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artin_reps • Show schema
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{'BadPrimes': [2, 3, 11], 'Baselabel': '16.8325384592016962870050816.24t1334.a', 'CharacterField': 1, 'Conductor': 8325384592016962870050816, '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, 14, 2, 10, 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], [-1]], [[1], [0], [0], [0], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T26', 'Galt': 26, 'HardPrimes': [2, 3, 11, 139, 6359, 4398139007], 'Hide': 0, 'Indicator': 1, 'Is_Even': True, 'NFGal': [36, 42, -24, -18, 24, 12, -6, -6, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [432, 734], 'Proj_Polynomial': [36, 42, -24, -18, 24, 12, -6, -6, 0, 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': '2.1452.3t2.a', 'Character': [[2], [2], [0], [2], [-1], [-1], [2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.17424.24t22.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': '2.17424.24t22.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': '3.52272.4t5.b', 'Character': [[3], [3], [1], [3], [0], [0], [-1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.17424.6t8.a', 'Character': [[3], [3], [-1], [3], [0], [0], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.2509056.8t23.a', 'Character': [[4], [-4], [0], [4], [1], [1], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.15869558403072.9t26.a', 'Character': [[8], [0], [2], [-1], [2], [-1], [0], [-1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.15869558403072.18t157.a', 'Character': [[8], [0], [-2], [-1], [2], [-1], [0], [1], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '16.8325384592016962870050816.24t1334.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': [1, 7, 5, 9, 3, 8, 2, 6, 4]}, {'Size': '36', 'Order': 2, 'Representative': [7, 2, 6, 8, 5, 3, 1, 4, 9]}, {'Size': '8', 'Order': 3, 'Representative': [5, 4, 1, 6, 3, 2, 8, 9, 7]}, {'Size': '24', 'Order': 3, 'Representative': [6, 5, 3, 4, 9, 8, 7, 1, 2]}, {'Size': '48', 'Order': 3, 'Representative': [6, 8, 4, 9, 2, 7, 1, 5, 3]}, {'Size': '54', 'Order': 4, 'Representative': [1, 8, 9, 3, 4, 2, 6, 7, 5]}, {'Size': '72', 'Order': 6, 'Representative': [4, 5, 1, 6, 9, 7, 8, 3, 2]}, {'Size': '72', 'Order': 6, 'Representative': [6, 7, 9, 2, 3, 1, 5, 8, 4]}, {'Size': '54', 'Order': 8, 'Representative': [4, 6, 1, 7, 9, 5, 2, 8, 3]}, {'Size': '54', 'Order': 8, 'Representative': [5, 1, 6, 9, 7, 4, 3, 8, 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': ['406590023764644900672477413376', '-312238076291007164761437093888', '289255258138735568625317498880', '511847233908030815886137613312', '156189328249908875658573219840', '21924059159362277887841046528', '1946542901912568230630206464', '164369558958178030088481792', '15387761368590681957281280', '1194115416769653414368256', '71821866416082852789504', '3194423489366447270400', '-45552311337917434752', '-18735664770052113024', '-311542015972489344', '96156304378963776', '4494967096754304', '-171695049586848', '-11931233561856', '200268199008', '14471641008', '-198717192', '2745288', '715824', '-5220', '-1080', '0', '1'], 'ConjugacyClass': 10}, {'RootOf': ['34760324593006964953813442985984', '685514313929141604980581662720', '305879129959370050791121526784', 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7, 6, 8, 4, 9, 1, 5, 3], [1, 2, 9, 8, 4, 3, 7, 5, 6], [1, 8, 9, 3, 4, 2, 6, 7, 5], [5, 4, 1, 6, 3, 2, 8, 9, 7], [4, 5, 1, 6, 9, 7, 8, 3, 2]], 'G-Name': 'H432', 'Polynomial': [36, 42, -24, -18, 24, 12, -6, -6, 0, 1], 'QpRts': [['2155709920961862760791690134083980610998448529841998559996990', '5702025428799427077561977278719785439448294265177995270556921', '-6737074807450124986697659686692983234300229236994813338981299', '-6641332231404997942326363079097242393153429783715115603462378'], ['-2618654334800421477816136249728251258141969928954320087666871', '0', '0', '0'], ['6112627386680157822196445174588162316670923727807194875999504', '-172228701261456869794054419178903204254071518604986160116503', '8126836999975870436701718625541126866525258019617412925531283', '-1474663816880784367364182196762967746157430380320270192474235'], ['7447872011880186040846623166407395649505540719909433304266566', '2929790127557706341201493262252380534322571924280775781253006', 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