Artin representation data - 18.89330065655584866215072366592.36t1758.a

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• artin_reps •

  Column	Type
  BadPrimes	jsonb
  Baselabel	text
  CharacterField	smallint
  Conductor	numeric
  Container	text
  Dets	text[]
  Dim	smallint
  GalConjSigns	jsonb
  Galn	smallint
  GaloisConjugates	jsonb
  GaloisConjugatesSigns	integer[]
  GaloisLabel	text
  Galt	integer
  HardPrimes	jsonb
  Hide	smallint
  Indicator	smallint
  Is_Even	boolean
  NFGal	jsonb
  NumBadPrimes	smallint
  Proj_GAP	integer[]
  Proj_Polynomial	numeric[]
  Proj_nTj	integer[]

  
  {'BadPrimes': [2, 3, 13], 'Baselabel': '18.89330065655584866215072366592.36t1758.a', 'CharacterField': 1, 'Conductor': 89330065655584866215072366592, 'Container': '36t1758', 'Dets': ['1.52.2t1.a.a'], 'Dim': 18, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[18], [-6], [2], [0], [0], [-2], [0], [0], [0], [0], [-2], [0], [0], [2], [0], [0], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 22, 15, 23, 15, 3, 6], 'LocalFactors': [[[1], [-18], [153], [-816], [3060], [-8568], [18564], [-31824], [43758], [-48620], [43758], [-31824], [18564], [-8568], [3060], [-816], [153], [-18], [1]], [[1], [6], [9], [-16], [-60], [-24], [116], [144], [-66], [-220], [-66], [144], [116], [-24], [-60], [-16], [9], [6], [1]], [[1], [-2], [-7], [16], [20], [-56], [-28], [112], [14], [-140], [14], [112], [-28], [-56], [20], [16], [-7], [-2], [1]], [[1], [0], [-9], [0], [36], [0], [-84], [0], [126], [0], [-126], [0], [84], [0], [-36], [0], [9], [0], [-1]], [[1], [0], [-9], [0], [36], [0], [-84], [0], [126], [0], [-126], [0], [84], [0], [-36], [0], [9], [0], [-1]], [[1], [2], [-7], [-16], [20], [56], [-28], [-112], [14], [140], [14], [-112], [-28], [56], [20], [-16], [-7], [2], [1]], [[1], [0], [-9], [0], [36], [0], [-84], [0], [126], [0], [-126], [0], [84], [0], [-36], [0], [9], [0], [-1]], [[1], [0], [0], [-6], [0], [0], [15], [0], [0], [-20], [0], [0], [15], [0], [0], [-6], [0], [0], [1]], [[1], [0], [0], [-6], [0], [0], [15], [0], [0], [-20], [0], [0], [15], [0], [0], [-6], [0], [0], [1]], [[1], [0], [3], [0], [0], [0], [-8], [0], [-6], [0], [6], [0], [8], [0], [0], [0], [-3], [0], [-1]], [[1], [2], [1], [0], [-4], [-8], [-4], [0], [6], [12], [6], [0], [-4], [-8], [-4], [0], [1], [2], [1]], [[1], [0], [3], [0], [0], [0], [-8], [0], [-6], [0], [6], [0], [8], [0], [0], [0], [-3], [0], [-1]], [[1], [0], [-1], [0], [-4], [0], [4], [0], [6], [0], [-6], [0], [-4], [0], [4], [0], [1], [0], [-1]], [[1], [-2], [5], [-8], [8], [-8], [0], [8], [-14], [20], [-14], [8], [0], [-8], [8], [-8], [5], [-2], [1]], [[1], [0], [1], [0], [-4], [0], [-4], [0], [6], [0], [6], [0], [-4], [0], [-4], [0], [1], [0], [1]], [[1], [0], [0], [2], [0], [0], [-1], [0], [0], [-4], [0], [0], [-1], [0], [0], [2], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [-3], [0], [0], [0], [0], [0], [3], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [-3], [0], [0], [0], [0], [0], [3], [0], [0], [0], [0], [0], [-1]], [[1], [0], [1], [0], [0], [0], [0], [0], [-2], [0], [-2], [0], [0], [0], [0], [0], [1], [0], [1]], [[1], [0], [0], [0], [0], [0], [1], [0], [0], [0], [0], [0], [-1], [0], [0], [0], [0], [0], [-1]], [[1], [1]], [[1]], [[1], [-1], [2], [-2], [0], [0], [-2], [2], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 3, 7, 13, 17, 6791, 63541], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-3, -18, 48, -66, 42, -18, 4, -2, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [-3, -18, 48, -66, 42, -18, 4, -2, 1], 'Proj_nTj': [8, 47]}
• artin_field_data •

  Column	Type
  ArtinReps	jsonb
  ComplexConjugation	smallint
  ConjClasses	jsonb
  FrobResolvents	jsonb
  Frobs	jsonb
  G-Gens	jsonb
  G-Name	text
  Polynomial	jsonb
  QpRts	jsonb
  QpRts-minpoly	jsonb
  QpRts-p	integer
  QpRts-prec	integer
  Size	numeric
  TransitiveDegree	smallint

