Lfunction data - 1-33e2-1089.391-r1-0-0

Formats: - HTML - YAML - JSON - 2022-07-03T03:32:04.836706

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_1089.391', 'a10': [0.6548607339452851, 0.7557495743542583], 'a2': [-0.8612262431802006, 0.5082217607085691], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.48342128388456385, -0.8753878353549357], 'a5': [-0.17989487036885388, -0.983685841930732], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8308078967080545, -0.5565592859413437], 'a8': [0.028556050793696254, 0.9995921928281892], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 117.02930310134664, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1089.391', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 1089, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_1089.376', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^137', 0, 'a^274', 'a^238', 0, 'a^299', 'a^81', 0, 'a^45', 0, 0, 'a^307', 'a^106', 0, 'a^218', 'a^3', 0, 'a^261', 'a^182', 0, 0, 'a^130', 0, 'a^146', 'a^114', 0, 'a^243', 'a^239', 0, 'a^232', 'a^25', 0, 'a^140', 'a^207', 0, 'a^144', 'a^68', 0, 'a^319', 'a^181', 0, 'a^125', 0, 0, 'a^267', 'a^116', 0, 'a^268', 'a^283', 0, 'a^251', 'a^222', 0, 0, 'a^50', 0, 'a^46', 'a^94', 0, 'a^83', 'a^39', 0, 'a^162', 'a^215', 0, 'a^280', 'a^277', 0, 'a^14', 'a^228', 0, 'a^9', 'a^281', 0, 'a^205', 0, 0, 'a^227', 'a^126', 0, 'a^318', 'a^233', 0, 'a^241', 'a^262', 0, 0, 'a^300', 0, 'a^276', 'a^74', 0, 'a^253', 'a^169', 0, 'a^92', 'a^75', 0, 'a^90'], 'euler_factors': [[1, 'a^137'], [0], [1, 'a^238'], [1, 'a^299'], [0], [1, 'a^307'], [1, 'a^3'], [1, 'a^261'], [1, 'a^130'], [1, 'a^239'], [1, 'a^232'], [1, 'a^144'], [1, 'a^181'], [1, 'a^125'], [1, 'a^116'], [1, 'a^222'], [1, 'a^94'], [1, 'a^83'], [1, 'a^280'], [1, 'a^228'], [1, 'a^9'], [1, 'a^227'], [1, 'a^233'], [1, 'a^300'], [1, 'a^92'], [1, 'a^17']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-33e2-1089.391-r1-0-0', 'leading_term': '0.153877331368812459310038460796-0.829913741737444945498853316982*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1089/391', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8440586779565942, -0.19901859027104513, -0.7473074338731225, -0.4863146540280816, 0.3230591154064392, 0.7958747055867954, -0.050927074473060725, -2.4003171883534353, -5.113515486116978, -6.265948759668154, -4.591455688697699, -0.7255342444830545, 2.9756336442784903, 4.1673174801126205, 2.446068211121275, -0.2943526667349162, -1.560732250371757, -0.5299273806087649, 1.280656407693796, 1.6404603568952392, -0.08466700191922273, -2.3177663001250886, -2.988077586781788, -1.7152576764927274, -0.0718176809800696, 0.3164147554152091, -0.4012243931414725, -0.6910741180386296, 0.26620316798115806, 1.4089848300486887, 1.1240121245013346, -0.5112581117793951, -1.5094198259582638, -0.3417862408233968, 1.9340978099725419, 2.6845500017483497, 0.9765842946898092, -0.8809163407553932, 0.17345823617698594, 4.07565053518266, 7.152296092839427, 6.063288412226026, 1.7445418787202218, -1.4494816527713732, -0.6127234633007392, 2.536990830776964, 3.922546669341641, 1.9668732938982652, -0.8692051929543815, -1.4845797420108409, 0.08243910747545713, 1.2059335961306465, 0.4095307843465123, -0.8908124772138009, -0.7675637810051716, 0.3540062150648097, 0.4798550382140767, -0.764939794870628, -1.3493114790899088, 0.19038210200680486, 2.282489081141894, 2.2020945489284056, -0.08124029274943942, -1.6477117570817308, -0.6549536837434311, 0.997076685569404, 0.4963862582622944, -1.280675579651755, -0.25606110828499107, 5.157672540738354, 10.76144074335721, 10.815532735559975, 4.927576948565758, -1.3154793627768375, -2.904652454898964, -0.7189577261239054, 0.8760958827695393, 0.1494248912995621, -0.5828749691352195, 0.637566637065986, 2.2562175849200896, 1.8242153410284085, -0.0065178328709563586, -0.3811344476902779, 1.3835480916195881, 2.7234981776664697, 1.7042543861462176, -0.15099238640396012, -0.41019753878774634, 