Lfunction data - 1-837-837.727-r0-0-0

Formats: - HTML - YAML - JSON - 2026-03-09T11:27:06.956027

• 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
  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_837.727', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [0.5591929034707468, 0.8290375725550417], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.374606593415912, 0.9271838545667874], 'a5': [-0.9396926207859084, 0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.882947592858927, 0.46947156278589075], 'a8': [-0.9781476007338057, 0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.727', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.175', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^14', 'a^20', 0, 'a^19', 'a^21', 0, 'a^27', 'a^4', 0, 'a^23', 'a^26', 0, 'a^28', 'a^21', 0, 'a^27', 'a^34', 0, 'a^11', 'a^41', 0, 'a^40', 'a^30', 0, 'a^33', 'a^7', 0, 0, 'a^35', 0, 'a^28', 'a^39', 0, 'a^30', 'a^34', 0, 'a^41', 'a^32', 0, 'a^7', 'a^18', 0, 'a^3', 'a^13', 0, 'a^38', 'a^2', 0, 'a^37', 'a^21', 0, 'a^24', 'a^40', 0, 'a^14', 'a^23', 0, 'a^40', 0, 0, 'a^42', 'a^43', 0, 'a^5', 'a^35', 0, 'a^1', 'a^36', 0, 'a^24', 'a^37', 0, 'a^41', 'a^23', 0, 'a^31', 'a^3', 0, 'a^39', 'a^37', 0, 'a^41', 'a^14', 0, 'a^25', 'a^39', 0, 'a^42', 'a^10', 0, 'a^20', 'a^2', 0, 'a^19', 'a^0', 0, 'a^9'], 'euler_factors': [[1, 'a^7'], [0], [1, 'a^20'], [1, 'a^19'], [1, 'a^4'], [1, 'a^23'], [1, 'a^21'], [1, 'a^27'], [1, 'a^41'], [1, 'a^7'], [0], [1, 'a^30'], [1, 'a^32'], [1, 'a^7'], [1, 'a^13'], [1, 'a^21'], [1, 'a^23'], [1, 'a^40'], [1, 'a^5'], [1, 'a^36'], [1, 'a^24'], [1, 'a^31'], [1, 'a^37'], [1, 'a^39'], [1, 'a^19'], [1, 'a^31']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-837-837.727-r0-0-0', 'leading_term': '0.0905216218920760175783634558529-0.0507143435626142042182630340731*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/837/727', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.10375986060591459, -0.9252048601771152, -2.8045518301282, -5.215087405653907, -7.065579115213007, -7.217173523520721, -5.309714175226135, -2.172545764945572, 0.574135197354807, 1.5753779242179207, 0.7117869582689105, -0.830160628008348, -1.5438552761309003, -0.8763255799917254, 0.3291080630360337, 0.6737908387348703, -0.40764130879233795, -2.041798140909653, -2.741462905566782, -1.8923666083794863, -0.3854447542091918, 0.3252637711561653, -0.19495561428282493, -0.859646104583571, -0.2971816929930058, 1.4521452483453647, 2.7474563298221026, 2.114643433130215, 0.1483441079902276, -0.7292961040218261, 1.236050997079647, 4.90697306816067, 6.914212107247291, 4.892801789313644, 0.04628734046567737, -3.7990380561753265, -3.8594060147698492, -0.9883524888675199, 1.526329114778199, 1.5691809110062356, 0.20322296568519682, -0.02265186805147735, 1.7024691307628887, 3.5327901286731143, 3.315549442862, 1.2263803446986419, -0.532774688377115, -0.47561198847379144, 0.5090055423850164, 0.6222499413863863, -0.3025450701505737, -0.6296734696902534, 0.6210976302808027, 2.08437048055695, 1.6792253364766179, -0.3764851811054019, -1.3290296935498849, 0.7638812942688527, 4.1897881962216115, 5.203705366637031, 2.541174118113273, -0.7875632717320834, -1.0102121401889539, 1.6965224268907861, 3.2433920798453406, 0.6093259899639137, -4.315261247864634, -6.825433825224636, -4.848133668205992, -1.0315125523190483, 0.8234983898708736, 0.15791096964921597, -0.5754554226197539, 0.17756871115447637, 1.0942892021920756, 0.37901097839031894, -1.2821852086682408, -1.6186421464606733, -0.1679749078782621, 0.9135467109389253, -0.03989399112153649, -1.6743319695302414, -1.5141082977324292, 0.32093396135227126, 1.1085667786091884, -0.46428529786719475, -2.0689453353543135, -0.9461382250578344, 1.6806065991799672, 1.6057432545099768, -2.589748856756935, -6.789873605406939, -5.97494318678202, -0.610632031670212, 3.667883440339844, 