Artin representation data - 18.1465285887652900039067594391552.36t1758.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], 'Baselabel': '18.1465285887652900039067594391552.36t1758.a', 'CharacterField': 1, 'Conductor': 1465285887652900039067594391552, 'Container': '36t1758', 'Dets': ['1.8.2t1.b.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, 21, 17, 13], '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]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 3, 53, 13781], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [1, -8, 14, -4, -7, 4, 2, -4, 1], 'NumBadPrimes': 2, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [1, -8, 14, -4, -7, 4, 2, -4, 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': '1.4.2t1.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': '1.8.2t1.b', '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': '1.8.2t1.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': '2.1152.4t3.c', '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': '4.373248.6t13.b', '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': '4.2985984.12t34.b', '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': '4.5971968.12t34.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': '4.746496.6t13.b', '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': '6.13759414272.12t201.q', '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': '6.382205952.12t202.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': '6.95551488.8t47.a', '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': '6.13759414272.12t200.e', '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': '9.17832200896512.16t1294.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': '9.71328803586048.18t272.b', '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': '9.570630428688384.18t273.c', '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': '9.570630428688384.18t274.c', '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': '12.425973332494163902464.36t1763.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': '12.106493333123540975616.24t2821.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': '18.1465285887652900039067594391552.36t1758.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, 7, 4, 8, 6, 3, 5]}, {'Size': '9', 'Order': 2, 'Representative': [4, 6, 7, 1, 8, 2, 3, 5]}, {'Size': '12', 'Order': 2, 'Representative': [2, 1, 3, 4, 5, 6, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [3, 5, 1, 7, 2, 8, 4, 6]}, {'Size': '36', 'Order': 2, 'Representative': [2, 1, 5, 4, 3, 6, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [2, 1, 7, 4, 8, 6, 3, 5]}, {'Size': '16', 'Order': 3, 'Representative': [4, 2, 3, 6, 5, 1, 7, 8]}, {'Size': '64', 'Order': 3, 'Representative': [4, 2, 3, 6, 7, 1, 8, 5]}, {'Size': '12', 'Order': 4, 'Representative': [1, 2, 5, 4, 7, 6, 8, 3]}, {'Size': '36', 'Order': 4, 'Representative': [2, 4, 5, 6, 7, 1, 8, 3]}, {'Size': '36', 'Order': 4, 'Representative': [2, 4, 7, 6, 8, 1, 3, 5]}, {'Size': '72', 'Order': 4, 'Representative': [3, 5, 4, 7, 6, 8, 1, 2]}, {'Size': '72', 'Order': 4, 'Representative': [2, 1, 5, 4, 7, 6, 8, 3]}, {'Size': '144', 'Order': 4, 'Representative': [5, 3, 1, 7, 2, 8, 4, 6]}, {'Size': '48', 'Order': 6, 'Representative': [6, 2, 7, 1, 8, 4, 3, 5]}, {'Size': '96', 'Order': 6, 'Representative': [2, 1, 3, 4, 8, 6, 5, 7]}, {'Size': '192', 'Order': 6, 'Representative': [5, 3, 2, 7, 4, 8, 6, 1]}, {'Size': '144', 'Order': 8, 'Representative': [3, 5, 2, 7, 4, 8, 6, 1]}, {'Size': '96', 'Order': 12, 'Representative': [4, 2, 5, 6, 7, 1, 8, 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': ['25633024', '-9588864', '1134096', '-80288', '3720', '-96', '1'], 'ConjugacyClass': 2}, {'RootOf': ['1449475107958877182772106165635170384636542976', '796797151593285676345130593739190669702856704', '129372008093199138520447967739169814949789696', '-7041018876940928302181228452583836955246592', '-4438642381561820753420197448170122023006208', '510574763475745818772144243653417893363712', '18629727704371224056172678009507095052288', '473894363067201381276759797535013797888', '-4027045390616824951474610171736631713792', '1126942391477088995275292922345864372224', '-149165815696451286123895839534499799040', '5081722926763186276571639527402512384', '2329094108756514078157746782850362496', '-648558447335335355143397251893396480', '105761582267631669689043272945822208', '-13159039168640423067045203026704384', '1350812717049430281699303368079744', '-118548728607377330431192873028736', '9069130465205574474288722021856', '-611762175404091855984367128240', '36635859897236249346422170065', '-1954985113773127204562029392', '93086400916340309657901240', '-3952592389221830180154000', '149315672301218658944964', '-4997647461251475073008', '147319955090859316824', '-3793940909433198544', '84471782092152534', '-1604517878071152', '25564923121800', '-334292481072', '3484058148', '-27761232', '158472', '-576', '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': ['-765853696', '927498240', '-344199168', '57584640', '-5927616', '503568', '-27264', '1368', '-36', '1'], 