0.46034910702990306, 0.15388223629287562, -1.227091176844666, -0.825204075462541, 2.267237946452444, 4.596934491521731, 2.8776185550610194, -0.6650561690519867, -0.6088173173139756, 4.053122622235026, 7.825644884892195, 5.754979541837484, 0.05849979866599167, -2.9477418264941777, -1.1867367325550224, 1.2763974565740657, 0.7718813524700746, -1.048084897396665, -0.6845923552091912, 1.4576491350513692, 1.9668062971122289, 0.017201396116787376, -1.4131672348289912, -0.36997376483029865, 1.1564706277606143, 0.7219451856862795, -0.6603651810720843, -0.5677690779282474, 0.5472431813449512, 0.280387416583474, -1.1124307397365736, -0.6131383134558464, 2.2627289790257925, 3.565065796753543, 0.5831613168591798, -3.2963001609908043, -2.884406503016656, 1.0854467261760468, 2.7350309749305106, -0.26789424650811744, -3.1748033995932583, -1.383598450809727, 2.4715751264348436, 2.409822309693268, -1.9701613553306256, -5.015141421483808, -3.3057895151312238, 0.05060022218941605, 0.8730382563005543, -0.23267515291934585, -0.29935546216449016, 0.5610893148885405, -0.011219398737190682, -1.7343421705521807, -1.792954613772633, 0.14302176155234758, 0.9856692942242387, -0.5783116153091701, -1.6376005695942977, 0.090043316526916, 2.1981785923825274, 1.5269399129927592, -0.40339121711650056, -0.08831825481035713, 1.2954436413677752, -0.8929005031477166, -6.46861300881816, -8.734132128606594, -3.6875819557449483, 3.4593308997221053, 5.0866592240089314, 1.5242329194215012, -0.4536360263148441, 1.9339397370721225, 4.273579756618845, 2.8070071258868166, -0.03538476373261803, -0.5155316152724119, 0.4189626232014142, -0.15055712100833707, -1.4741314068778617, -0.7326297448518494, 1.4010175817006, 1.542885172729816, -0.499793013912169, -1.2607915689822107, 0.4097717079589358, 1.4475548910363978, 0.12637646005812386, -0.92719432632077, 0.19919327018887062, 0.8506649835622867, -1.1172456992779325, -2.018843321905237, 2.471220436623149, 8.85896439652981, 8.988854037409642, 1.7679652462815565, -4.59147079636358, -3.9424131136923495, 0.02077368532982404, 0.8127753725852472, -1.1833761306831507, -1.36857581067673, 0.3237775337662073, -0.1826875348116599, -3.231677148923276, -4.37712793620702, -1.8135573578682243, 0.7996986487687971, 0.6209095457163605, -0.2895694822047133, 0.38013123019152906, 1.0191151901481437, -0.13042844215758076, -0.9846570874818779, 0.5400376389943661, 1.9819719103296323, 0.3506939640479144, -1.93022886625449, -0.5935517838370461, 2.698082582489274, 2.49894868114175, -0.9083690742995654, -1.159768860594595, 3.583587654343454, 6.730398489392686, 3.495561096414879, -1.2183720446906863, -0.5168642530066755, 3.747867857821037, 4.5585030779352715, 0.9938516751697033, -1.4048366530544714, -0.39236009358771906, 0.22761621735332213, -1.6919602648442655, -2.998801523051948, -1.4439993821391528, 0.33761623079204867, -0.01899952401037281, -0.5475583555513938, 0.5673921670765917, 1.0756865595768959, -0.7869588454189687, -2.0334872289400963, 0.11101403571754243, 2.634161277662871, 1.4593295624419125, -1.3655824072181435, -1.3135329799539477, 0.26913522062379647, -1.331309411787917, -4.608431959445059, -3.0388614441037567, 3.3168184976135113, 5.8969897176265125, 0.4218231379720513, -6.051181493566957, -5.652659644431894, -0.8117942312803148, 1.2030365455989518, -0.3442750215882788, -0.8615105044645216, 0.5282387024133551, 0.763273575005035, -0.0947427522170306, 1.044979564461696, 3.58565962224478, 3.4646528431229875, 0.44512678522330656, -1.1999827378208727, -0.07712920540009571, 0.5012211568029514, -0.7564151850579166, -0.9868091604051837, 0.4337369601114602, 0.0025469590375351357, -2.7347042396288, -2.9657733252349376, 0.5999866795726907, 1.6341779209046705, -3.6788576715126444, -8.779490403313128, -6.100540672448982, 0.8227898889162559, 2.913470973905596, -0.37723012377633747, -1.723157302854247, 1.165439207456926, 2.8758613340552603, 0.7989193822262992, -0.8735659317112776, 0.3606622563417055, 