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artin_reps • Show schema
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{'BadPrimes': [2, 3, 13], 'Baselabel': '2.3744.16t60.a', 'CharacterField': 12, 'Conductor': 3744, 'Container': '16t60', 'Dets': ['1.468.6t1.c.b', '1.468.6t1.c.a', '1.468.6t1.c.a', '1.468.6t1.c.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': [15, 16, 17, 12, 13], '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]], [[1], [0, 0, 0, -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': [15, 16, 17, 12, 13], '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]], [[1], [0, 0, 0, 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': [15, 16, 17, 12, 13], '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]], [[1], [0, 0, 0, -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': [15, 16, 17, 12, 13], '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]], [[1], [0, 0, 0, 1]], [[1], [1]]]}], 'GaloisConjugatesSigns': [0, 0, 0, 0], 'GaloisLabel': '16T60', 'Galt': 60, 'HardPrimes': [2, 3, 13, 19, 563], 'Hide': 0, 'Indicator': 0, 'Is_Even': False, 'NFGal': [1, 0, 8, 0, 116, 0, 328, 0, 1766, 0, -328, 0, 116, 0, -8, 0, 1], 'NumBadPrimes': 3, 'Proj_GAP': [12, 3], 'Proj_Polynomial': [129, -8, -18, 0, 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': '1.4.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [-1], [-1], [1], [1], [1], [-1], [-1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.117.3t1.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': '1.468.6t1.c', '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': '1.117.3t1.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': '1.468.6t1.c', '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': '2.438048.24t21.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': '2.438048.24t21.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': '2.3744.16t60.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': '2.3744.16t60.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': '2.3744.16t60.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': '2.3744.16t60.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': '3.876096.6t6.a', 'Character': [[3], [3], [1], [0], [0], [-3], [-3], [-1], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.876096.4t4.c', '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': [2, 1, 12, 11, 6, 5, 16, 15, 10, 9, 4, 3, 14, 13, 8, 7]}, {'Size': '4', 'Order': 3, 'Representative': [14, 12, 9, 7, 5, 3, 10, 8, 6, 4, 1, 15, 13, 11, 2, 16]}, {'Size': '4', 'Order': 3, 'Representative': [11, 15, 6, 10, 5, 9, 4, 8, 3, 7, 14, 2, 13, 1, 12, 16]}, {'Size': '1', 'Order': 4, 'Representative': [12, 3, 10, 1, 16, 7, 14, 5, 4, 11, 2, 9, 8, 15, 6, 13]}, {'Size': '1', 'Order': 4, 'Representative': [4, 11, 2, 9, 8, 15, 6, 13, 12, 3, 10, 1, 16, 7, 14, 5]}, {'Size': '6', 'Order': 4, 'Representative': [11, 4, 1, 10, 15, 8, 5, 14, 3, 12, 9, 2, 7, 16, 13, 6]}, {'Size': '4', 'Order': 6, 'Representative': [3, 7, 14, 2, 13, 1, 12, 16, 11, 15, 6, 10, 5, 9, 4, 8]}, {'Size': '4', 'Order': 6, 'Representative': [6, 4, 1, 15, 13, 11, 2, 16, 14, 12, 9, 7, 5, 3, 10, 8]}, {'Size': '4', 'Order': 12, 'Representative': [15, 9, 4, 14, 16, 10, 11, 5, 7, 1, 12, 6, 8, 2, 3, 13]}, {'Size': '4', 'Order': 12, 'Representative': [2, 6, 7, 11, 16, 4, 1, 5, 10, 14, 15, 3, 8, 12, 9, 13]}, {'Size': '4', 'Order': 12, 'Representative': [7, 1, 12, 6, 8, 2, 3, 13, 15, 9, 4, 14, 16, 10, 11, 5]}, {'Size': '4', 'Order': 12, 'Representative': [10, 14, 15, 3, 8, 12, 9, 13, 2, 6, 7, 11, 16, 4, 1, 5]}], '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': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['3235266560', '25923584', '78336', '256', '1'], 'ConjugacyClass': 4}, {'RootOf': ['1836924928', '-9605120', '47616', '64', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 3, 3, 3, 3]}, {'Data': {'Powers': [1], 'Resolvent': [1, -3, 1]}, 'Classes': [{'RootOf': ['-48', '1'], 'ConjugacyClass': 2}, {'RootOf': ['-12230590464', '0', '-605159424', '0', '-6912', '0', '1'], 'ConjugacyClass': 3}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['1836924928', '9605120', '47616', '-64', '1'], 'ConjugacyClass': 9}, {'RootOf': ['3235266560', '-25923584', '78336', '-256', '1'], 'ConjugacyClass': 10}], 'Algorithm': 'RES', 'CycleType': [2, 2, 6, 6]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['-16', '1'], 'ConjugacyClass': 6}, {'RootOf': ['16', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-1073741824', '0', '3145728', '0', '116736', '0', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [4, 4, 4, 4]}, {'Data': {'Powers': [1], 