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artin_reps • Show schema
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{'BadPrimes': [3, 7, 13], 'Baselabel': '2.273.16t60.a', 'CharacterField': 12, 'Conductor': 273, 'Container': '16t60', 'Dets': ['1.273.6t1.d.b', '1.273.6t1.d.a', '1.273.6t1.d.a', '1.273.6t1.d.b'], 'Dim': 2, 'GalConjSigns': [0, 0, 0, 0], 'Galn': 16, 'GaloisConjugates': [{'Sign': 0, 'Character': [[2], [-2], [0], [0, 0, 1], [1, 0, -1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [-1, 0, 1], [0, 0, -1], [0, -1, 0, 1], [0, 1], [0, 1, 0, -1], [0, -1]], 'GalOrbIndex': 1, 'HardFactors': [12, 15, 16, 17, 3, 3, 4, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0], [1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 0, 0, -1]], [[1], [-1]], [[1], [1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [1, 0, -1], [0, 0, 1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [0, 0, -1], [-1, 0, 1], [0, -1], [0, 1, 0, -1], [0, 1], [0, -1, 0, 1]], 'GalOrbIndex': 2, 'HardFactors': [12, 15, 16, 17, 3, 3, 4, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0], [1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, 0, 0, 1]], [[1], [-1]], [[1], [1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [1, 0, -1], [0, 0, 1], [0, 0, 0, 2], [0, 0, 0, -2], [0], [0, 0, -1], [-1, 0, 1], [0, 1], [0, -1, 0, 1], [0, -1], [0, 1, 0, -1]], 'GalOrbIndex': 3, 'HardFactors': [12, 15, 16, 17, 3, 3, 4, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0], [1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 0, 0, -1]], [[1], [-1]], [[1], [1]]]}, {'Sign': 0, 'Character': [[2], [-2], [0], [0, 0, 1], [1, 0, -1], [0, 0, 0, -2], [0, 0, 0, 2], [0], [-1, 0, 1], [0, 0, -1], [0, 1, 0, -1], [0, -1], [0, -1, 0, 1], [0, 1]], 'GalOrbIndex': 4, 'HardFactors': [12, 15, 16, 17, 3, 3, 4, 2], 'LocalFactors': [[[1], [-2], [1]], [[1], [2], [1]], [[1], [0], [-1]], [[1], [0, 0, -1], [-1, 0, 1]], [[1], [-1, 0, 1], [0, 0, -1]], [[1], [0, 0, 0, 2], [-1]], [[1], [0, 0, 0, -2], [-1]], [[1], [0], [1]], [[1], [1, 0, -1], [0, 0, -1]], [[1], [0, 0, 1], [-1, 0, 1]], [[1], [0, -1, 0, 1], [1, 0, -1]], [[1], [0, 1], [0, 0, 1]], [[1], [0, 1, 0, -1], [1, 0, -1]], [[1], [0, -1], [0, 0, 1]], [[1], [0, 0, 0, 1]], [[1], [-1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '16T60', 'Galt': 60, 'HardPrimes': [2, 3, 7, 13, 101, 263, 541, 19819], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [7, -7, -28, -9, 78, 112, -61, -183, 32, 183, 7, -101, -8, 31, 0, -5, 1], 'NumBadPrimes': 3, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [24, 9, 7, -1, 1], 'Proj_nTj': [4, 4]}
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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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.3.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.91.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [-1, -1], [0, 1], [-1, -1], [0, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '1.273.6t1.d', 'Character': [[1, 0], [1, 0], [-1, 0], [-1, -1], [0, 1], [-1, 0], [-1, 0], [1, 0], [0, 1], [-1, -1], [1, 1], [0, -1], [1, 1], [0, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.91.3t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [0, 1], [-1, -1], [1, 0], [1, 0], [1, 0], [-1, -1], [0, 1], [0, 1], [-1, -1], [0, 1], [-1, -1]], 'CharacterField': 3}, {'GalConj': 2, 'Baselabel': '1.273.6t1.d', 'Character': [[1, 0], [1, 0], [-1, 0], [0, 1], [-1, -1], [-1, 0], [-1, 0], [1, 0], [-1, -1], [0, 1], [0, -1], [1, 1], [0, -1], [1, 1]], 'CharacterField': 3}, {'GalConj': 1, 'Baselabel': '2.24843.24t21.a', 'Character': [[2, 0], [-2, 0], [0, 0], [-1, 0], [-1, 0], [0, -2], [0, 2], [0, 0], [1, 0], [1, 0], [0, 1], [0, 1], [0, -1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '2.24843.24t21.a', 'Character': [[2, 0], [-2, 0], [0, 0], [-1, 0], [-1, 0], [0, 2], [0, -2], [0, 0], [1, 0], [1, 0], [0, -1], [0, -1], [0, 1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '2.273.