2, 9, 7, 1, 5, 8]}, {'Size': '24', 'Order': 3, 'Representative': [8, 5, 3, 1, 6, 2, 7, 4, 9]}, {'Size': '48', 'Order': 3, 'Representative': [8, 7, 1, 6, 4, 5, 9, 3, 2]}, {'Size': '54', 'Order': 4, 'Representative': [9, 8, 3, 6, 7, 2, 1, 4, 5]}, {'Size': '72', 'Order': 6, 'Representative': [8, 9, 6, 4, 3, 7, 2, 1, 5]}, {'Size': '72', 'Order': 6, 'Representative': [2, 9, 7, 3, 8, 5, 6, 4, 1]}, {'Size': '54', 'Order': 8, 'Representative': [1, 6, 4, 9, 8, 3, 5, 2, 7]}, {'Size': '54', 'Order': 8, 'Representative': [1, 7, 8, 2, 4, 5, 3, 9, 6]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 5, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 4, 4]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-1962962211374316472998886061063433190794', '-2763703817308932560123063966395961695731', '-492683978291948856515539142769972981312', '53559538056673823461527900048540810546', '12494732853333793671341484594276596544', '-685868895681463271119286567494140282', '-134745650311771841865645979368278811', '7303840588080825814685408693948586', '681161409522960668616274905664863', '-50344491884522488161710555522322', '-764710895245046693661575634447', '119887000270813826948466208836', '-706173749074258017511984227', '-140580107779410687280118004', '2506385308549081724784522', '83573574983102478478212', '-2542575558626525340855', '-18356298983059074345', '1275521725154523231', '-5266319528417409', '-315285904242738', '3817562243913', '26283943368', '-730343304', '2472282', '39123', '-378', '1'], 'ConjugacyClass': 10}, {'RootOf': ['57704199738325239020207885221053610372797', '5521937702443931057050066775657665201902', '1089209352437810451949868207099710663770', '39054145357118317045328809718600920842', '2122075799718908700936733561474556193', '-178719550186827604048905523212946836', '-18503674944649142472907009862046255', '-339608121348675542845578621727428', '66953560921539437349709563395826', '3779451164419615788538173475320', '-24285307394799240202223939583', '-6678030669181644495245731830', '-130859341103939089599137313', '4298910229246135895170677', '218786117064174745273809', '890979263452327855986', '-198291603992744869380', '-3878750213234679753', '166925945341428921', '2555345939085774', '-119351673491796', '58049766261', '40954918194', '-559685862', '613008', '44361', '-378', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-502281', '29727', 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