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artin_reps • Show schema
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{'BadPrimes': [2, 3, 37], 'Baselabel': '2.1776.12t18.b', 'CharacterField': 3, 'Conductor': 1776, 'Container': '12t18', 'Dets': ['1.111.6t1.b.b', '1.111.6t1.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, 20, 15, 12, 3, 16, 10, 21, 11], '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], [0, 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, 20, 15, 12, 3, 16, 10, 21, 11], '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]], [[1], [-1, -1]], [[1], [-1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '12T18', 'Galt': 18, 'HardPrimes': [2, 3, 5, 7, 11, 17, 19, 37, 379], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, -7, 0, 20, 0, -9, 0, 9, 0, -2, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [6, 1], 'Proj_Polynomial': [-37, 0, 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': '1.12.2t1.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': '1.3.2t1.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': '1.4.2t1.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': '1.148.6t1.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': 1, 'Baselabel': '1.444.6t1.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': '1.444.6t1.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': 1, 'Baselabel': '1.111.6t1.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': '1.111.6t1.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': '1.148.6t1.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': 1, 'Baselabel': '1.37.3t1.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': '1.37.3t1.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': '2.4107.3t2.a', 'Character': [[2], [2], [0], [0], [2], [2], [-1], [-1], [-1], [2], [2], [-1], [-1], [-1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.65712.6t3.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': '2.111.6t5.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': '2.1776.12t18.b', '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': '2.111.6t5.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': '2.1776.12t18.b', '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': [8, 7, 9, 10, 12, 11, 2, 1, 3, 4, 6, 5]}, {'Size': '3', 'Order': 2, 'Representative': [7, 8, 10, 9, 11, 12, 1, 2, 4, 3, 5, 6]}, {'Size': '3', 'Order': 2, 'Representative': [2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11]}, {'Size': '1', 'Order': 3, 'Representative': [12, 11, 8, 7, 3, 4, 6, 5, 1, 2, 10, 9]}, {'Size': '1', 'Order': 3, 'Representative': [9, 10, 5, 6, 8, 7, 4, 3, 12, 11, 2, 1]}, {'Size': '2', 'Order': 3, 'Representative': [12, 2, 8, 4, 3, 6, 7, 5, 1, 10, 11, 9]}, {'Size': '2', 'Order': 3, 'Representative': [9, 2, 5, 4, 8, 6, 7, 3, 12, 10, 11, 1]}, {'Size': '2', 'Order': 3, 'Representative': [12, 10, 8, 6, 3, 7, 4, 5, 1, 11, 2, 9]}, {'Size': '1', 'Order': 6, 'Representative': [3, 4, 12, 11, 1, 2, 10, 9, 5, 6, 7, 8]}, {'Size': '1', 'Order': 6, 'Representative': [5, 6, 1, 2, 9, 10, 11, 12, 8, 7, 4, 3]}, {'Size': '2', 'Order': 6, 'Representative': [5, 7, 1, 10, 9, 11, 2, 12, 8, 4, 6, 3]}, {'Size': '2', 'Order': 6, 'Representative': [3, 7, 12, 10, 1, 11, 2, 9, 5, 4, 6, 8]}, {'Size': '2', 'Order': 6, 'Representative': [5, 4, 1, 11, 9, 2, 10, 12, 8, 6, 7, 3]}, {'Size': '3', 'Order': 6, 'Representative': [6, 8, 2, 9, 10, 12, 1, 11, 7, 3, 5, 4]}, {'Size': '3', 'Order': 6, 'Representative': [7, 3, 10, 12, 11, 1, 9, 2, 4, 5, 8, 6]}, {'Size': '3', 'Order': 6, 'Representative': [11, 1, 7, 3, 4, 5, 8, 6, 2, 9, 12, 10]}, {'Size': '3', 'Order': 6, 'Representative': [2, 9, 4, 5, 6, 