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, -1, 0, 1], [0, 1, 0, 0], [0, 1, 0, -1], [0, -1, 0, 0]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '2.273.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, -1, 0, 0], [0, 1, 0, -1], [0, 1, 0, 0], [0, -1, 0, 1]], 'CharacterField': 12}, {'GalConj': 3, 'Baselabel': '2.273.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, 0, 1, 0], [0, 0, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 1, 0], [0, 1, 0, 0], [0, -1, 0, 1], [0, -1, 0, 0], [0, 1, 0, -1]], 'CharacterField': 12}, {'GalConj': 4, 'Baselabel': '2.273.16t60.a', 'Character': [[2, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [1, 0, -1, 0], [0, 0, 0, -2], [0, 0, 0, 2], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 0, -1, 0], [0, 1, 0, -1], [0, -1, 0, 0], [0, -1, 0, 1], [0, 1, 0, 0]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '3.24843.6t6.a', 'Character': [[3], [3], [1], [0], [0], [-3], [-3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.74529.4t4.a', 'Character': [[3], [3], [-1], [0], [0], [3], [3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]}, {'Size': '1', 'Order': 2, 'Representative': [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [5, 3, 2, 14, 1, 12, 16, 15, 13, 11, 10, 6, 9, 4, 8, 7]}, {'Size': '4', 'Order': 3, 'Representative': [4, 6, 1, 3, 5, 7, 2, 8, 12, 14, 9, 11, 13, 15, 10, 16]}, {'Size': '4', 'Order': 3, 'Representative': [3, 7, 4, 1, 5, 2, 6, 8, 11, 15, 12, 9, 13, 10, 14, 16]}, {'Size': '1', 'Order': 4, 'Representative': [15, 4, 14, 10, 8, 3, 1, 13, 7, 12, 6, 2, 16, 11, 9, 5]}, {'Size': '1', 'Order': 4, 'Representative': [7, 12, 6, 2, 16, 11, 9, 5, 15, 4, 14, 10, 8, 3, 1, 13]}, {'Size': '6', 'Order': 4, 'Representative': [16, 6, 12, 3, 7, 10, 13, 1, 8, 14, 4, 11, 15, 2, 5, 9]}, {'Size': '4', 'Order': 6, 'Representative': [11, 15, 12, 9, 13, 10, 14, 16, 3, 7, 4, 1, 5, 2, 6, 8]}, {'Size': '4', 'Order': 6, 'Representative': [12, 14, 9, 11, 13, 15, 10, 16, 4, 6, 1, 3, 5, 7, 2, 8]}, {'Size': '4', 'Order': 12, 'Representative': [10, 3, 15, 14, 8, 1, 4, 13, 2, 11, 7, 6, 16, 9, 12, 5]}, {'Size': '4', 'Order': 12, 'Representative': [14, 1, 10, 15, 8, 4, 3, 13, 6, 9, 2, 7, 16, 12, 11, 5]}, {'Size': '4', 'Order': 12, 'Representative': [2, 11, 7, 6, 16, 9, 12, 5, 10, 3, 15, 14, 8, 1, 4, 13]}, {'Size': '4', 'Order': 12, 'Representative': [6, 9, 2, 7, 16, 12, 11, 5, 14, 1, 10, 15, 8, 4, 3, 13]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['118863', '-15600', '1363', '-43', '1'], 'ConjugacyClass': 4}, {'RootOf': ['47040', '-8232', '1120', '-46', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-13', '1'], 'ConjugacyClass': 2}, {'RootOf': ['56133', '-190890', '-93583', '-16486', '-1206', '-20', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['2080', '-1032', '244', '-24', '1'], 'ConjugacyClass': 9}, {'RootOf': ['910', '987', '217', '-27', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['0', '1'], 'ConjugacyClass': 6}, {'RootOf': ['-35', '1'], 'ConjugacyClass': 7}, {'RootOf': ['905247', '518658', '76104', '-713', '-256', '-25', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['18564', '3303', '313', '22', '1'], 'ConjugacyClass': 11}, {'RootOf': ['111475', '11634', '-140', '-42', '1'], 