Artin representation data - 5.7591385845750000.20t88.b

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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, 5, 7, 97], 'Baselabel': '5.7591385845750000.20t88.b', 'CharacterField': 4, 'Conductor': 7591385845750000, 'Container': '20t88', 'Dets': ['1.35.4t1.a.b', '1.35.4t1.a.a'], 'Dim': 5, 'GalConjSigns': [0, 0], 'Galn': 10, 'GaloisConjugates': [{'Sign': 0, 'Character': [[5], [-3], [1], [-1], [-1], [1], [0, 1], [0, -1], [0], [0, -1], [0, 1]], 'GalOrbIndex': 1, 'HardFactors': [12, 11, 13, 14, 15, 3, 6, 4], 'LocalFactors': [[[1], [-5], [10], [-10], [5], [-1]], [[1], [3], [2], [-2], [-3], [-1]], [[1], [-1], [-2], [2], [1], [-1]], [[1], [1], [-2], [-2], [1], [1]], [[1], [1], [2], [2], [1], [1]], [[1], [-1], [0], [0], [-1], [1]], [[1], [0, -1], [0], [0], [-1], [0, 1]], [[1], [0, 1], [0], [0], [-1], [0, -1]], [[1], [0], [0], [0], [0], [-1]], [[1], [0, 1], [0], [0], [1], [0, 1]], [[1], [0, -1], [0], [0], [1], [0, -1]], [[1], [0, 1]], [[1]], [[1], [0], [1]], [[1], [0, -1]]]}, {'Sign': 0, 'Character': [[5], [-3], [1], [-1], [-1], [1], [0, -1], [0, 1], [0], [0, 1], [0, -1]], 'GalOrbIndex': 2, 'HardFactors': [12, 11, 13, 14, 15, 3, 6, 4], 'LocalFactors': [[[1], [-5], [10], [-10], [5], [-1]], [[1], [3], [2], [-2], [-3], [-1]], [[1], [-1], [-2], [2], [1], [-1]], [[1], [1], [-2], [-2], [1], [1]], [[1], [1], [2], [2], [1], [1]], [[1], [-1], [0], [0], [-1], [1]], [[1], [0, 1], [0], [0], [-1], [0, -1]], [[1], [0, -1], [0], [0], [-1], [0, 1]], [[1], [0], [0], [0], [0], [-1]], [[1], [0, -1], [0], [0], [1], [0, -1]], [[1], [0, 1], [0], [0], [1], [0, 1]], [[1], [0, -1]], [[1]], [[1], [0], [1]], [[1], [0, 1]]]}], 'GaloisConjugatesSigns': [0, 0], 'GaloisLabel': '10T24', 'Galt': 24, 'HardPrimes': [2, 3, 5, 7, 97, 331, 5419, 979291], 'Hide': 0, 'Indicator': 0, 'Is_Even': True, 'NFGal': [-672615, 1601880, 723545, -225290, -104680, 9684, 5570, -130, -125, 0, 1], 'NumBadPrimes': 4, 'Proj_GAP': [320, 1635], 'Proj_Polynomial': [-672615, 1601880, 723545, -225290, -104680, 9684, 5570, -130, -125, 0, 1], 'Proj_nTj': [10, 24]}
• 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]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.5.2t1.a', 'Character': [[1], [1], [1], [1], [1], [1], [-1], [-1], [1], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '1.35.4t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [0, 1], [0, -1], [1, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '1.35.4t1.a', 'Character': [[1, 0], [1, 0], [1, 0], [-1, 0], [-1, 0], [-1, 0], [0, -1], [0, 1], [1, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '4.2450000.5t3.c', 'Character': [[4], [4], [4], [0], [0], [0], [0], [0], [-1], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.216896738450000.10t24.b', 'Character': [[5], [-3], [1], [1], [1], [-1], [1], [1], [0], [-1], [-1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.1084483692250000.10t25.b', 'Character': [[5], [-3], [1], [1], [1], [-1], [-1], [-1], [0], [1], [1]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '5.7591385845750000.20t88.b', 'Character': [[5, 0], [-3, 0], [1, 0], [-1, 0], [-1, 0], [1, 0], [0, 1], [0, -1], [0, 0], [0, -1], [0, 1]], 'CharacterField': 4}, {'GalConj': 2, 'Baselabel': '5.7591385845750000.20t88.b', 'Character': [[5, 0], [-3, 0], [1, 0], [-1, 0], [-1, 0], [1, 0], [0, -1], [0, 1], [0, 0], [0, 1], [0, -1]], 'CharacterField': 4}, {'GalConj': 1, 