1.0279712787716035, -1.0787847871027867, -2.5678264848196037, -0.9700096239755795, 0.7598712846795229, 0.11500635420069368, -0.4264911802819059, 1.2198111840808659, 2.3821801172123824, 0.9362239887711974, -0.4550852191407582, 0.03435075937898942, -0.8187910298612839, -4.540354868797621, -5.802409566770417, -0.6975892045357615, 5.090722687338399, 4.2874467143107236, -0.1747400434803758, -0.2837140195162265, 3.4417309105293654, 3.5353765876958825, -0.8153522904484797, -2.434212810611477, 1.0194298760980196, 3.2225381108631113, 0.5411105384488903, -2.2047820206828055, -0.9075897068223364, 1.230443496225349, 0.5683086530038447, -0.7823032254322805, -0.20429701285606922, 0.45077175452515156, -0.32191831946276483, 0.05452866922789682, 2.617981707831243, 3.422553754265803, 0.3919868058607441, -2.2488591871159267, -1.2314709984355225, 0.16125251918746838, -0.9875316794451876, -1.2642514399695322, 1.8166700663939446, 3.273833794119185, -0.8245714273368387, -4.447451955383412, -0.4585998526287301, 6.584752664764519, 6.790835533301507, 0.6023123252492708, -2.7505959388953567, -0.493589593309418, 1.1032706470919182, -0.9408961035638301, -2.2422416872758726, -0.5844429511778473, 0.3430548573258443, -1.0886232107610108, -1.484346934304467, 0.2512437625798918, 0.6569649792661723, -1.0179521535892382, -1.0268275141256722, 1.2994684175685343, 1.872868508408999, -0.22550040888937545, -0.9482739980655244, 0.6006784458654502, 0.43569002771868265, -1.8595697162309597, -1.8012039107010527, 0.4275155877193634, -1.1222378228154675, -6.1482487891370265, -5.500450771258451, 3.979658597671915, 12.167115060589696, 10.168346516799106, 2.958710727724362, -0.276384247080366, 0.09481955184650008, -1.110306945606641, -2.8440570269540033, -1.303849695732591, 1.1539457125782577, 0.04810671993294622, -2.580246261971617, -2.106213017467691, 0.056512739888893194, -0.24875052269433787, -1.9004224791088742, -1.4030094849913415, 0.08756501542553263, -0.1000385985320206, -0.220876520138174, 1.5752859980844465, 1.8321352988724446, -1.8813614585449765, -4.571560833886928, -1.8316749568600865, 1.4467635995044683, -0.6434089058985744, -3.9172173190673107, -1.5646452975830027, 2.762018305791407, 0.9983564133890777, -4.503015667138542, -4.665516501318841, 0.6186725721650961, 3.062852467461376, 0.7029402130537589, -0.2812741227979745, 1.981179770767564, 2.542824812334355, 0.060757326287704985, -1.0448483240796338, 0.3202373893059394, 0.4026766234222494, -1.2796485776881503, -1.3269152815253278, 0.03781273329250793, -0.45089169345854474, -1.6913159552860302, -0.09811900153301831, 2.44372885531297, 1.5371535225635788, -0.7403828316843428, 0.5720417979905703, 3.119122731901469, 1.1348148067857138, -2.963700744633196, -2.452175271153294, 0.5096980411156253, -1.7242708809105312, -7.1895201589269035, -6.273495754311936, 1.285404994140047, 5.138993985226334, 1.3740758416061647, -2.3962473552131147, -1.157431556785415, 0.7819644073758723, -0.015081076273955277, -0.6977811894657764, 0.09756895731090692, -0.600534724287436, -2.652190072646985, -2.033380747741474, 0.8170864917906342, 1.0543235516083849, -1.3844690196363238, -1.8149261700839734, 0.021311065722999886, 0.20471425982837063, -0.75800256561463, 0.6566888051631172, 2.5788547704203357, 1.1654604933669996, 0.05182718461161066, 4.739127639437784, 10.109519599211835, 6.63205693047267, -2.8279848671677716, -6.278564471023017, -1.6564054919172526, 1.5905392434941508, -0.29380878556680634, -1.0678204214458997, 1.70862419260335, 2.5825741515856695, -0.12794861170717653, -1.2358575566978272, 0.7463210667711844, 1.3190821901693683, -0.3884224024357118, -0.34401959589857356, 1.4720862942688528, 0.9970559723159875, -1.2688880998704295, -1.1932645993387236, 0.5761285241993209, 0.4280714437432394, -0.3816523966730983, 0.9706477328101775, 1.4715133499666777, -2.057613280807785, -4.767653749813864, -1.836081619476787, 1.0879752191765206, -2.7956968552525217, -7.892213885994051, -4.962527983207176, 