Artin representation data - 9.31139331552243712.18t274.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, 7, 53], 'Baselabel': '9.31139331552243712.18t274.a', 'CharacterField': 1, 'Conductor': 31139331552243712, 'Container': '18t274', 'Dets': ['1.7.2t1.a.a'], 'Dim': 9, 'GalConjSigns': [1], 'Galn': 8, 'GaloisConjugates': [{'Sign': 1, 'Character': [[9], [-3], [1], [3], [-3], [1], [-1], [0], [0], [-3], [1], [1], [1], [-1], [-1], [0], [0], [0], [1], [0]], 'GalOrbIndex': 1, 'HardFactors': [21, 15, 22, 14, 23, 3], 'LocalFactors': [[[1], [-9], [36], [-84], [126], [-126], [84], [-36], [9], [-1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [-3], [0], [8], [-6], [-6], [8], [0], [-3], [1]], [[1], [3], [0], [-8], [-6], [6], [8], [0], [-3], [-1]], [[1], [-1], [-4], [4], [6], [-6], [-4], [4], [1], [-1]], [[1], [1], [-4], [-4], [6], [6], [-4], [-4], [1], [1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [0], [0], [-3], [0], [0], [3], [0], [0], [-1]], [[1], [3], [6], [10], [12], [12], [10], [6], [3], [1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [-1], [2], [-2], [0], [0], [-2], [2], [-1], [1]], [[1], [-1], [0], [0], [-2], [2], [0], [0], [1], [-1]], [[1], [1], [2], [2], [0], [0], [-2], [-2], [-1], [-1]], [[1], [1], [0], [0], [-2], [-2], [0], [0], [1], [1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [0], [0], [-1], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [1], [0], [0], [-1], [0], [0], [-1]], [[1], [-1], [0], [0], [0], [0], [0], [0], [-1], [1]], [[1], [0], [0], [1], [0], [0], [1], [0], [0], [1]], [[1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [-1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '8T47', 'Galt': 47, 'HardPrimes': [2, 3, 7, 37, 53, 8013189871], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [7, 0, -18, -18, 13, 8, 0, -4, 1], 'NumBadPrimes': 3, 'Proj_GAP': [0, 0], 'Proj_Polynomial': [7, 0, -18, -18, 13, 8, 0, -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': '1.7.2t1.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': '1.371.2t1.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': '1.53.2t1.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': '2.371.4t3.a', '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': '4.29179892.12t34.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': '4.15415792.12t34.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': '4.10388.6t13.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': '4.314608.6t13.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': '6.91508141312.12t201.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': '6.640556989184.12t202.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': '6.266787584.8t47.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': '6.1867513088.12t200.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': '9.209161465856.16t1294.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': '9.71742382788608.18t272.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': '9.10680790722419593216.18t273.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': '9.31139331552243712.18t274.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': '12.1196248560910994440192.36t1763.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': '12.24413235936959070208.24t2821.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': '18.2234009844002447320153793232896.36t1758.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, 4, 8, 2, 5, 6, 7, 3]}, {'Size': '9', 'Order': 2, 'Representative': [6, 4, 8, 2, 7, 1, 5, 3]}, {'Size': '12', 'Order': 2, 'Representative': [1, 3, 2, 4, 5, 6, 7, 8]}, {'Size': '24', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4, 8, 7]}, {'Size': '36', 'Order': 2, 'Representative': [5, 3, 2, 4, 1, 6, 7, 8]}, {'Size': '36', 'Order': 2, 'Representative': [6, 3, 2, 4, 7, 1, 5, 8]}, {'Size': '16', 'Order': 3, 'Representative': [1, 2, 3, 4, 7, 5, 6, 8]}, {'Size': '64', 'Order': 3, 'Representative': [1, 4, 3, 8, 6, 7, 5, 2]}, {'Size': '12', 'Order': 4, 'Representative': [1, 3, 4, 8, 5, 6, 7, 2]}, {'Size': '36', 'Order': 4, 'Representative': [5, 