'Resolvent': [-5, 11, -7, 1]}, 'Classes': [{'RootOf': ['7628406784', '-29495296', '52224', '320', '1'], 'ConjugacyClass': 11}, {'RootOf': ['3369009152', '-20750336', '62976', '-352', '1'], 'ConjugacyClass': 12}, {'RootOf': ['7628406784', '29495296', '52224', '-320', '1'], 'ConjugacyClass': 13}, {'RootOf': ['3369009152', '20750336', '62976', '352', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [4, 12]}], 'Frobs': [5, 11, 5, 3, 12, 9, 9, 12, 3, 9, 12, 10, 8, 6, 13, 8, 13, 8, 3, 12, 1, 11, 11, 10, 8, 5, 12, 11, 8, 10, 13, 14, 8, 11, 10, 11, 9, 14, 3, 2, 13, 8, 7, 2, 10, 12, 3, 12, 3, 9, 8, 12, 8, 14, 8, 14, 9, 11, 1, 10, 3, 4, 3, 12, 10, 10, 3, 5, 13, 5, 9, 3, 14, 10, 11, 11, 10, 9, 8, 4, 3, 10, 13, 5, 14, 13, 5, 5, 1, 12, 3, 14, 14, 3, 12, 14, 8, 1, 13, 1, 13, 10, 13, 5, 12, 8, 14, 2, 14, 5, 11, 10, 4, 11, 12, 8, 13, 13, 8, 6, 8, 9, 10, 14, 14, 2, 8, 14, 13, 9, 13, 6, 3, 10, 4, 8, 5, 13, 4, 4, 3, 5, 13, 7, 4, 6, 10, 4, 14, 7, 10, 4, 6, 3, 12, 11, 14, 8, 8, 9, 12, 9, 12, 14, 8, 11, 13, 8], 'G-Gens': [[11, 4, 1, 10, 15, 8, 5, 14, 3, 12, 9, 2, 7, 16, 13, 6], [9, 10, 11, 12, 13, 14, 15, 16, 1, 2, 3, 4, 5, 6, 7, 8], [12, 3, 10, 1, 16, 7, 14, 5, 4, 11, 2, 9, 8, 15, 6, 13], [14, 12, 9, 7, 5, 3, 10, 8, 6, 4, 1, 15, 13, 11, 2, 16], [6, 13, 8, 15, 2, 9, 4, 11, 14, 5, 16, 7, 10, 1, 12, 3]], 'G-Name': 'SL2(F3):C2', 'Polynomial': [1, 0, 8, 0, 116, 0, 328, 0, 1766, 0, -328, 0, 116, 0, -8, 0, 1], 'QpRts': [['-339725430846873426253864867', '-527609321157028682889313465', '294131453303108282952609266', '-249289778025331417760645443', '-128564737869520555149609836', '138250406003475502295196745'], ['186528622551859106192523115', '-116292401294389550508197151', '-162010428842610972495611739', '136570168098951741752316081', '82602280218111825978829675', '-371620734825504916005414314'], ['-52489734530050170173012316', '-333533630373997400836147890', '219744149086979259247847305', '576980819932027610079208522', '-103268544695430230249686801', '-172504871957269635062382416'], ['521015569371147636769953258', '420824539454649670449260575', '-332641292445071586124204613', '581707684108011796254508242', '-165261863053777989906590506', '-368285279403124141635692051'], ['533269854553363971558041669', '34551809980416154733577811', '-301753042435830637339705355', '396683858386845381317233037', '371335748679339525404298468', '519546982273304768828822361'], ['-220648748076448045521922001', '367392031312713742773068178', '-333655402318102583070014139', '560821358272603403059536129', '-557400838539828127133739112', '328490954157039271914232437'], ['431838654865652320330274935', '-338098415018780412954038236', '-366530274187611492473844950', '-373323799579784204672802506', '507435840954510248370033633', '-498836158567691614671186406'], ['-29912965333719433430728984', '126632032268176383196235964', '-355973419590991478860438964', '-143874194368598147343917558', '413743746115807989393264453', '453174802332944599857194832'], ['339725430846873426253864867', '527609321157028682889313465', '-294131453303108282952609266', '249289778025331417760645443', '128564737869520555149609836', '-138250406003475502295196745'], ['-186528622551859106192523115', '116292401294389550508197151', '162010428842610972495611739', '-136570168098951741752316081', '-82602280218111825978829675', '371620734825504916005414314'], ['52489734530050170173012316', '333533630373997400836147890', '-219744149086979259247847305', '-576980819932027610079208522', '103268544695430230249686801', '172504871957269635062382416'], ['-521015569371147636769953258', '-420824539454649670449260575', '332641292445071586124204613', '-581707684108011796254508242', '165261863053777989906590506', '368285279403124141635692051'], ['-533269854553363971558041669', '-34551809980416154733577811', '301753042435830637339705355', '-396683858386845381317233037', '-371335748679339525404298468', '-519546982273304768828822361'], ['220648748076448045521922001', '-367392031312713742773068178', '333655402318102583070014139', '-560821358272603403059536129', '557400838539828127133739112', '-328490954157039271914232437'], ['-431838654865652320330274935', '338098415018780412954038236', '366530274187611492473844950', '373323799579784204672802506', '-507435840954510248370033633', '498836158567691614671186406'], ['29912965333719433430728984', '-126632032268176383196235964', '355973419590991478860438964', '143874194368598147343917558', '-413743746115807989393264453', '-453174802332944599857194832']], 'QpRts-minpoly': [3, 3, 10, 0, 2, 0, 1], 'QpRts-p': 17, 'QpRts-prec': 22, 'Size': 48, 'TransitiveDegree': 16}