2.477470443425126, 4.256150552222264, 0.7052082558063523, -0.3495823552741078, 1.0609122921753371, -1.0028823225402745, -4.987979986589083, -4.226328292766129, 0.27934339993706825, 1.918143083456607, 0.34135175330325024, 0.14644099453884563, 1.2254475544029562, 0.5439723212602263, -0.5410774254577969, 0.25687706633168333, 0.3932356040902038, -1.8530273587962294, -2.296398446984879, 1.2360647141632681, 3.5128676145095037, 1.3541728632268974, -0.3809058761935282, 1.179228593963003, 1.2636665358172245, -1.5453881584385871, -0.5017324283944579, 5.817133659235495, 7.965031827056307, 1.7394435813504137, -3.1800272577227147, 0.47181282012765813, 5.510585077390272, 3.827084267444682, -0.46361239925309566, -0.7959976106721932, 0.4645485895906696, -0.6184745599893948, -1.3592747859745096, 0.5009041080894043, 1.3087256920746313, -0.6772934522273859, -1.4393019273574412, 0.3851566559601519, 0.9354385336641153, -0.24881724478624023, 0.7515604778903151, 3.1903578724478665, 2.31968505160145, -0.7783818302589263, -1.0274903720071724, 0.40511531018373304, -0.732316983631539, -1.54155123346817, 2.3118327681925175, 5.027454639757953, -0.8230741519203743, -8.854640660484215, -7.394967107742586, 0.9370088344980787, 4.022779056753617, 0.42036763177195874, -1.1818918570001118, 1.12877251657227, 1.669524090586411, -0.01124900940324606, 0.2892188505626547, 1.3221500717299246, -0.6304636730190708, -2.755409971973198, -0.7269180546826027, 2.3722261177693498, 1.834119939047559, -0.15589658692040984, -0.11425134382385307, 0.04215436577421356, -1.062892068710264, -0.2982693546167995, 2.2887947322520805, 1.8949974504391707, -0.5900715705606815, 1.5745677308204349, 7.285371075096355, 7.467011798601443, 1.682958874579251, -0.3292373158383595, 3.339133465085973, 3.5832051988869944, -1.762889842058342, -3.7180747809356887, 0.5849815865755504, 3.0579316500720033, 0.5251188804880983, -0.4592623912175334, 2.39658061210562, 3.2728762100295024, 0.5482464230223556, -0.7374481364667519, 0.39926209280655733, 0.13053829465899477, -1.059133446638453, 0.1299497397071307, 1.8049344415781403, 0.7057251452579878, -0.46647542220131855, 1.1521908296760313, 2.0490075250244497, 0.04571394690014766, -0.16247873536687774, 3.0000824014847827, 3.180468468068455, -1.36126515367128, -2.938836307768921, 0.857628883576835, 1.854674203102342, -2.5283224240389215, -3.4489983204025765, 2.051179847980761, 4.324969510120764, -1.0908240979949213, -5.256632927750293, -2.367812570532462, 1.1396251632271508, 0.18289911695103622, -1.0497963933773689, 0.2639879587670158, 0.6658892393359616, -0.6314766367194884, -0.2841109277564388, 0.8001698560197903, -0.850461358996967, -2.813370888906949, -1.0261845809510635, 1.3610900414002085, -0.09977356747748736, -2.2623242994344266, -1.1588760215306644, 0.18582278767599647, -0.5873533407200434, 0.16764493590221305, 2.0611317312755744, -1.962129739615147, -10.732548063028174, -12.198607531876664, -3.310490860294862, 3.4580223676031645, 0.9072600406416321, -2.4350377814819275, 0.11901260773499903, 2.618005962553201, 0.4117705021725464, -1.4906821846178544, -0.2670075302088877, -0.4523334456024555, -2.9263716241257396, -2.6921687144213564, 0.24013479214429787, 0.7780705577742935, -0.7213076067311356, -0.010568715115235192, 1.5815150330615824, 0.5415493029727737, -0.7523401007942102, 0.5108975538169233], 'positive_zeros': ['0.245746660051939964152425621580', '1.132437072097854789191727488965', '1.86535437103633731825431119038', '3.491203123887680421253817305926', '4.64973298646012608985951583389', '5.39956337232325289667259294446', '6.23877795242144061533182767274', '7.51995674170802334505084181353', '7.97289461256466043264399704218', '8.68682273170615729236763090313', '9.59748892300591795061950484699', '10.36079081722288999646707117018', '11.38230226364846548525996815497', '11.85536392570978277854815026350', '13.256926929597694043302194507573', '13.81655538996565741813102901905', '14.88923828