2.866497653268958, -0.8749697752851061, -2.681217168388338, -1.2259262911051665, 0.4649397420256517, -0.034216330287028564, -1.3426882186799216, -1.021152122362772, 0.4559539535749034, 0.6042176247244242, -0.9444214653687841, -1.6618663022341282, 0.019269811800224367, 2.1719532590400803, 2.1559977638934407, 0.4936500208227029, -0.1401885920784581, 0.7985523381892579, 1.0209567140137448, -0.4158786102315255, -0.7969476902977497, 2.2676050029467882, 6.087257690334496, 5.224149155147697, -1.190265601568742, -7.334363331718318, -7.491086585033317, -2.941363436144238, 0.33069619812335616, -0.3203006205796378, -1.613704502141163, -0.1482725335263193, 2.4434873910854717, 2.3401334880675924, -0.4871910328803276, -2.286370457922752, -1.129777826270926, 0.6120399493827309, 0.325145114070693, -0.9876172680565252, -0.9035069383252992, 0.21826197197851843, 0.024110524574185405, -1.5538512304100454, -1.912059909189084, -0.19915962303907284, 0.8484060470869528, -0.7688086161059792, -2.577981866975839, -1.085428691348786, 2.3872574736259944, 2.965994266312848, -0.46090325387815917, -2.930953170653803, -0.3544285994858205, 4.20054036997423, 4.515917079998262, 0.011459488557272423, -3.4988170971175525, -2.0551342180701417, 1.3962236991527481, 2.082443406939321, 0.32273082031748845, 0.06165903457992713, 2.2373635060907766, 3.61169186835759, 2.221215832987563, 0.22882067755414173, -0.014182385802640064, 0.41051663615522493, -0.3406633506188822, -0.9895866322057018, 0.8191752023291077, 3.84126520102555, 4.303479131459723, 1.6800729615343315, -0.27204647129775883, 0.6342796800311798, 1.7039616386766019, 0.2954130181753449, -1.077497449242842, 1.4098441337437129, 5.607258235763184, 4.982232892329509, -1.8949735313665765, -8.144183641549768, -7.30422337377311, -1.6836015676252742, 1.5779096065217866, 0.33245452981726964, -1.2397951536869796, -0.2358955468247439, 1.1085322427478377, 0.37672580569559283, -0.6817835722964862, 0.3654292807060094, 1.9515492593709025, 1.0106142143147148, -1.6445927171621983, -2.4104957809219747, -0.6652857193271826, 0.572500344614727, 0.0061905877018017495, -0.03788782489454401, 1.5718147649079537, 2.0975152087196385, -0.1965357577123436, -1.9418419983739936, 0.5114690268985983, 4.455267453193249, 4.084309978649614, -0.24279114997265694, -1.5748067371375414, 3.4205970789527678, 9.005987293114964, 8.373872387917311, 3.034916943957602, -0.3495398114042392, 0.11782828659535716, 0.3566503885187321, -1.7603274305178858, -3.1214693383916727, -1.4145660653727656, 0.6183773612216514, -0.11457186619642609, -1.904585076607845, -1.4634603191121265, 0.42601054933309646, 0.6151729646471923, -0.7915701571261347, -0.9819352288286607, 0.19882071615818417, 0.16522962776573305, -0.9216159030860578, 0.4033239267443929, 4.439870156860188, 6.2224028533257565, 2.944840488640192, -0.8027040935131466, 0.3487328174239324, 3.9438362033097087, 3.378644516607693, -1.5155653874638486, -4.081886368096369, -1.428129837095275, 1.1508802049161873, -1.068737058829324, -4.744226396408675, -4.114754575625374, -0.031770247840616814, 2.0540549900740634, 0.7375554821490566, -0.43274935196856595, 0.19810051130113115, 0.3600788389212004, -0.8144652775731156, -0.8209172563990219, 1.1512374599288693, 1.9671357797366902, -0.08712969347293933, -1.9041256801423359, -0.7445053193535164, 0.9641262350891481, 0.025932275658899752, -1.6640813740791485, -0.7147076646574912, 0.8212713739622692, -1.6790152583102596, -6.585413825787218, -7.023638842915863, -1.7497963786570268, 1.8625251814145025, -1.240892206849258, -5.9876830865300885, -5.097344119344565, 0.01476889624745256, 2.378062988100586, 0.4176797875128046, -1.1027242880409545, 0.0898434450614875, 0.9514262120837913, -0.22847321068413606, -0.7412857668654326, 0.9313767242159249, 1.9336388767501227, 0.34856758844541424, -1.036679291266313, 0.2696643112360476, 1.8611514429560656, 