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artin_reps • Show schema
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{'BadPrimes': [3, 11], 'Baselabel': '16.5340285714719489633060049.24t1334.b', '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': [12, 13, 2], '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], [0], [0], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [3, 11, 71], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [4, -9, 6, -6, -18, 3, 9, 0, -3, 1], 'NumBadPrimes': 2, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [4, -9, 6, -6, -18, 3, 9, 0, -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': '8.2824440448203.9t26.b', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.2824440448203.18t157.b', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [0], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.5340285714719489633060049.24t1334.b', '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': [6, 9, 8, 4, 7, 1, 5, 3, 2]}, {'Size': '36', 'Order': 2, 'Representative': [4, 5, 7, 1, 2, 6, 3, 8, 9]}, {'Size': '8', 'Order': 3, 'Representative': [2, 3, 1, 5, 7, 8, 4, 9, 6]}, {'Size': '24', 'Order': 3, 'Representative': [8, 2, 5, 4, 6, 3, 1, 7, 9]}, {'Size': '48', 'Order': 3, 'Representative': [5, 7, 4, 6, 8, 3, 9, 1, 2]}, {'Size': '54', 'Order': 4, 'Representative': [9, 1, 5, 4, 8, 2, 3, 7, 6]}, {'Size': '72', 'Order': 6, 'Representative': [4, 1, 6, 8, 5, 3, 2, 9, 7]}, {'Size': '72', 'Order': 6, 'Representative': [5, 7, 4, 2, 3, 8, 1, 9, 6]}, {'Size': '54', 'Order': 8, 'Representative': [4, 8, 3, 9, 1, 2, 5, 7, 6]}, {'Size': '54', 'Order': 8, 'Representative': [8, 4, 3, 7, 2, 1, 6, 9, 5]}], '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': ['6595416681233431167849287648088', '-10946346892724168974729764805797', '8214754316016934515760685480367', '-3716444369354322112534833622335', '1139479884292166235195563917557', '-251970095243010079423918164249', '41649496336370356355148720498', '-5241462569608858489909730934', '502272426586204757418099327', '-35380138174559480997103104', '1542683460659958074575935', '11670344823805278182181', '-10318431621269294690310', '1264851322304131644723', '-109028972978244641754', '7708704381221655780', '-469509167845839951', '25136090226062811', '-1192497671857725', '50186068574796', '-1867921482969', '61138570608', '-1741536045', '42394266', '-859248', '13905', '-162', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-1751684354213490081973263273831', '1583963688571698260725857571212', '-1453522917707741403401111382897', '627169834013365685954241825633', '-144882113440389397716907352493', '12497430502589126671986458157', '2319805704473002776899293911', '-944015665894183671257724426', '137395500429580924127850162', '-8416805263736175296873397', '-390621669442745992261929', '180584047103261186781693', '-28573775804120974120629', '3161742555481525271502', '-273689109858026383200', '19503290151644308110', '-1183335667922851929', '62361421517122299', '-2871909717235020', '115252962066495', '-4000686621093', '119307683646', '-3028572909', '64753425', '-1139184', '15957', '-162', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [1, 8]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-729', '-1782', '270', '-27', '1'], 'ConjugacyClass': 4}, {'RootOf': ['49704194187142118176934007', '-17814216266430424842709089', '4374295752477558423567465', '-1566345418913469499877097', 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8, 11, 9, 8, 10, 7, 11, 2, 10, 6, 11, 7, 3, 7, 11, 8, 11, 7, 9, 8, 9, 5, 9, 9, 10, 2, 11, 9, 9, 8, 6], 'G-Gens': [[2, 3, 1, 7, 4, 6, 5, 8, 9], [5, 8, 2, 9, 3, 1, 7, 4, 6], [5, 9, 1, 3, 4, 6, 8, 2, 7], [1, 5, 9, 4, 8, 6, 3, 2, 7], [2, 3, 1, 5, 7, 8, 4, 9, 6], [4, 5, 7, 6, 8, 1, 9, 2, 3]], 'G-Name': 'H432', 'Polynomial': [4, -9, 6, -6, -18, 3, 9, 0, -3, 1], 'QpRts': [['1558511105982751769975090291690400087317525804392141136843636637411', '-500764799832313620174594187548679379849489561256217379608210615431', '977134132311835871423794008090940170929053495420216844240067656492', '-1269282396449939654823036021626505840102495320810852748335893581302'], ['-404848111008248639609928119003942365928894702033858980846549836482', '1374771885406354927623707310417224151693492718793290219743372118995', '-876371071716823215686563207633635478728107660723902982465582316880', '1197152636185603278748793860375694010967845225978505302785869460271'], 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['-838169526743471901496589320197510799778484249183319878604725598356', '-466990779882348615981859762332954324002592185038956419067031683434', '1300432640417640509155387139693446882550483406570535369814745053689', '-256472527886267706800794614757870306813934842799486432882414942217'], ['-1201690610165952443741441544916009348434244417944414415882788105600', '185419844044298079957844052567839333005154906180946736030538237812', '-1013262446409141017071591698474419336965411672885746366195903663764', '-20087800200897890560536843430674225497554853624312226975434795525'], ['-773534492387691881352222358880399699171565759128952956299073703942', '-1093200949568304391599691600652109160696055439935280536706878673373', '589200877708323723602767766414607933143035927039113978846740926955', '-920592308098437681387462402187149478656355529554706642928019722529']], 'QpRts-minpoly': [2, 11, 2, 0, 1], 'QpRts-p': 19, 'QpRts-prec': 52, 'Size': 432, 'TransitiveDegree': 9}