Artin representation data - 12.49204012094098099.18t218.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': [7, 211], 'Baselabel': '12.49204012094098099.18t218.a', 'CharacterField': 1, 'Conductor': 49204012094098099, 'Container': '18t218', 'Dets': ['1.211.2t1.a.a'], 'Dim': 12, 'GalConjSigns': [1], 'Galn': 9, 'GaloisConjugates': [{'Sign': 1, 'Character': [[12], [0], [2], [0], [3], [-3], [0], [0], [0], [-1], [0], [0], [0], [0]], 'GalOrbIndex': 1, 'HardFactors': [13, 15, 13, 16], 'LocalFactors': [[[1], [-12], [66], [-220], [495], [-792], [924], [-792], [495], [-220], [66], [-12], [1]], [[1], [0], [-6], [0], [15], [0], [-20], [0], [15], [0], [-6], [0], [1]], [[1], [-2], [-4], [10], [5], [-20], [0], [20], [-5], [-10], [4], [2], [-1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [-3], [3], [-4], [9], [-9], [6], [-9], [9], [-4], [3], [-3], [1]], [[1], [3], [6], [5], [0], [-9], [-12], [-9], [0], [5], [6], [3], [1]], [[1], [0], [0], [-4], [0], [0], [6], [0], [0], [-4], [0], [0], [1]], [[1], [0], [0], [0], [-3], [0], [0], [0], [3], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [-2], [0], [0], [0], [0], [0], [1]], [[1], [1], [2], [1], [2], [1], [0], [-1], [-2], [-1], [-2], [-1], [-1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [-1], [0], [0], [0], [0], [0], [-1], [0], [0], [1]], [[1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [-1]], [[1], [0], [0], [0], [0], [0], [-1]], [[1], [-1], [-3], [3], [3], [-3], [-1], [1]]]}], 'GaloisConjugatesSigns': [1], 'GaloisLabel': '9T30', 'Galt': 30, 'HardPrimes': [2, 7, 17, 211], 'Hide': 0, 'Indicator': 1, 'Is_Even': False, 'NFGal': [-4, 14, -15, 14, -21, 8, -9, 7, -4, 1], 'NumBadPrimes': 2, 'Proj_GAP': [648, 703], 'Proj_Polynomial': [-4, 14, -15, 14, -21, 8, -9, 7, -4, 1], 'Proj_nTj': [9, 30]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.211.2t1.a', 'Character': [[1], [1], [-1], [1], [1], [1], [1], [-1], [1], [-1], [1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '2.211.3t2.a', 'Character': [[2], [2], [0], [2], [2], [2], [-1], [0], [2], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.2181529.6t8.a', 'Character': [[3], [-1], [-1], [3], [3], [3], [0], [1], [-1], [-1], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '3.10339.4t5.a', 'Character': [[3], [-1], [1], [3], [3], [3], [0], [-1], [-1], [1], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.460302619.18t217.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [-2], [-1], [0], [0], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.460302619.9t30.a', 'Character': [[6], [2], [0], [3], [-3], [0], [0], [2], [-1], [0], [0], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '6.22554828331.36t1121.a', 'Character': [[6, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, -1], [0, -2, 0, 1]], 'CharacterField': 12}, {'GalConj': 2, 'Baselabel': '6.22554828331.36t1121.a', 'Character': [[6, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 1], [0, 2, 0, -1]], 'CharacterField': 12}, {'GalConj': 1, 'Baselabel': '8.4759068777841.12t177.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [-1], [2], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.4759068777841.12t177.b', 'Character': [[8], [0], [0], [-4], [-1], [2], [-1], [0], [0], [0], [2], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '8.4759068777841.12t178.a', 'Character': [[8], [0], [0], [-4], [-1], [2], [2], [0], [0], [0], [-1], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.2190611822441341465579.36t1123.a', 'Character': [[12], [0], [-2], [0], [3], [-3], [0], [0], [0], [1], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '12.49204012094098099.18t218.a', 