3, 4, 8, 6, 7, 1, 2]}, {'Size': '36', 'Order': 4, 'Representative': [5, 4, 8, 2, 6, 7, 1, 3]}, {'Size': '72', 'Order': 4, 'Representative': [2, 6, 7, 1, 3, 4, 8, 5]}, {'Size': '72', 'Order': 4, 'Representative': [5, 3, 2, 4, 6, 7, 1, 8]}, {'Size': '144', 'Order': 4, 'Representative': [2, 5, 1, 6, 3, 4, 8, 7]}, {'Size': '48', 'Order': 6, 'Representative': [1, 4, 8, 2, 6, 7, 5, 3]}, {'Size': '96', 'Order': 6, 'Representative': [1, 3, 2, 4, 7, 5, 6, 8]}, {'Size': '192', 'Order': 6, 'Representative': [3, 5, 1, 6, 4, 8, 2, 7]}, {'Size': '144', 'Order': 8, 'Representative': [2, 5, 6, 7, 3, 4, 8, 1]}, {'Size': '96', 'Order': 12, 'Representative': [1, 3, 4, 8, 7, 5, 6, 2]}], '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': ['28408832', '-10343936', '1537536', '-119200', '5072', '-112', '1'], 'ConjugacyClass': 2}, {'RootOf': ['431208100747583505630713505482987060330496', '-1382568650284079499792862122481928292532224', '2151102796841533983562256438206534074236928', '-2156777963657810563422208865617534110400512', '1562828227299110753904615523908763930066944', '-870577250625386337567610497106361257558016', '387358217972493279644663359473108366917632', '-141257473458767327512518868203337100034048', '42997626251790211132502163918912179142656', '-11072550868970861914620962725759339724800', '2436682166340556890722502082456501354496', '-461767480971896426706697012378356154368', '75800194466827561935002128247263592448', '-10827075604389254030015337323021991936', '1350459201874864997077294026915315712', '-147495651663364157525258887174815744', '14136056708918634951587993229459456', '-1190734985830521862024490228121600', '88248174433630415025241418891264', '-5757688662920857490143905316864', '330722814566014275949428604928', '-16715969579771779780912873472', '742605875089857972339736576', '-28943201460480863500500992', '987060270445535659442176', '-29347921128007081984000', '757121807664505511936', '-16841951223808638976', '320425067269874688', '-5158894376366080', '69307460349952', '-762314482688', '6683994192', '-44912768', '217112', '-672', '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': ['-373850112', '-203358208', '-19308544', '5134336', '788992', '-30720', '-9056', '-208', '24', '1'], 'ConjugacyClass': 3}, {'RootOf': ['3858155122093334391697702912', '4044711747119908535547199488', '1669437384010000919083089920', '307958518619106433885536256', '9627442375591896812617728', '-5455204326143628148736000', '-672605401458690719481856', '30818941157647526658048', '9117648516159241584640', '1123050512652435456', '-72691076587487821824', '-821227085750337536', '413304032838332416', '2902492392726528', '-1737853035206656', '11162633568256', '5017687252992', '-125369340416', '-7789251968', '411496448', '-114880', '-458688', '14384', '-192', '1'], 'ConjugacyClass': 5}], 'Algorithm': 'RES', 'CycleType': [2, 2, 2, 2]}, {'Data': {'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-244719960719410331648', '-188331194920210530304', '-63940316890295959552', '-10950897297713528832', '-612136750826913792', '109579932471918592', '22132624763912192', '954873313492992', '-111510198419456', '-13447914749952', '-171886657536', '43943911424', '2247753728', '-22069760', '-4467200', '-88096', '2032', '96', '1'], 'ConjugacyClass': 12}, {'RootOf': ['474942805775867846838634090229430953184820565766098092810140631647540638026402087647508414775427072', '-237257430928831179686031224646475749321906203096239859030288367829531277318023450154439752514797568', '13595416177098180708183215381050672813719678888491085220313867914533871624932939330588088763154432', '13184195063236836506003726692169921364158247064175792975212250011806475682983046146008861464592384', '-2467935278899748169721498147904514597264212644332531669733223716799055252841746312530595781017600', '-222746423066951080212585375894932877368161532820901316988222141717775983309212080786706425446400', '98290622085842270077856830720632660715432939122924900928381228933385733736377385957290198171648', '-2527571314746235614555676035230113713259992761379389219064483930155971864903904