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artin_reps • Show schema
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{'BadPrimes': [3, 71], 'Baselabel': '16.15569728991930180478065769.24t1334.a', 'CharacterField': 1, 'Conductor': 15569728991930180478065769, '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': [12, 8, 13, 6], '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], [0], [-1]], [[1], [0], [-3], [0], [3], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [3, 13, 71, 1129], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [87, 13, -104, -8, -14, -8, -11, 7, -2, 1], 'NumBadPrimes': 2, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [87, 13, -104, -8, -14, -8, -11, 7, -2, 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': '2.15123.3t2.a', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.45369.24t22.a', '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], [0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, -1], [0, 1, 0, 1]], 'CharacterField': 8}, {'GalConj': 2, 'Baselabel': '2.45369.24t22.a', '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], [0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 1], [0, -1, 0, -1]], 'CharacterField': 8}, {'GalConj': 1, 'Baselabel': '3.136107.4t5.a', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.45369.6t8.a', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.408321.8t23.a', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.280155320935227.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.280155320935227.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.15569728991930180478065769.24t1334.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': [3, 4, 1, 2, 8, 9, 7, 5, 6]}, {'Size': '36', 'Order': 2, 'Representative': [1, 6, 9, 4, 7, 2, 5, 8, 3]}, {'Size': '8', 'Order': 3, 'Representative': [8, 5, 2, 1, 3, 7, 9, 4, 6]}, {'Size': '24', 'Order': 3, 'Representative': [5, 4, 3, 7, 9, 6, 2, 8, 1]}, {'Size': '48', 'Order': 3, 'Representative': [3, 1, 2, 9, 6, 7, 5, 4, 8]}, {'Size': '54', 'Order': 4, 'Representative': [4, 1, 2, 3, 6, 8, 7, 9, 5]}, {'Size': '72', 'Order': 6, 'Representative': [4, 9, 7, 8, 6, 3, 2, 1, 5]}, {'Size': '72', 'Order': 6, 'Representative': [5, 2, 4, 1, 7, 3, 6, 9, 8]}, {'Size': '54', 'Order': 8, 'Representative': [9, 8, 6, 5, 3, 2, 7, 1, 4]}, {'Size': '54', 'Order': 8, 'Representative': [6, 5, 9, 8, 1, 4, 7, 3, 2]}], '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': 9, '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': ['140262868689621220518374639262747072190745', '5724681687708668825152480742816504857746', '408106803164244018667552757242138266792', '14648460545581789775665273752935779001', '1820192810738461054575729166452543885', '148604187651044301111098350003291521', '11680059489315207807855313498757044', '675153572317398609325754726618703', '34178527733574076393780147156515', '1369131672448548207038573499167', '46531696770199430545753194693', '1165924799810970288358688292', '18751186812362847764694574', '-148547403334649557010220', '-22647567226328030533464', '-996205249464670056121', '-29215878586465447911', '-638583530976976353', '-10116594937933778', '-41158635849516', '2440721026380', '136933021859', '3190459692', '74853507', '1058029', '15945', '120', '1'], 'ConjugacyClass': 10}, {'RootOf': ['103729359827944758871270191915797292731', '-58290166983909098730763573321122694692', '15601889940987036516067942315867947000', '-2535699918804372708721270208036936029', '276541143085046759895226315661697498', '-22050666930451882388393283280920177', '1262014320534034120189266088128202', '-56392571314786430491279194522795', '1871132899525813505154809347191', '-57634700681320017405049950220', '1244558713539609002341819725', '-46351421062069821297044895', '31938059365326417973180', '-68586466976079003240849', '-2010896108152840241736', '-39607077561511305682', '1338606435808922970', '147282477618589257', '4292563516500184', '63393248001606', '-912633621483', '-14942239915', '707377686', '36346941', '630964', '9342', '120', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['11908', '244', '27', '19', '1'], 'ConjugacyClass': 4}, {'RootOf': 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