'Character': [[12], [0], [2], [0], [3], [-3], [0], [0], [0], [-1], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 3, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9]}, {'Size': '27', 'Order': 2, 'Representative': [6, 2, 5, 4, 3, 1, 7, 8, 9]}, {'Size': '54', 'Order': 2, 'Representative': [2, 1, 5, 6, 3, 4, 9, 8, 7]}, {'Size': '6', 'Order': 3, 'Representative': [1, 2, 8, 4, 3, 6, 7, 5, 9]}, {'Size': '8', 'Order': 3, 'Representative': [6, 4, 5, 7, 8, 9, 2, 3, 1]}, {'Size': '12', 'Order': 3, 'Representative': [9, 2, 8, 4, 3, 1, 7, 5, 6]}, {'Size': '72', 'Order': 3, 'Representative': [3, 1, 2, 6, 4, 5, 9, 7, 8]}, {'Size': '54', 'Order': 4, 'Representative': [3, 2, 6, 4, 1, 5, 7, 9, 8]}, {'Size': '54', 'Order': 6, 'Representative': [6, 4, 5, 2, 8, 1, 7, 3, 9]}, {'Size': '108', 'Order': 6, 'Representative': [3, 4, 9, 2, 1, 5, 7, 6, 8]}, {'Size': '72', 'Order': 9, 'Representative': [3, 1, 4, 6, 7, 5, 9, 2, 8]}, {'Size': '72', 'Order': 9, 'Representative': [3, 1, 7, 6, 2, 5, 9, 4, 8]}, {'Size': '54', 'Order': 12, 'Representative': [2, 6, 8, 1, 3, 4, 9, 5, 7]}, {'Size': '54', 'Order': 12, 'Representative': [2, 6, 5, 1, 8, 4, 9, 3, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 4, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 3]}, {'Data': 0, 'Classes': 2, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 2, 2]}, {'Data': 0, 'Classes': 8, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 2, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 3, 3]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [1, 1, 2, 2, 3]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 2, 2, 2, 2]}, {'Data': 0, 'Classes': 10, 'Algorithm': 'CYC', 'CycleType': [1, 2, 6]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['8637391094533388137082047976833582850423538768495835648', '-15527576122381799444246621549850118143070332649036843936', '16765921167116632332039022024700785126742439174992872928', '-10998301164263764194638288044611665942067113701192689400', '4729025334650222663335387951684192455681607584627333008', '-1414558999267636682627732221878327786967173306498171826', '306695700751914437777660490783982369047879872612881781', '-46553421822792390876438467232300722933050933545447112', '4506057976405675350009350778195286200287527583351260', '-154281329510850514836077328194547843359371977072654', '-15893450324548410361321147897400038112286385671650', '-1160879373937861846916909279646929466126564142602', '1460848322379028181822633439116424937671093862148', '-286476000076353758666570237352078250892887226949', '32638545970773309661207918680280786648751751168', '42620140404102113721549874503731208245564929', '-332809160341503120791984357722978204365978263', '60854323762498849271406175386754260524838483', '-522540477661497432795286092310596104161013', '-647083813821120992642855958624542023100507', '100152297950956991713604970028705018769951', '-6185862143876263094985117940227887641704', '-256402487893247761932298508383031935548', '97540041902532168276277935812607839888', '-11658865483971881556359412518549422533', '790545568330905520225068354620294988', '-28311250817520001543525272014402124', '945301232616326691856178424958692', '-87410375867945018255568100714452', '11448826146394288793809045585758', '-227420427802446773271178374930', '-140944054239546797493068885447', '28441991400652381731783862918', '-3429739530696793195850204650', '309992754774551675469669171', '-25407066429552982563609009', '1935925763583169156987825', '-144335564236120181646840', '10426888167526573918427', '-722477180468699128695', '46862235116343188308', '-2808654734183133556', '160379594256491779', '-8617501352306225', '446249891732152', '-21874794746695', '1026895724653', '-44243648911', '1789643125', '-64753497', '2314601', '-65431', '2093', '-36', '1'], 