0.8472629747319672, -0.7868330906547573, 0.10731445029255968, 1.8727358232978, 1.1464810277270643, -0.5868712877259658, 0.13880633249113103, 0.8951928470471351, -4.142819171712647, -13.351509348199826, -17.097706747142574, -10.805639273167328, -1.7400793877455383, 1.441483771820912, -0.12211151193720045, -0.2581275737609922, 1.4341662117977285, 0.7861545462813755, -1.9336305094954611, -2.0841638705117584, 0.9268688598644381, 2.4793188900431096, 0.7035345794288455, -0.8438428194584883, 0.04933201340443339, 0.8137099880905518, -0.3377033804563401, -0.9936478665650907, 0.4078722569369386, 1.2849673198130556, 0.10951263092997453, -0.05273166001083681, 2.638257256992918, 4.208202243824244, 1.3020824991107731, -2.0821459016001045, -0.6616793847978231, 2.766575244491759, 1.606590804542425, -2.9438916078988817, -3.1590612482484883, 2.38014653522401, 6.019806383779732, 3.2115227928702015, -0.7883853199960097, -0.2896269598193102, 2.0540216447281363, 1.2319437411104952, -1.2779897145747021, -1.078923557019327, 0.9854259810861726, 0.9495695795384467, -0.845912259067701, -0.9740973307382781, 0.37655816121004515, 0.25272427212709936, -0.8992377081902749, -0.2586046267327428, 1.1147481888879505, -0.35987825025637304, -3.5100656474855914, -3.399637494355784, 0.009543695539083834, 1.3835811132025568, -0.6124169833705668, -1.1679421906338965, 1.055644374118149, 0.34876465014724445, -5.607124002449467, -9.491223815517705, -5.020909435262788, 2.4037601867312204, 3.465908596325748, -1.2863688683205652, -3.818748317189397, -1.6724701658164798, 0.2252769810458573, -0.5394290402355715, -0.9653377117356705, 0.04020975493076184, -0.4533942246199163, -2.747610195829074, -2.984507550408524, -0.23460121454226146, 1.4835548254395323, 0.42534654887959233, -0.03684671834647273, 1.7786617813392145, 2.6443905511380343, 0.9236226915376892, -0.1962723950253148, 0.5851045208650946, -0.48994410323060616, -4.293872502921375, -4.7216917401890734, 1.4382972221180816, 7.023076190770669, 4.438106858381011, -2.253021710785283, -3.818232130591712, -0.3465308595959903, 0.4082918807984086, -3.206036452493609, -4.883086137028851, -2.0395632620095925, 0.4718071081668481, -0.21821284816417763, -0.7644054526587826, 0.7607429541061065, 1.0640108559340493, -1.393233341265192, -2.8240605571214297, -1.0115364223231667, 0.7180461069718986, -0.1014462753373726, -0.9280029462185501, 0.024901742890721616, 0.18566198432797373, -1.4320624067520884, -1.2231208680212307, 1.7311940320247878, 2.2056121911496627, -2.054151425884552, -4.688090776239701, -0.8021712743142733, 3.886380781103016, 2.006685277394951, -3.0842149873601477, -3.1779128365425753, 0.9477222035069197, 1.851384130658054, -1.1430521753748377, -1.6044778317401023, 1.7408732101697175, 2.9186650123721805, -0.24150250394875733, -2.588990110566137, -1.1106562301579928, 0.6909089067979332, 0.20805661363242933, -0.3405224873517467, 0.16278444049807164, -0.6720461024614364, -2.6907887279975053, -1.983376576117458, 1.6605600612001106, 3.2536119251730775, 1.1714509042265178, -0.21389784794952021, 0.8440146196032499, 0.34881730451984794, -2.5300986615742054, -2.237698939128164, 2.7350237057388442, 5.127391581060762, 0.8582186598755802, -2.864278395175644, 0.8911722219087435, 6.828555909288853, 6.091520297602945, 0.49094050135849887, -1.814165394910224, 0.01824406009251859, 0.40030686409253663, -1.4795797215518256, -1.426405259854978, 0.7187322323064445, 1.1298120109520728, -0.09395473176827002, 0.4590686821445351, 2.089161494438802, 1.217366672284085, -1.1295734073236448, -0.9698289646367557, 0.7760790862918443, 0.046016809693311275, -2.16001292868157, -1.5969228666241442, 0.7215498697594301, 0.6023004841519234, -0.380771776388371, 2.188130458946409, 4.983459536590087, 0.4681052042686456, -8.843676959476172, -11.50202036048908, -4.44370484516224, 2.363434767490867, 