'ConjugacyClass': 12}, {'RootOf': ['178213', '-32606', '2331', '-77', '1'], 'ConjugacyClass': 13}, {'RootOf': ['23352', '4269', '271', '-13', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [4, 12]}], 'Frobs': [12, 8, 11, 1, 3, 9, 13, 8, 14, 13, 5, 9, 11, 9, 11, 12, 11, 8, 8, 14, 9, 10, 3, 12, 5, 3, 10, 12, 9, 12, 4, 13, 13, 5, 3, 9, 9, 8, 13, 3, 3, 8, 7, 8, 11, 10, 10, 4, 11, 10, 11, 3, 10, 12, 12, 3, 13, 5, 10, 6, 8, 14, 8, 12, 4, 13, 8, 8, 11, 4, 3, 11, 8, 8, 10, 3, 14, 8, 12, 4, 11, 8, 7, 9, 9, 11, 14, 5, 12, 8, 11, 3, 4, 13, 10, 12, 14, 14, 5, 4, 8, 3, 13, 14, 5, 9, 13, 13, 14, 4, 2, 1, 12, 5, 5, 11, 5, 6, 12, 14, 8, 10, 11, 11, 5, 7, 8, 3, 8, 10, 8, 11, 9, 10, 3, 10, 13, 10, 14, 3, 8, 12, 4, 3, 1, 12, 8, 14, 4, 11, 8, 13, 1, 14, 8, 3, 8, 7, 8, 12, 14, 14, 8, 3, 6, 14, 8, 10], 'G-Gens': [[15, 4, 14, 10, 8, 3, 1, 13, 7, 12, 6, 2, 16, 11, 9, 5], [16, 6, 12, 3, 7, 10, 13, 1, 8, 14, 4, 11, 15, 2, 5, 9], [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8], [4, 15, 16, 9, 6, 13, 2, 3, 12, 7, 8, 1, 14, 5, 10, 11], [8, 15, 3, 9, 10, 6, 5, 12, 16, 7, 11, 1, 2, 14, 13, 4]], 'G-Name': 'SL2(F3):C2', 'Polynomial': [7, -7, -28, -9, 78, 112, -61, -183, 32, 183, 7, -101, -8, 31, 0, -5, 1], 'QpRts': [['-3089942992857924182', '-1723383807237293522', '-2482844643118483966', '2083116375943862907', '-1995180534289183472', '3063877389285441849'], ['-374908702716311687', '696539925862177124', '2007010649991195892', '-485754633514910244', '2445954962795352236', '-1938333164913243280'], ['2116823344058777609', '-1680301341081723821', '2937770236703809411', '-1259599957587785735', '3235248502468642151', '265638081967000313'], ['-3096559665458546964', '-3066300402057053568', '539769452207909679', '357113163715041569', '1764616091480621161', '-1395591607145882178'], ['475090715587503534', '2684576657704630307', '-3279375393734012316', '-3011766469381780457', '-1071541697218693125', '2126187649001360097'], ['1691640379792799368', '-2701792398183009002', '-501090151782738316', '-1425240571141412253', '-3056955579496386512', '-2647552544924868995'], ['714012200974500474', '-2920726868968264641', '-677705590978625709', '-2056742797201794510', '-841557305897700298', '2188764163478481242'], ['-1091548571829247798', '-2541883515727771201', '-2512587952426456380', '-611651548120228923', '581148579490620871', '3175433792766665588'], ['2118182461775572569', '-2714693002049767700', '3140640281967120735', '2538884738216185000', '-374923191040730643', '-160048125341561140'], ['707769516785405774', '-823728665851335487', '-2243226963597666423', '2607374923623884131', '-1183725456975365576', '1022788282811104423'], ['306037734488422223', '1680301341081723821', '-2937770236703809411', '1259599957587785735', '-3235248502468642151', '-265638081967000313'], ['2139763220054325040', '2212626102404614796', '2536267273520114488', '2470726085040993098', '123025999900488075', '1678638143480369839'], ['-156823058445193584', '-1948292378546966952', '720645421091045907', '-2629525845111712184', '-2552296920705405917', '718585830427180298'], ['-1620744139128009247', '2701792398183009002', '501090151782738316', '1425240571141412253', '3056955579496386512', '2647552544924868995'], ['2771498700041069566', '2311631329799759649', '-3110300128611972632', '-1006537184253722017', '3203166418001812680', '2464959245035152501'], ['2972660862716892591', '1250682618827235914', '-1221244412150204556', '-255236808955818370', '-98686945541815992', '220642412795001323']], 'QpRts-minpoly': [2, 30, 4, 35, 0, 0, 1], 'QpRts-p': 37, 'QpRts-prec': 12, 'Size': 48, 'TransitiveDegree': 16}