8, 3, 7, 10, 12, 1, 11]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['1372', '-74', '1'], 'ConjugacyClass': 7}, {'RootOf': ['1084', '-56', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 1, 1, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-12', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-65664', '432', '-36', '1'], 'ConjugacyClass': 3}, {'RootOf': ['65664', '432', '36', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['1372', '74', '1'], 'ConjugacyClass': 12}, {'RootOf': ['1084', '56', '1'], 'ConjugacyClass': 13}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-58', '1'], 'ConjugacyClass': 5}, {'RootOf': ['-40', '1'], 'ConjugacyClass': 6}, {'RootOf': ['2764', '-98', '1'], 'ConjugacyClass': 9}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]}, 'Classes': [{'RootOf': ['128', '1'], 'ConjugacyClass': 10}, {'RootOf': ['-204', '1'], 'ConjugacyClass': 11}, {'RootOf': ['88144', '-76', '1'], 'ConjugacyClass': 14}, {'RootOf': ['-39320000', '52272', '396', '1'], 'ConjugacyClass': 15}, {'RootOf': ['41564664', '52272', '396', '1'], 'ConjugacyClass': 16}, {'RootOf': ['39320000', '52272', '-396', '1'], 'ConjugacyClass': 17}, {'RootOf': ['-41564664', '52272', '-396', '1'], 'ConjugacyClass': 18}], 'Algorithm': 'RES', 'CycleType': [6, 6]}], 'Frobs': [18, 17, 15, 12, 4, 7, 16, 10, 4, 3, 14, 1, 15, 14, 4, 16, 18, 6, 12, 17, 9, 12, 18, 16, 9, 3, 2, 17, 8, 16, 13, 18, 3, 13, 3, 12, 8, 11, 17, 16, 4, 7, 4, 9, 16, 14, 14, 14, 17, 7, 3, 18, 7, 4, 16, 17, 3, 13, 6, 16, 12, 15, 14, 18, 8, 16, 13, 7, 4, 5, 16, 4, 12, 7, 11, 17, 15, 9, 3, 8, 18, 1, 17, 1, 12, 4, 15, 6, 16, 12, 4, 18, 2, 4, 10, 18, 16, 15, 12, 9, 14, 16, 4, 3, 13, 5, 17, 3, 17, 8, 11, 5, 16, 14, 13, 16, 14, 17, 15, 17, 7, 6, 3, 18, 13, 16, 9, 18, 12, 7, 2, 17, 14, 8, 16, 9, 15, 14, 16, 15, 10, 15, 13, 17, 8, 18, 5, 3, 14, 18, 9, 15, 10, 4, 12, 4, 14, 15, 8, 16, 18, 16, 12, 18, 16, 18, 2, 5], 'G-Gens': [[1, 10, 3, 6, 5, 7, 4, 8, 9, 11, 2, 12], [12, 2, 8, 4, 3, 6, 7, 5, 1, 10, 11, 9], [7, 8, 10, 9, 11, 12, 1, 2, 4, 3, 5, 6], [8, 7, 9, 10, 12, 11, 2, 1, 3, 4, 6, 5]], 'G-Name': 'C6*S3', 'Polynomial': [1, 0, -7, 0, 20, 0, -9, 0, 9, 0, -2, 0, 1], 'QpRts': [['112402847367975', '138154832433418', '276418775372300', '291018317000251', '258417976159783', '41421502752118'], ['262921215228088', '-229051920013154', '-15226148163352', '238334147695163', '-144182579877336', '-88120976259347'], ['-69218102543445', '102641838244609', '-180484562120632', '154735420896681', '163300439549555', '138165494292882'], ['66977406707883', '76305287036254', '-8481174977328', '45298103745905', '-220533956290469', '-5414222835685'], ['-219576861391093', '36028640107123', '250890867908782', '245648901584245', '43349382884213', '-169530694521132'], ['-205254002782308', '277780676098667', '-212757442770174', '-280220187799828', '24583222687118', '-155493456404030'], ['-262921215228088', '229051920013154', '15226148163352', '-238334147695163', '144182579877336', '88120976259347'], ['-112402847367975', '-138154832433418', '-276418775372300', '-291018317000251', '-258417976159783', '-41421502752118'], ['69218102543445', '-102641838244609', '180484562120632', '-154735420896681', '-163300439549555', '-138165494292882'], ['-66977406707883', '-76305287036254', '8481174977328', '-45298103745905', '220533956290469', '5414222835685'], ['205254002782308', '-277780676098667', '212757442770174', '280220187799828', '-24583222687118', '155493456404030'], ['219576861391093', '-36028640107123', '-250890867908782', '-245648901584245', '-43349382884213', '169530694521132']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 12, 'Size': 36, 'TransitiveDegree': 12}