372436785692672', '-2012918803724546654875329558608071123570059971630391362722066392881743680541265019759671377920', '188920197197482202020017501225848220652925812877651052211358509388061646657369426850517876736', '22652394860350710048956256169293115433215130151760822765329576136274349811700651349327740928', '-4241047715196277760018194246789142762089416555695059327679455550928764119868293029679857664', '-77012545330576466178382463264737028241497005848695349205242593802932638092074873442533376', '56773585242584670140552098800379935736375117891248709756945225643020181813667826283577344', '-1932113159460763156696405371745819827156712330882574574263785337394800102594898154225664', '-494534418202744178251380523040670959241582492944367586368087394268525421392710535741440', '40384350214027889737873528380907842355776613678116080354028606974019017057121448493056', '2560024790742626433691634276670316065147999307722270600582178177097164104564020871168', '-428487072595305989361402539118331627582747212139711005849491517881994292041032400896', '-1930050546445828924770827619154716351520464381857730065157916801819968946225283072', '3008174034175325797650341021550625365406810687349284815990179454423173155914776576', '-99239681690153078708343560382686289475737613643543901083269877587113289730490368', '-14205204742598392782942729709902387437345271870492521114926951792299819933892608', '1042130573942731373356339785338177240743125535001518029334037958956209204625408', '37403694370141393632923225873802453867043830900247989439602363662679630938112', '-6228365759412016792420472743932940429508474209111470445163746382543455256576', '34527911532378221265848016138999303619331350731183971564269016984905056256', '24948151630390721713048083469180789130837190488860186136659146477907476480', '-909836049714548958421227829841469973689998448351876369947251397925797888', '-63687934031874280264089286249196932239937678548284245124112428010831872', '5029809230519545476621776541789529267507631019402401943175581264773120', '56826268538892676866296620041961220343819091984312094050189163102208', '-16825753824209495599666104555489548307969000264442528364636934242304', '320366698558366794576746654862704805605573313613280451426259042304', '35640630001458457632301372856452891218295010523919500784477143040', '-1792854331936800759541634684685003840753919147230544997356929024', '-33881692211059247044721733330209634608934699570603260976824320', '4861963488035348124933485076984373150330148939125771638669312', '-61877038335356360995909867804243117710484441808400627531776', '-7739158000897277182405316905353011338085107663780930650112', '318688819790935963976442138321260060949488676080573218816', '4729127665401201224189110454246348164090065981680910336', '-633349953841958828101712832912843193853538623717113856', '9520842336506877032993109543310869799089504522338304', '639937015300295498656575634352043653006583746527232', '-29137579359191714152666933746062634896000221708288', 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{'Powers': [1, 3], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['1806258160009216', '-551486685708288', '-393106008571904', '161659750449152', '28346012401664', '-18063357378560', '-355498721280', '1008177512448', '-44875120640', '-30754275328', '2000912384', '563773440', '-25545728', '-7081984', '-30464', '48576', '3424', '96', '1'], 'ConjugacyClass': 11}, {'RootOf': ['26093237930430693464643995924519332002477899776', '-31573511349234507816585680181047731836185214976', '17596919293208224427557093498759568042473029632', '-5912630449657487502263145054825445291431297024', '1305031659285085323863193002521117831548895232', '-188719870682521851336492273614534124930859008', '15115621926076783734765717658429231189721088', '205608634970694669496662852503147831623680', '-234997810514533021122570442281968753180672', '31966781708997689781490883204140782059520', '-1930638556014693791147750759233157595136', '-38214681825937074068873078387804995584', '18700688098956439717163413581496057856', 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