'ConjugacyClass': 3}, {'RootOf': ['1034806667992880335814656', '354308407593237171142656', '-42741218148843572428800', '-26909477632574054465536', '-110548471020247842816', '951316353893664817152', '48285979173257347072', '-20864071171967090688', '-1632946283706249216', '320364909347078144', '31096746590306304', '-3704501234761728', '-400387406274560', '34056941813760', '3688984584192', '-258878427136', '-24410915712', '1639544832', '109872640', '-8205312', '-278400', '28160', '96', '-48', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['9001203725560830754816', '-9468128735396351705088', '4387364041088670105600', '-1205621525489903468544', '224222350144412123136', '-30609402508992282624', '3237651523914436608', '-274590564850704384', '19073108209637376', '-1099947392253952', '53071148093184', '-2149819573248', '73122998784', '-2075755392', '48765168', '-922656', '13752', '-144', '1'], 'ConjugacyClass': 12}, {'RootOf': ['1863999181757102033089358169667136217058936095340940723786231848299926306947072', '-7909453530105352491442583326505517055218440862031879873009412755812974780743680', '17037763043553521382638738634214682997220812343991728263919158147824410297368576', '-24542460179439527786898728072218022246085513800973251654104742735641415906230272', '25650094963240195206571359932486628821115538152260820843538847167817575066238976', '-19939946883298027912034005640429375382641914152148947605382763513071060224311296', '11626617288996800908496986054592069059721354819285451258545649805880577056833536', '-5084704738678321925869687473757333235712173032149102685389591684372397415202816', '1646335224904265400136164566389080344674546244687696546005651735122024377352192', '-377504498049881744047518630306770431192991752005789866391546605072420182163456', '52528114014169767086108645985229679592696679961403001476895799826336530300928', '-740888998502426371554782648128165076372602326146217024581206150170751795200', '-1514532803864206802146416346914092882022688684315333811224787298456478679040', '341342163774840293727786097438364139089269225771905552469823299210803412992', '-24761893971533090349383275494700950326930726211558413611092335688048181248', '-3870187491374703467534521148348131924918558296756812689108023706619215872', '1114981007808437615114041623291112600999454033514481221171530645247098880', '-76160357729411553507301900667867440226743886205302769686655048597110784', '-10727701451879152304835444765734044502895814387150342256726997657976832', '2487953679708939613767126094889617128878229015009443159680188401319936', '-91479020707403040381182919544105646211590454695683967908710457540608', '-27150119010077867914181829396619174719727829910857064437258253238272', '3604972915572974880628900861101281476893094145103800710087946797056', '49232948125422048070789667120988850460057701643550640052002357248', '-45940153211815289447203013505217550812365226090612945136646094848', '2633973565240491213944794467168199355907676029417719788751290368', '304428570321009306703474796028417776567719595844513288752726016', '-43600015903830941361716135758990434594554030795077947307851776', '-353323269862055293275014934438654072698309981850219099193344', '391111794285057109099503883998347413645715201520839908392960', '-15983900086850082767970925972649804368060013844302867202048', '-2247286848884709936994175435855927724061248758672844128256', '208931392043105652095677813767738118827516089545909075968', '6902189593560352487333015189420198190341863593027305472', '-1585492246252129753927813769613037485134358156341673984', '13863751856798694367069280921587147414802590718754816', '8539243241199075877936618515027809743267603758972928', '-339166422966443117356264642796988334869940317192192', '-33298594810320231619570081101605965416364637159424', '2545006654551897278226698566791625116399546925056', '83642522826722155448504574880949248399478095872', 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'CycleType': [2, 2, 4]}, {'Data': 0, 'Classes': 18, 'Algorithm': 'CYC', 'CycleType': [2, 6]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['399319288891442200576', '-408478169900550979584', '194679598432905068544', '-58052198747615526912', '12274918272465371136', '-1974090597478170624', '252156592960438272', '-26299188691992576', '2279951635267584', '-166106763943936', '10227384652032', '-532705360896', '23385096960', '-857311488', '25819488', '-621120', '11376', '-144', '1'], 'ConjugacyClass': 11}, {'RootOf': ['69807171317148319455687838007296', '-325775642079616200288078202404864', '717624193229339965513493139947520', '-994288240953653041068184493359104', '974122531845268138704087262691328', '-719071651424889341944063831572480', '415902287157976956624566734553088', '-193372769902058863855712933511168', '73503489779087558339104352501760', '-23079420906226995241009606033408', '6014124175905023233461911027712', '-1298831184980035105058054995968', 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