1.7750667606893769, -1.294897634895679, -0.8872100213851742, 0.5619125627392356, -0.3988475260681445, -0.9614685008880595, 1.301456215107918, 2.5690424449353175, -0.0954193576851625, -2.788046858914992, -1.7574410647071028, 0.2716017812885459, 0.07475374616265368, -0.3896111884752891, 0.7090396545490916, 0.8431781068668895, -0.9504887152314893, -0.9605454020975804, 1.6698864224383836, 1.9398917631844408, -1.565664222523359, -2.6556221046497472, 1.3699296593670953, 3.6460079280808517, -0.30883607514022327, -3.738448004596118, -0.12914635124148055, 5.109042518850173, 4.1013589497537, -0.020088523306661346, 0.3400602543071198, 3.6476637869096185, 3.220211050538783, -0.20622605479979914, -0.7953967668487076, 1.265395453625496, 1.2077150958158054, -0.7779745851829479, -0.8838336985624139, 0.2020233883850871, -0.765940070336608, -2.381192041845042, -1.419791021468729, 0.3304867187401719, -0.23064755310580984, -0.8956591227821213, 1.0523223715457448, 2.096706840555373, -1.1936446369596256, -4.23416507451561, -1.780938518657408, 2.1480795834080055, 1.4194743707447914, -0.7762416797293302, 1.4486694494198007, 4.0234792676382165, -0.6651620281006668, -8.794608391037178, -9.705108264953559, -3.04045230179504, 1.5422075181425217, 0.3629018278927424, -1.0188330246103812, 0.10007007876654325, 0.184363465116857, -1.5348237909788085, -1.4990794989862959, 0.24789189774505266, 0.14453875445619524, -1.080611081067025, 0.27251622929787944, 2.7159420379590093, 1.7199811987674618, -1.4510508904618415, -1.9476563252564323, -0.2662581747871151, -0.022423557734410005, 0.18912454020452896, 3.156171905898578, 5.023589204411374, 1.5492583541538616, -1.5901386524491734, 3.3332339220441716, 11.471655457511682, 11.58262197502553, 4.1499433258860385, -0.163855507047576, 1.6162432515654062, 2.3336476972178866, -0.5093144514494915, -1.31856339311902, 1.4663987896063113, 2.527482060612304, 0.33535348378698737, -0.649864688394163, 0.5164288162151005, 0.004908798135087283, -2.0634121652655275, -1.566712309919386, 0.9862800035560724, 1.1974410631334562, -0.6329956629763364, -0.7223619575117013, 0.18813680628819396, -0.8642707826961618, -1.6021784483828188, 1.1502235854609135, 3.46163992219057, 0.882953929046238, -1.5354390770410358, 2.729318333053701, 8.409383013801012, 5.979488971434181, -1.7760575067682542, -4.285255596037805, -0.7788857918806081, 0.6007043294331758, -1.4749395258711417, -0.9145265055873316, 2.31931727369451, 1.938747979823161, -2.101845703325861, -3.3619881528770628, -0.7880645859801576, 0.5275057685008292, -0.4367469080227755, -0.14077070614606588, 1.2552809064450636, 0.8293962474283788, -0.14880504779077502, 0.8388417685538503, 1.0973636955353723, -2.111282261395026, -4.579278293419683, -2.1215464425020856, 1.119327833174367, 0.2535299792549055, -1.2694286442750131, 0.4728887152588148, 0.9159841146354948, -3.5688159828496797, -5.822529267850033, 0.6472497075601509, 8.49091022967183, 7.427714670872882, 0.8492788745234913, -1.307527685825725, 0.7481668146788134, 0.14528064196863247, -2.686518241780377, -2.375387791714673, 0.146859424776866, 0.3304555121692947, -0.7316265997773412, 0.29599282703427043, 1.4440418892237248, 0.025620052378671414, -1.0533863610994663, 0.7044764215405519, 1.7415478148275279, -0.33527771373821, -1.5116166484593045, 0.4972018212146956, 1.501419539930053, -0.25471721089382804, -0.26948021369661695, 2.086679409583672, 0.8931666462534852, -3.8148376249382765], 