'ConjugacyClass': 13}, {'RootOf': ['21070259079328454205551550634114987999428869827334437616', '-28658312020820267874553614955986179512987280153744369880', '24008286774115769759056042371306382079842105353675945884', '-13006064729016144873163549286807459747544952570601383802', '4948916347987144111941894646274612541453594425489165551', '-1278776546527287651536703539072926170288704659723837875', '222685814008655672512053183738264038676319465123561552', '-21709623659176295258144694675644502239137764263492919', '-429996388444244346358388213749973972057268132735680', '449491515458305718668002523553856611685640752341284', '-49495427147206233598645454109534051397422500685390', '-3890015585766430840680546164340402184679512292845', '2212366859322326137862157574987798320626320088650', '-281610752218061250104893997570999815272382167719', '16886196247583777081527126787961690277788101340', '3570903065979246222032107364414584455572242525', '-632975429506200858847570400914600738103770241', '71856280587217548774308308533885752816056877', '914808110230133804010662536881588059805173', '-725426086645924933040560505142916203474711', '96386218971890668458669327044548915598836', '-5528335295176781830627626773679622034483', '-84828268629469935216754044180836376842', '60494559380672115793740542435578988906', '-7642658048464699462923700683927880505', '475970629896109644115952537137026005', '-6738998137564696090056306180065853', '-748775512421553252824605223474245', '112782744851992673446334063286344', '-11171468122178677176886873156994', '1446291287078593259296744861879', '-228016680199854938099593810847', '29966117432932551907055450265', '-3233658951664079796208307664', '278415179221419147259688656', '-22459609411406717453926798', '1704022986158890891516806', '-125165519692912368854911', '8968620738718193446684', '-616532967435808808593', '40196575313268418426', '-2435640989756889824', '142050105677723755', '-7839159798063931', '415258816319736', '-20771383629159', '987940421252', '-43120736029', '1757039827', '-64274949', '2314601', '-65431', '2093', '-36', '1'], 'ConjugacyClass': 14}], 'Algorithm': 'RES', 'CycleType': [2, 3, 4]}, {'Data': {'Powers': [1, 2], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['10000', '-4000', '600', '-40', '1'], 'ConjugacyClass': 5}, {'RootOf': ['25716965959753848383721558258718417870511', '40630486344322398208647427360094084793088', '26110230771520430117180137713659864994885', '9217118018079674555577912040557839819819', '2151222861594285053809024214277675934143', '392050488658385775467756820117790864316', '59987175004720479350211289396987762755', '7532671919732286048315345271168945881', '768395989358924561406882728055186388', '60783538403190669587116142393252307', '2773317717997268703705137875234870', '-116027948982954769781470682478605', '-44817143187786129029351820646415', '-6122789931242200634250294457951', '-571475520404866993837231998701', '-38702626352994984072103797441', '-1516106964229786433293009831', '31902958654737830451138525', '12627063376807202836047580', '1335459917958015347066464', '95681198637332209432213', '4811844743507521906848', '142652082291445555477', '-2289717147181528986', '-631814529689557578', '-48927378681465083', '-2483466918430930', '-85505708727422', '-1362367589302', '62703160796', '6558144706', '339060880', '12434211', '347514', '7350', '108', '1'], 'ConjugacyClass': 7}], 'Algorithm': 'RES', 'CycleType': [3, 3, 3]}, {'Data': [2, 3, 4, 5, 6, 7, 8, 9, 1], 'Classes': [{'RootOf': ['519203902', '1'], 