'Baselabel': '10.2656985046012500000000.16t711.b', 'Character': [[10], [2], [-2], [2], [-2], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}, {'GalConj': 1, 'Baselabel': '10.650961336273062500000000.20t77.b', 'Character': [[10], [2], [-2], [-2], [2], [0], [0], [0], [0], [0], [0]], 'CharacterField': 1}], 'ComplexConjugation': 1, 'ConjClasses': [{'Size': '1', 'Order': 1, 'Representative': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}, {'Size': '5', 'Order': 2, 'Representative': [10, 7, 9, 6, 5, 4, 2, 8, 3, 1]}, {'Size': '10', 'Order': 2, 'Representative': [1, 7, 9, 4, 5, 6, 2, 8, 3, 10]}, {'Size': '20', 'Order': 2, 'Representative': [8, 4, 3, 2, 10, 7, 6, 1, 9, 5]}, {'Size': '20', 'Order': 4, 'Representative': [6, 3, 7, 1, 5, 10, 9, 8, 2, 4]}, {'Size': '40', 'Order': 4, 'Representative': [4, 3, 7, 1, 8, 10, 9, 5, 2, 6]}, {'Size': '40', 'Order': 4, 'Representative': [2, 8, 3, 1, 6, 10, 5, 4, 9, 7]}, {'Size': '40', 'Order': 4, 'Representative': [4, 1, 3, 8, 7, 5, 10, 2, 9, 6]}, {'Size': '64', 'Order': 5, 'Representative': [5, 10, 7, 3, 4, 9, 1, 6, 2, 8]}, {'Size': '40', 'Order': 8, 'Representative': [9, 10, 4, 7, 8, 2, 1, 5, 6, 3]}, {'Size': '40', 'Order': 8, 'Representative': [2, 4, 1, 9, 8, 3, 6, 5, 10, 7]}], 'FrobResolvents': [{'Data': 0, 'Classes': 1, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]}, {'Data': 0, 'Classes': 3, 'Algorithm': 'CYC', 'CycleType': [1, 1, 1, 1, 1, 1, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-111645012696', '-4196378920', '-45883740', '-137800', '210', '1'], 'ConjugacyClass': 2}, {'RootOf': ['368296594281735517795473262396723039206400000', '-9674221927113441844493729094606761523200000', '-1555528231452107895118192937502287877120000', '-29406145680356346803504678816799156736000', '218132169032439239378620864651089459200', '8651259908517413418495935214745806336', '22355422392529846022154981265305600', '-679687024941716077966394142979840', '-2909505287366518631630152505600', '27224722838651872662269182720', '116779462819409946834872960', '-683323641812360359473920', '-2218396509993246830720', '11151624403559163200', '19869200065418800', '-109761915893952', '-55226533960', '561885200', '-219800', '-1080', '1'], 'ConjugacyClass': 4}], 'Algorithm': 'RES', 'CycleType': [1, 1, 2, 2, 2, 2]}, {'Data': {'Powers': [1], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['-4310325996441124245366077520565956760468230144', '-512223314475320460224201243086343667192995840', '-7817503209228528326206135674207680175708160', '377568281831079104652537627684092301158400', '-714834820688539123107592625730957962240', '-51098912138097452422108342881278071808', '318816635128082905886899916123696640', '1883723379591760259381757685551360', '-19852736666327710522210453747200', '-10768083394213232136032434560', '515085097355539241321850304', '-719141933123030958228480', '-6539499239903572887520', '16934179480110152000', '39309249965181120', '-156981562616912', '-67044272880', '670179880', '-297400', '-1080', '1'], 'ConjugacyClass': 5}, {'RootOf': ['1273467873624352195984042904104932519005549650899035736482740868651279302401249456947200000', '-202574144916615503179159771611292204176743633378760756781854279060587602369330859212800000', '-19608489624685806752474048881941725486802821992779491029894099333816082023235148840960000', '174760509838323525806238489723706011418688767969897546195518805788477303052918849536000', '36462596444139197835734328803938990900477122634276306985221299770436820259512202035200', 