'positive_zeros': ['0.04219650045041716881365930878', '2.42010295156675898278965184765', '3.26625696261632147775813424394', '4.28160331283068429516282613116', '4.91517964479406220819464187692', '6.35584048035190313433494832223', '6.801146541030231282316701541010', '7.563726992846697181797162946156', '8.775428662083665464394362483002', '9.23494404510957028772914705794', '10.62787750588607384277275760818', '11.6610939384546656407285875556', '12.56211806178466029159694184863', '12.8203854096153113889231326159', '14.24754464960501016573324149298', '14.83615612408903991615487655075', '15.53148757767008685434238633478', '16.13153252566435385106351052676', '17.13213670590108325503764173709', '17.736160361428059128527607557855', '18.96994825880279226368957485577', '19.51091625630147207841047342284', '20.35339725605381193502861646622', '21.677055141974897057075821763843', '22.229998177450852714688037678454', '22.76636416661685373871074522853', '23.50940041625277566428486124027', '24.4059237214627832001861217584', '24.99283504765020709544929051889', '25.88436288932427250086252583474', '26.49522473949569694002223453768', '27.29643217874967900863792910441', '27.959672284445246243680179518422', '29.09535867559574038162027467505', '29.92577186217523260516247140157', '30.81362969823279552311601819300', '31.24225934015182260198500628533', '32.08455369662105045703091070548', '32.64100964254429289649057179940', '33.43505415883814171630858976665', '34.50025226382542849782144262095', '34.761610643542880589347760524011', '35.54584076429670259647502647988', '36.05860035246405960518709319561', '37.13824187414415377787385232822', '38.37423676374133803251421361538', '38.69137717754020684687816782724', '39.39190321614749284533360414996', '40.26283995172289227963439129615', '41.11156773600667470329128358521', '41.63694638640255442450244319769', '42.428222257592021304241342025007', '42.81869083193215280802050048263', '43.78208941439616934181723850832', '44.270763541856145486481564607628', '45.09711967497021296790446418452', '45.9021332821602280355818700769', '46.58591147691390812747769177323', '47.50069600907551839076550355915', '48.29986091517029770046252723527', '49.13671966501485204297706163736', '49.35884298835106570175451089057', '50.6969892057902837276466023110', '50.9459388741479127999155752231', '51.46840317681052202561315206911', '52.093656268927509248521582043442', '53.34668313713687980439128496318', '53.62047297687656616974810956553', '54.41705772135884857843792684576', '54.88374752646245310433214676467', '55.86419832272131382065746053808', '56.983366496106425780793445152723', '57.545577048055764984672964793714', '58.1654374431825389723017288107', '58.82970054479949091154273902793', '59.31214626375780571380058925697', '60.119706113627340429338121017002', '61.05009700465567880019730171998', '61.56491561083708419008961225542', '61.88676230458928462710040986331', '62.79142552263189074173386482427', '63.39838930405677353225307777858', '64.35682574063868421368655860128', '64.82444389976516665742544966111', '66.18148628967412323919388080188', '66.53118245772388959881900250525', '66.95174980416439447172920223159', '67.99253412407771409238153994699', '68.418447498660087857723152654946', '69.29495035259256979741189614794', '69.83051039436122185565102795607', '70.56740456444418784436016667682', '70.98409111730514515548314226474', '71.51986915867822829778505578041', '72.71337095259253315209413877381', '73.092241299330709058971551996111', '73.97136786944030043799234911986', '74.81025669357447350034410678465', '75.22339396078789339784487021868', '76.2525556903569623890865444404', '77.01028117692220081127589321994', '77.43203437296489872504854107621', '77.924790670133643102597103878964', '78.58497482915736039731487102320', '79.36491511595196885536203977166', '80.10591877031195999510097638853', '80.62895358984826002563286638887', '81.35412830820507187511841845535', '81.73991259291878395763736837794', '82.91202705908401075130044777501', '83.36168953737866403426101820904', '84.3740284203205483855499293892', '85.05130029644642543510354109297', '85.60853774238402198416343837898', '86.20228482431509515120199694310', '86.730403139933851221822101128495', '87.55054703293972019347380325575', '88.085428391655388729409087489659', '88.87958142715391179647686700774', '89.35814