  
  {'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], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.39.2t1.a', 'Character': [[1], [1], [1], [-1], [1], [1], [-1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.52.2t1.a', 'Character': [[1], [1], [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], [-1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.468.4t3.d', 'Character': [[2], [2], [2], [0], [0], [-2], [0], [2], [2], [0], [-2], [0], [0], [-2], [0], [2], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.657072.6t13.c', 'Character': [[4], [4], [4], [0], [2], [0], [0], [-2], [1], [0], [0], [0], [2], [0], [0], [-2], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.34167744.12t34.h', 'Character': [[4], [4], [4], [-2], [0], [0], [-2], [1], [-2], [-2], [0], [-2], [0], [0], [0], [1], [1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.2628288.12t34.a', 'Character': [[4], [4], [4], [0], [-2], [0], [0], [-2], [1], [0], [0], [0], [-2], [0], [0], [-2], [0], [1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '4.202176.6t13.a', 'Character': [[4], [4], [4], [2], [0], [0], [2], [1], [-2], [2], [0], [2], [0], [0], [0], [1], [-1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.378473472.12t201.a', 'Character': [[6], [2], [-2], [-2], [0], [-2], [2], [3], [0], [-4], [2], [0], [0], [0], [0], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.1640051712.12t202.c', 'Character': [[6], [2], [-2], [-4], [0], [2], [0], [3], [0], [-2], [-2], [2], [0], [0], [0], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.1640051712.8t47.d', 'Character': [[6], [2], [-2], [4], [0], [2], [0], [3], [0], [2], [-2], [-2], [0], [0], [0], [-1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.63962016768.12t200.a', 'Character': [[6], [2], [-2], [2], [0], [-2], [-2], [3], [0], [4], [2], [0], [0], [0], [0], [-1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.89802671542272.16t1294.a', 'Character': [[9], [-3], [1], [3], [3], [1], [-1], [0], [0], [-3], [1], [1], [-1], [-1], [1], [0], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.20723693432832.18t272.a', 'Character': [[9], [-3], [1], [-3], [3], [1], [1], [0], [0], [3], [1], [-1], [-1], [-1], [-1], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.110526364975104.18t273.a', 'Character': [[9], [-3], [1], [-3], [-3], [1], [1], [0], [0], [3], [1], [-1], [1], [-1], [1], [0], [0], [0], [-1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '9.4310528234029056.18t274.a', 'Character': [[9], [-3], [1], [3], [-3], [1], [-1], [0], [0], [-3], [1], [1], [1], [-1], [-1], [0], [0], [0], [1], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.944109135929979961344.36t1763.a', 'Character': [[12], [4], [-4], [-2], [0], [0], [-2], [-3], [0], [2], [0], [2], [0], [0], [0], [1], [1], [0], [0], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.5586444591301656576.24t2821.a', 'Character': [[12], [4], [-4], [2], [0], [0], [2], [-3], [0], [-2], [0], [-2], [0], [0], [0], [1], [-1], [0], [0], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '18.89330065655584866215072366592.36t1758.a', 'Character': [[18], [-6], [2], [0], [0], [-2], [0], [0], [0], [0], [-2], [0], [0], [2], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 7, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8]}, {'Size': '6', 'Order': 2, 'Representative': [1, 2, 5, 8, 3, 6, 7, 4]}, {'Size': '9', 'Order': 2, 'Representative': [6, 7, 5, 8, 3, 1, 2, 4]}, {'Size': '12', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [3, 4, 1, 2, 6, 5, 8, 7]}, {'Size': '36', 'Order': 2, 'Representative': [2, 1, 4, 3, 5, 6, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [2, 1, 5, 8, 3, 6, 7, 4]}, {'Size': '16', 'Order': 3, 'Representative': [6, 2, 3, 4, 5, 7, 1, 8]}, {'Size': '64', 'Order': 3, 'Representative': [6, 2, 3, 5, 8, 7, 1, 4]}, {'Size': '12', 'Order': 4, 'Representative': [1, 2, 4, 5, 8, 6, 7, 3]}, {'Size': '36', 'Order': 4, 'Representative': [2, 6, 4, 5, 8, 7, 1, 3]}, {'Size': '36', 'Order': 4, 'Representative': [2, 6, 5, 8, 3, 7, 1, 4]}, {'Size': '72', 'Order': 4, 'Representative': [3, 4, 6, 7, 1, 5, 8, 2]}, {'Size': '72', 'Order': 4, 'Representative': [2, 1, 4, 5, 8, 6, 7, 3]}, {'Size': '144', 'Order': 4, 'Representative': [4, 3, 1, 2, 6, 5, 8, 7]}, {'Size': '48', 'Order': 6, 'Representative': [7, 2, 5, 8, 3, 1, 6, 4]}, {'Size': '96', 'Order': 6, 'Representative': [2, 1, 3, 8, 4, 6, 7, 5]}, {'Size': '192', 'Order': 6, 'Representative': [4, 3, 2, 6, 7, 5, 8, 1]}, {'Size': '144', 'Order': 8, 'Representative': [3, 4, 2, 6, 7, 5, 8, 1]}, {'Size': '96', 'Order': 12, 'Representative': [6, 2, 4, 5, 8, 7, 1, 3]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 3]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-922854848', '-66677952', '1208592', '126736', '-1236', '-72', '1'], 'ConjugacyClass': 