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'-821671265869419436942345178280088863048502972712375138713600', '-10344622734424535490379915783917334822380547275450998784000', '41946938444851690765903317303436270208939130673055334400', '204222398768957343131251174358697795242725421599047680', '-1240813771956144045700452830637737556856531209216000', '-2286683842891891613448331813222292765944987545600', '23950304583511780869224603337639013756905472000', '4789436644370164161650106790843978605772800', '-312686279251231378355155533895038028544000', '281781550161642436170640511456485939200', '2752412216412092145700920945404083200', '-5019707089875446469827705304608000', '-15548617088182793540599702598400', '45164141817028932684974220288', '46948315004024426009902080', '-246271308729237106360000', '3004770728649984000', '806786162882427040', '-577684076416864', '-1379216965040', '1918489680', '573000', '-2160', '1'], 'ConjugacyClass': 7}, {'RootOf': ['-1014075775901427376816395840167345486374545975038900893150103320584902245803366966886400000', '55723700385985914414723828940195602197191127621350689404572872744012143170315039539200000', '1612114757515061358159560162660514438422267089547279420066284253540780979465255649280000', '-99310949079246227695287073775886621756101803909868973273603520281973254380121489408000', '-1123014517633281565721318942683599146025960391416268522141258028609898535237504204800', '69665991079296544464574813062528837554387537886482604927804356962543556198836207616', '439348984560059385443162369864798797478813689720578456276922889908277030902824960', '-25349955125762606394087478835068499484298807608385657906314869839188161724416000', '-85601954502500411334252071575846554024166974405647730087496837135515045068800', '5565560417943233539142689746911244449080449233063705544414379772408409620480', '5493240808300075387371074784890746395864376913871462152353659048398159872', '-791222532976764396972670599245068912946260850901036959944044495587246080', '862298377795362213148406602495007447045491499813011714226556201205760', '74848720721199676687171393933748725062131640715384964589852626124800', '-220434626192313129662253662725136496915214211579787972468971601920', '-4712838995948285327870025271647069384475071880508282388170702848', '22480636307167483412520441447415309565016154072768524612403200', '191756497679015392636073827293875564621643183859371239014400', '-1349579072949841381266593511430113213548208949102194688000', '-4528442664457590808019685380795409095485326846626201600', '51989943634346770946840275516808150310546771765063680', '30823763718276619988387651503878726868796368384000', '-1312413255614896207713394744963680628941484185600', '1611834370276433738930214856477299989162240000', '21259322819721408162824069129420641735500800', '-59513091160763538618871939915496726720000', '-200568081882698662463630524833857484800', '1003056123032125733365889144180787200', '649333443016781926800409546176000', '-9754110776312786071127943702400', '7542527664713242485889732288', '54160657157718476614122880', '-104104821929000342911200', '-137565499931091058400', '545654791562023040', '-97433580356464', '-1311944477640', '1349127680', '884400', '-2160', '1'], 'ConjugacyClass': 8}], 'Algorithm': 'RES', 'CycleType': [1, 1, 4, 4]}, {'Data': 0, 'Classes': 6, 'Algorithm': 