'ConjugacyClass': 12}, {'RootOf': ['-519203902', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'ALT', 'CycleType': [9]}], 'Frobs': [13, 10, 7, 14, 7, 11, 14, 11, 10, 8, 13, 12, 10, 7, 12, 9, 9, 8, 13, 12, 6, 12, 9, 8, 8, 7, 11, 12, 9, 12, 14, 13, 11, 12, 14, 7, 14, 2, 14, 12, 11, 10, 13, 12, 8, 12, 2, 3, 2, 10, 3, 3, 7, 10, 11, 9, 12, 10, 11, 11, 10, 9, 12, 5, 13, 8, 11, 11, 12, 10, 8, 2, 10, 10, 10, 12, 11, 10, 10, 10, 7, 10, 7, 9, 8, 11, 10, 10, 13, 3, 9, 10, 9, 12, 8, 11, 7, 11, 11, 7, 5, 14, 14, 3, 14, 10, 14, 7, 8, 12, 9, 10, 8, 10, 2, 14, 14, 11, 6, 8, 8, 13, 12, 10, 11, 3, 7, 14, 13, 12, 10, 10, 8, 3, 10, 11, 3, 4, 10, 2, 12, 11, 10, 11, 7, 10, 9, 11, 14, 11, 10, 7, 10, 9, 10, 14, 10, 3, 5, 8, 7, 7, 7, 10, 8, 2, 3, 14], 'G-Gens': [[3, 1, 2, 6, 4, 5, 9, 7, 8], [2, 6, 3, 1, 5, 4, 9, 8, 7], [6, 2, 3, 4, 5, 9, 7, 8, 1], [1, 4, 3, 7, 5, 6, 2, 8, 9]], 'G-Name': 'H648', 'Polynomial': [-4, 14, -15, 14, -21, 8, -9, 7, -4, 1], 'QpRts': [['1303242481236080232230758075670516821467070552097372403630547911089421881822899846894513996087272733194276321844758', '9767315860160392579452322082213961870730675927829728435605772328342384121973123062875198123182404229064725785915031', '-13687550878217802910192508588522929580313093270646699156910658186042924674791204298890039478026086498322452297417594'], ['3690436953399691871930485121095148428095772153128013084804294488807541163677096453279151402636880468861470057863466', '-174552484783651860570199234487776646390479975203936680262684331800560076128957757179310112459800152172149973064162', '6304186582901925317771238445599366500240521112687595168021020374878298018102935065855272441951236323522566448496536'], ['-12905335005951290542795510996830363897523846855363215411998408033003353092157580657377531047670407175619259863386901', '0', '0'], ['-7810430519069604622664838826851166559901161863178126792884323022194322408739768099680890472358354834346709818337332', '-13831364639187372435579564848531260741497298730688284974473003453131279914481926419683164541705824393514488262987607', '14466086466524146345380093509135264912009471905081023733321223438555386377215563468310392502772084796539988906341802'], ['6955280934149261425358101145171685713314896139922990905768043141829951330140051312460888478694737923820276690461689', '0', '0'], ['-8299837875753225074880325925803929484841423526022809633593624288710537666082531099182534423628795018765934552005887', '-14097445408824750042398355482442323695227146983006574541932694937351199731808670429720943207401625643411308069945636', '4291464586001508207307200447114687669105513127697714525521211959499834721917637717314901407787775113342725594688219'], ['-10025441905738712904559144713356002584869378281316227709591169499703787336317779257181896490172829522020615859921880', '14005917123971024296149764083019037387887778705892221654735687784931839990610884176862474654165624545686638236051769', '12804827926522315133959364094256637893283309591477448045791088580423287681532055100184637989411228780784559375153391'], ['-4989340437420410767620704261341300579236563422826280967499381159319021924384982853393118837361641152720684631891959', '0', '0'], ['-1493675600800176414109515666745857162038667505687782825769311932652864024807959280168885540361413323249933074617679', '4330129548664357462946033400228361824496471055176846106326922609008815609835547366845745084219221414346582284030605', '9396086292216294702885308141408241911207580142948984631389446226543089952873566581575138070238311384979726702729375']], 'QpRts-minpoly': [68, 2, 0, 1], 'QpRts-p': 73, 'QpRts-prec': 62, 'Size': 648, 'TransitiveDegree': 9}