904369017635385117682690', '90.17709046154747571169845631694', '90.600093472863091047854517533769', '91.04309381634133503394864819243', '92.593912903095304811828513426167', '93.10260485163936417214834209563', '93.48908927909299691559090643987', '94.15530954387652433166893537363', '94.91183393817187667183178757476', '95.72115155816582663085513542519', '96.239393968577270250012917195113', '96.80534004522174164915791691743', '97.42828788702914333419449684577', '98.1508156108756083440680635140', '98.44825483159996572386812824372', '99.469470369653747149539901462113', '100.05446454085009042498531197484', '100.73590270473308437552370095916', '101.44408489561082761012768606151', '102.4116363572019121162779850768', '102.84767726339076087414094947445', '103.577871393734331468008530867291', '104.218965952104862584170817346195', '104.85016038204342949145732639994', '105.52859078125616192620246336845', '106.00142854121588105142266882324', '106.61011131838280238389321404629', '107.14922408322661218060570836475', '108.12409005331953726308823918293', '108.66798625449524244995603403483', '109.23511913297909380296033640342', '109.71404912453947994370962829140', '110.82124464673125934748381285149', '111.48457594681614677383183569432', '112.41431299579283755184419718323', '112.671112008588881546362619252894', '113.422097712954199949287748533093', '113.65222782859637712303506402766', '114.71239916313125729283656941644', '115.418988405922129981077868493063', '115.63702465395442112640726574233', '116.73645990503495977097131413141', '116.987597728014045710474213945437', '117.44234816713787319326876699416', '118.37880728766583969583118719115', '119.26073687913628823993236965790', '120.03494140908124264240957227313', '120.363314795143797301502588865998', '121.458101737619497614640353664737', '121.82608084968391661507545788025', '122.36637825391853764869538537134', '122.971070022081192965796902495912', '123.88370069792186257687859397807', '124.353387188717423957688389091393', '124.99319760491309055481189370330', '125.35994738564721065693275593563', '126.078468395949822992278246513177', '126.746507502052245145008082710050', '127.54189384561093894291049425628', '128.24034289231016716738995996021', '128.98784721449324763841912890901', '129.57464062556195935090876293270', '130.16430177912626212572036624421', '130.91787526736735066554471042705', '131.712238055025705132283524710225', '132.25127068011064657057760074970', '132.705020883825364729211943314877', '132.98195371664243370176885316842', '133.92678590413563096682386639524', '134.86896741891781735331039634318', '135.103363535117340509581843794984', '135.66908760939560867264074237766', '136.4065676362069867654785875127', '137.23438559860180176250154244642', '137.769167584592217966577924148343', '138.78193542526348425591389405829', '139.37208453363642754329446825405', '139.76482306295219832607446586571', '140.518180050727327144364773440034', '141.216143792626158409606030835', '141.46091739683572798864121371978', '142.336796975808811746676479128967', '142.969421910616625836453369315761', '143.44395385451487666212700770396', '144.26235682844167539143949419242', '144.81198861454099343224301130292', '145.09985592491425621887127573406', '145.95431885718034417504076915362', '147.04355137998803302564007436674', '147.657101311380234882988250069', '148.27183118851003878114736932400', '148.67104302949805237111073646473', '149.226153913758905056609071243871', '149.99194174701622804709211733544', '150.87240626810987278848764782056', '151.27451163064225793117933330968', '151.70496183344432060068448376061', '152.34510499535716447304558266793', '152.93872991797555287201758175761', '153.623275858834747296551790340200', '154.286246948713016320166598002232', '154.9822811488064015449324401770', '155.631526105731358421540917363090', '156.56013748029873272218473902690', '156.83657707