'CYC', 'CycleType': [2, 2, 2, 4]}, {'Data': {'Powers': [1, 5], 'Resolvent': [0, 0, 1]}, 'Classes': [{'RootOf': ['4227611942230875116881353255485932896256', '4009035233499788567049811307640266424320', '1475244501174687045127235397374696488960', '260559996865995197122120732757742387200', '21910354452615978640719623246439055360', '757826209489270189297394562889990144', '11942131642798539553143081019432960', '64893286249152070287050347642880', '-493505040689375432321815859200', '-8231754280815494400755589120', '-24100759215639987408751104', '197409194640943408040960', '1543710168744610970880', '1296343233058272000', '-22730357515192320', '-88665608535616', '-23092827680', '630536960', '1808400', '2160', '1'], 'ConjugacyClass': 10}, {'RootOf': ['1549403979233611067689773436068163480802758656', '16693400192859121667491202998352689457233920', '-2274407717729630089294266152591135468298240', '-23206936290955477370753897436679731609600', '1257740050007089358383926749709749647360', '12169383460313514067626121279177529344', '-311737854067057827696410413113354240', '-2899158398386587834575537377694720', '29695785398080744926657771014400', '285622822647419951946624314880', '-110943749789443853996939904', '-6155775063953920305322240', '-10008808839794203662720', '48704864780531769600', '149318112218419680', '-91206623901216', '-772726094080', '-583696240', '1185600', '2160', '1'], 'ConjugacyClass': 11}], 'Algorithm': 'RES', 'CycleType': [2, 8]}, {'Data': 0, 'Classes': 9, 'Algorithm': 'CYC', 'CycleType': [5, 5]}], 'Frobs': [8, 11, 1, 8, 9, 11, 10, 9, 7, 5, 6, 8, 4, 10, 10, 7, 9, 5, 8, 9, 8, 6, 11, 9, 7, 6, 8, 8, 6, 7, 11, 5, 11, 9, 5, 9, 7, 7, 7, 11, 6, 6, 9, 7, 11, 9, 9, 8, 10, 9, 7, 6, 6, 6, 10, 10, 9, 5, 11, 9, 11, 11, 7, 5, 11, 8, 3, 11, 11, 9, 8, 6, 10, 7, 6, 8, 6, 7, 9, 1, 9, 9, 9, 8, 9, 7, 4, 8, 4, 10, 10, 9, 11, 3, 5, 8, 9, 6, 11, 9, 11, 11, 11, 6, 9, 7, 10, 8, 6, 5, 7, 10, 11, 9, 9, 9, 8, 10, 10, 4, 4, 10, 7, 7, 4, 2, 6, 9, 10, 8, 5, 10, 9, 8, 6, 9, 11, 10, 7, 4, 5, 9, 7, 8, 9, 9, 11, 10, 9, 10, 8, 4, 7, 7, 11, 9, 6, 3, 10, 4, 11, 7, 11, 6, 11, 11, 9, 7], 'G-Gens': [[1, 2, 9, 6, 5, 4, 7, 8, 3, 10], [5, 10, 7, 3, 4, 9, 1, 6, 2, 8], [1, 2, 3, 6, 8, 4, 7, 5, 9, 10], [9, 10, 4, 7, 8, 2, 1, 5, 6, 3], [4, 3, 7, 1, 8, 10, 9, 5, 2, 6], [10, 2, 3, 6, 5, 4, 7, 8, 9, 1], [1, 7, 3, 6, 5, 4, 2, 8, 9, 10]], 'G-Name': 'H320', 'Polynomial': [-672615, 1601880, 723545, -225290, -104680, 9684, 5570, -130, -125, 0, 1], 'QpRts': [['-12879913064876155978601684599700370688883687191953683556191779803740770313665510598240003811410503821270412409680074963450500218515926124299281222', '-10247922255477140128354511039022027814044150288734406483675824981629825172564918291545494406368904143318895842279311374725697564456298395471435502', '5235214126667281916186815878266635130167544437240345000554091996021695812280806706325517912533620641662034164808482268521978511679319486824768712', '16073753061292697685452570012819384553029067832289790201962336716969203242152857938843739173495797079757635738568089722950780609587294684545152457'], ['11240911650035898047862075645887128259754027830737248986725834791042358410488951692024114269523035701526320162937594957114651284240076538399712010', '-8584744286515882205962360621597751530424210832218212983229093018794609216076197129398303304725214707385738287668612677834980810735398091563413459', 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