2}, {'RootOf': ['25812657267202988842140758404908768559104', '-19730930321215899439946390963782787530752', '10550428001473962963124705999184531030016', '-4323464605652297201301107898548427423744', '1449209419879532920419239525507351445504', '-396820020231371832240303791888224223232', '90194060513802504349526061760150241280', '-16147459281806209794538671097163808768', '2053392299868804714388461103859367936', '-108732054434247131899831718342819840', '-28762476727847286508656734490329088', '10420948359062366348562306101673984', '-1749521536821384121477907940900864', '137334436292861365259848761999360', '7618227266682835449906966036480', '-3267120826348700414381540769792', '332647722913571963485676371968', '-3526540969940991686687588352', '-2614871153765785617845714944', '271162505222033835327750144', '-6683249073011139879763968', '-924753541319344209002496', '99329079545127334969344', '-3370914740560265773056', '-105584025752196415488', '16282649417453961216', '-736886359384068096', '9667401982982144', '740607238950912', '-54968884167168', '2025801059328', '-49673506176', '859201776', '-10469088', '86160', '-432', '1'], 'ConjugacyClass': 6}], 'Algorithm': 'RES', 'CycleType': [1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 4]}, {'Data': 0, 'Classes': 17, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 3]}, {'Data': 0, 'Classes': 7, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 2]}, {'Data': 0, 'Classes': 14, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 4]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 3, 3]}, {'Data': 0, 'Classes': 16, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 3]}, {'Data': 0, 'Classes': 20, 'Algorithm': 'CYC', 'CycleType': [1, 3, 4]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['14983386624', '10073104128', '3029621760', '532416384', '60013440', '4484448', '221520', '6960', '126', '1'], 'ConjugacyClass': 3}, {'RootOf': ['13347534718981696426868736', '146917078314963223707648', '-177453277844783813885952', '-76141474208244641562624', '-3360241442953290055680', '-444982514472723677184', '133820493431842013184', '13185980374218964992', '3384302156811141120', '189157020139192320', '44339947825692672', '3315236366942208', '790078505803776', '75533421662208', '11248893849600', '891978289152', '91465254912', '5542547712', '428851456', '18905472', '1160256', '33536', '1680', '24', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['67894205311627017181986816', '45820954573982037920710656', '14579469008068419765927936', '2905591296062539330486272', '406374290167415221518336', '42348637307270278545408', '3407290042315965677568', '216381546044569092096', '10993353582155710464', '450095618891685888', '14883540215943168', '396495244541952', '8445004755840', '141840528768', '1837048320', '17700816', '119472', '504', '1'], 'ConjugacyClass': 12}, {'RootOf': ['137025135198700685832609526190004914186799029168924101982343344803882027201029847646208', '-80902639558985978376313089263665884185493697929823058342896800165541503008866465480704', '66788572556793668430616350237267647349832065543139679215554708392478204489506752561152', '-6590597731491378453479285586333876289716278090737113191260303302486148967498923376640', '8592475596141146954176864860564737254548634610958997470583878027306125127504504029184', '1578686926256029958467923227448631457780347059866963189942546265885327043121809195008', '718719925544133201146270047534486235936992156743653442139839852435009317195055366144', '117693754194676530556051683428781612933230962879845023151223257567604239406435663872', '5209509849012313356399720587292460997215801223173897798409037972141882945835106304', '-5564077616469175113226243886384973661151380110172404001461729280638332045956743168', '-2154869600406301018393939365235618322550448566792144751724990462915604877915717632', '-531505007487803989644871789243997530016788785640563698346355071197144985825705984', '-101792971091448169786750293365534289151612589511299324996049150162867228071952384', '-16520163259049691247278550498304371928729686396849850908158104023108560378396672', '-2347681733886627013996130229677388634178637296942811202260346235542252038389760', '-299543559794045815688376336489689400326601491319320824915933682745457237819392', '-34782705645128631897686942458760607263098556651340891946893499583054745698304', '-3711888061748471721979892616257884674797297878192817723493145725236385153024', '-366217023195317674032527694040615980769378706615612691971453389381174296576', '-33523841470342811909595328459464637940110877505922660660890403954048892928', '-2853648282226330697098425031123181355883930020722496218020205207318691840', '-226042783710256666231339941830141136954365096673868397627880178389614592', '-16688289519627013304308075425352771866596230874237273612825837917175808', '-1152695782834358923397814550045167697757132681570839960418195154665472', 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