111432909502900541578', '157.7899987564429746735925302325', '158.25109961550567193665819260563', '158.93337882343735916688228310049', '159.59632868188739673267627129995', '159.85162245517459979882222046953', '160.84704342407312570729845059607', '161.196037318290856592556543134323', '161.74258258914310975023181335318', '162.41503451321675884368133819840', '163.24421461597250967698584788861', '163.90624620117857408813989070930', '164.24684038721787681342119899237', '164.974068585622361070442171386186', '166.09128728185449180024226766960', '166.61071629441158573420061184110', '167.163890076572479455574752282968', '167.54087539306288304815682382594', '168.384123452552430563230012439137', '168.782499252337832380595818618795', '169.342714370308393350401128780699', '170.16195203369308438048589462058', '171.02045479861114231249748130409', '171.2354341446033446977579126030', '171.518062786579220250625748781060', '172.600274731640458745690406341343', '172.97996687152282852029502821612', '174.32821942415254541401001854777', '174.47508643055181060106358076315', '175.26001342406107809556865686306', '175.79102979854920564833970201556', '176.60978767166652050621516610271', '177.05590345155261013604862083642', '177.5008022230401144292708025120', '178.30979843240181635559187613292', '178.94832106296260549200372005872', '179.57601643727176044569361332118', '179.81818165637531205115728590818', '180.52617702215476133422334210412', '181.31935966600471909988579009690', '181.73364279167120004843992163291', '182.73550101294101279148128750261', '183.51225512240736933781299857653', '183.85680077841833710080638518263', '184.46457346254571821230552298596', '185.15530616072423235283627252370', '186.0411829403438740211890248511', '186.43580207258504875917488942402', '186.90565352914083025466104108195', '187.709909838568731864263000858759', '187.924720070938624222620630685445', '188.57660254699326621899731234356', '189.543767479591929216456544424431', '190.03379122746972902886111854257', '190.564193222664551109085914170216', '191.02784110636550758675232496353', '191.85327065581436058055786129230', '192.865521914971548383739915756885', '193.32438533984556613181493275280', '193.766786871642207120646738842610', '194.663557367383172660486252410123', '195.079525873539710981014818601185', '195.57324735778286015920902103549', '196.25387866730954775425062653436', '196.779918536109868204170414195231', '197.45976084001345897391019044236', '198.062619663210003673494156389502', '198.70715918073809501151080276411', '199.10315101579473563123246728843', '199.75080499310917762130113669330'], 'prelabel': '1-837-837.727-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.16255299544167204, 'root_number': '0.522214623479177205430315013460-0.852814098748667020067201025451*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.162552995442', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.635860769282722684840122005646+0.454072764938715466298423266954*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0421965004504', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '2.42010295157', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.26625696262', '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': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.727', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/727'], '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': '1-837-837.727-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-837-837.727-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.16255299544167204, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0421965004504', 'prec': 50}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_837.727', 'Lhash_array': ['dirichlet_L_837.727'], 'factors': ['1-837-837.727-r0-0-0'], 'label': '1-837-837.727-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/727'}