751792834195775242305', '15.610903947661555761295678745504', '16.335474035236309427308772503913', '17.08450860801661576220663790983', '17.64111862093173681004431889765', '18.41139077497208451273234983852', '19.364835793511698421565754947411', '20.10496333023633361256800404419', '20.70829965881608610045892848251', '21.27207944015634751291578126375', '22.72994240429505090645930870198', '23.53200843164952284383989271202', '24.09948577799284207450034154253', '24.57453380258430802005285147811', '25.62367562244771550908208691837', '26.0314064651806373140510664334', '27.153617703303156434663831430567', '27.6447534914548119550296391030', '28.16278059862183687109292968323', '28.8537437164168406532878567910', '29.929098212811995732525614992141', '30.36995829338925573925921666665', '31.56596495054721817720446206072', '32.31061586522759427894968888992', '32.9328510125242887455280380767', '33.54297091208470117627184907398', '34.37733966331384884709656499484', '35.06163582671845371525147050416', '35.77485485421992230738484821907', '36.400557447773656022204310449542', '36.93941231938997479644897797810', '37.57999094400670503032870760320', '38.47805100150127929190805092356', '39.29183544683572701039109013087', '39.97952997611643678381228249180', '40.729611242254369905767556783912', '41.436961050783906779848992424184', '42.493652425988352200797026728824', '43.0571134348626315113894593091', '43.54031683470248161632533738348', '44.06022280303249949187942634946', '44.97770782567153389316709193707', '45.5347205200189679461800542918', '46.23926828615467400340613758699', '47.10325990284310684000585767196', '47.51714913755471558082307064813', '48.05785218336485352958957700663', '49.2106742424986831968296374289', '50.15082034376574469335874436844', '50.42068656968029385550147487406', '51.55695383409432868189415348627', '52.03232698647747264239322362050', '52.46603414234533609589215794493', '53.23036460833848114600674395935', '53.98960508485160692953265384227', '54.62470584988666818925167620882', '55.334423666119069729117967716804', '55.89850637197476491458186530289', '56.419936840064764723013748203540', '57.06010427650244275884699843756', '58.1918344571736939472176465837', '59.060379463074245470696352008165', '59.51120512356592126068929895185', '60.243092081180551660152607423461', '60.59859282972665136256361046843', '61.74501354331225074768909972158', '62.35397932005140757945618747954', '62.70423724406434143463477919620', '63.41198129465608435423574174163', '63.98447452617043552000238586229', '64.72588278493681143250787999264', '65.36725965432135249776600184103', '66.16414803741855907363368454143', '66.66154669765026708344521286369', '67.70647894168206882565337348282', '68.16675339038330577828979880926', '69.14705939363268626718705389283', '69.770259831409401526581601990355', '70.06318872583514382487389693891', '71.15557881624731923324676809466', '71.55658276333903016845427744586', '72.06329072167916556530724107186', '72.707289588263362913438028831298', '73.42679420455584566857596012997', '74.20936240916027608169477923458', '74.9145819061517972756771572708', '75.154359107299992147178208730968', '76.09424959310942477466557572979', '76.891903665248674849641296653321', '77.87703943190395740746931104365', '78.37901003296955944975394916178', '78.949822909114348038107626585268', '79.62587826999229001938958998794', '79.80595061665895558924839217325', '80.98525164633635635763641499916', '81.578926284762916108422894035287', '82.02322762311557975707854245556', '82.71418116978243874765812765707', '83.125377211851409877175139726616', '84.01332819132140127762024140540', '84.50685634689661369894128033046', '85.582301821586714973656200405681', '86.21763944352045151268002080410', '86.77031417623353209381404536350', '87.59583988018340793901526048226', '88.06210423098174944166947460889', '88.62023699330846410358023311473', '89.50742117812100926488176547304', '90.02879263164136695660603490998', '90.43119390032633743036621369374', '91.40590214493644605969721029154', '91.857287284546058626559171860453', '92.04309331728742777110803249462', '93.15579670624282679401155311474', '94.046287113547892912059626018742', '94.40367164314639761128244944598', '95.255645600400805255929561016716', '95.86214882054201218025418716701', '96.60625214593154858864300159614', '97.293055148849898689569483407172', '97.91447492335272447776887737651', '98.49306917710727238655981538118', '98.953718608005488251574145302872', '99.36526612513909896360477601738', '100.344812972903762362637948238676', '101.15679264258447222383403171527', '101.35558432255102473725933201398', '102.02905718137422366826434036823', '102.76583114557786247016140119056', '103.45684594726355008203177039701', '104.4061570010831909361643325140', '105.05110450307380839254213877592', '105.513863290938941503625141748201', '106.35064909360251987619566819041', '106.66998739911033122365658233678', '107.45632205540011842838584796155', '107.94831597305133759719015716580', '108.58575024065986234143656517290', '109.34297211874786827052373463736', '109.88555737999460465657524371995', '110.37869069717688272728626515521', '111.17271880647574223606589231161', '111.46416379802426839709621842940', '112.38760130136663522382086047581', '113.67034785377762912202385420123', '113.98273006825766698358943412274', '114.161627168222728857252225425785', '115.13614629246551990426459877788', '115.63035642479346374742477805729', '116.54973351796061792457152908571', '116.82377682350488377947784756714', '117.7818341471477028436149549955', '118.08353349573633212889928601969', '118.495060324618860262127209140612', '119.242444638442973764036273074360', '120.13298256819549184686337512025', '120.5748575806632431910287733803', '121.345755371210008575590230512756', '121.931990051768287843196408218196', '122.776377092458822581331600036310', '123.52981746900388403412827707967', '123.80841348880889122737603179213', '124.6949686607212687393243496050', '125.24516264195102223566275817171', '125.707848381200715703882686544649', '126.54864216343075591312887623408', '126.76448451166110136114937894160', '127.51035383055081367709574719436', '128.303780569276050682411707104998', '128.68693300040546771207903785973', '129.453370006437415262483675626478', '130.23143648764655568595768872420', '130.49868920751303256627974038807', '131.51100576316077611913502198943', '132.26972622727800583160307890077', '132.953307588516765261101071511', '133.43419460606549614872848028809', '134.01744821600063820880023843301', '134.249531435819629217972861363900', '135.21564249755784144646293057367', '135.76714913315081466152572189397', '136.55816331514826552466018416728', '136.930796393478981069615574010982', '137.41269113449362247749639470188', '138.30149789163998676159854614291', '138.42590950183929721476153026540', '139.59026477406770849244060712340', '140.41399700200223421758823624028', '140.90262360098530913841183939426', '141.39161700441208577832636114912', '142.173658545680448187304385802615', '142.70909419900827596254108460970', '143.36460149464031712311073755660', '143.81206089042838137707420590099', '144.506735042442086082904478903594', '145.19656796113359435073748026145', '145.735226322095071673656442429530', '146.07960407534031520268412474003', '146.72601150070122611249206501402', '147.63339005975142670911339904192', '147.96594747623342217105045336114', '148.94946121401585088000885405939', '149.765369489226999902254630060184', '150.07492710407487679173297855040', '150.54127984681912899926366626819', '151.54099146142348562346416474449', '152.28222734997961850230581024029', '152.44669951651036162600003455257', '153.238450851390092239978849592', '153.68384055368930548835444189721', '154.13628752235057196300091107695', '154.90740750543243489836602860530', '155.789298902213247168394318218762', '156.06049902166568711417592357826', '156.70744937357357712487375947907', '157.21927783551613024012455862961', '158.19789346331614699080064903639', '158.72660174709183721374950749904', '159.64064588676532020630274329574', '160.153581813618364026128011492100', '160.50976695253166564868923091313', '161.18044317089886533098333599933', '161.783511067508759608931859769893', '162.43949364772748696949801474699', '163.04262627122645771949903339525', '163.32205939934816359881400230241', '164.28452432210060200673389432200', '164.87716656508361874598749063705', '165.194739742115328442997544268696', '165.788385552627495793138309776616', '166.53412416868961969380716988247', '167.462078567009633772074584365164', '168.15970355146588426690195729534', '168.614705910388841820282930178349', '169.371993592887704028023071484117', '169.618681871258608862150257246353', '170.2462383077846179958274006025', '170.99851293752377052503610684067', '171.8366550543964628946029420932', '172.23863341443916935428266023185', '172.516788248062353272235247996210', '173.16280311986428281917073428711', '173.96206749936190187414786705516', '174.25860392700516228624244181015', '175.43347717771568821188531607303', '175.66929084940268977003639485377', '176.46629522111663801296087900894', '177.151242047269795440091027898519', '177.8716922849390566280139294268', '178.19608497684167154626468188804', '179.12825521952604168968572980263', '179.583605032675800463364679160727', '180.02876958873389609658858333335', '180.6065646795866395039283799442', '181.36730171311706927649544643686', '181.702110617267199208297332612919', '182.50686961611508314077742572271', '182.8352424126717545805503283052', '183.66267817457625513846384193443', '184.31159870865210628454848163316', '184.83767245691615374283544004517', '185.521590621980539260161518944672', '186.200046962030423991035026534692', '187.042718496883115211453716495362', '187.52661392734966795649370199905', '188.07444054458442373634488066150', '188.597256969044816361067583642664', '189.12228031406998701360794436022', '189.58342683399175757167581355106', '190.413678168677103658137821100323', '190.926561085184637608248010840895', '191.76922475783856418402090147067', '192.000011018140071132308952218305', '192.47594455993594156731398795317', '193.03698247712347614871662876144', '194.17084702077724724082081457839', '194.74427615274160877287999549561', '195.303379241378855404471272235589', '195.9780527059170724866120415687', '196.63748362057450488256051645730', '196.77565870797355657214261476802', '197.78299790207910739439765479932', '198.27620339781520541379712727589', '198.75170267963058532727860319706', '199.46087227271375363216511627947', '199.91029941096096724248218327987'], 'prelabel': '1-33e2-1089.391-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 117.02930310134664, 'root_angle': -0.8832874196510561, 'root_number': '-0.933528725044511271387858920892-0.358502607405816888494283058214*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.441643709826', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.724731676296364310037674869330-0.166089686507358306194884135834*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.245746660052', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.1324370721', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '1.86535437104', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 117.02930310134664, 'bad_primes': [3, 11], 'central_character': '1089.391', 'conductor': 1089, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1089/391'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-33e2-1089.391-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-33e2-1089.391-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 117.02930310134664, 'root_angle': -0.44164370982552803, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.245746660052', 'prec': 47}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_1089.391', 'Lhash_array': ['dirichlet_L_1089.391'], 'label': '1-33e2-1089.391-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1089/391'}