-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2009.1836', 'a10': [0.07473009358642425, -0.9972037971811801], 'a2': [0.9888308262251285, 0.14904226617617444], 'a3': [-0.5633200580636221, -0.8262387743159949], 'a4': [0.9555728057861407, 0.2947551744109042], 'a5': [-0.07473009358642425, -0.9972037971811801], 'a6': [-0.4338837391175581, -0.9009688679024191], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [-0.36534102436639504, 0.9308737486442042], 'algebraic': True, 'analytic_conductor': 9.329756776881393, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '2009.1836', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 2009, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_2009.1649', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^55', 'a^4', 'a^62', 'a^57', 0, 'a^6', 'a^26', 'a^64', 'a^79', 'a^59', 'a^51', 0, 'a^33', 'a^8', 'a^73', 'a^28', 'a^77', 'a^66', 0, 'a^81', 'a^32', 'a^61', 'a^40', 'a^53', 'a^81', 0, 'a^3', 'a^35', 'a^28', 'a^10', 'a^50', 'a^75', 0, 'a^30', 'a^80', 'a^79', 'a^22', 'a^68', 0, 0, 'a^78', 'a^83', 'a^4', 'a^34', 'a^65', 'a^63', 0, 'a^42', 'a^44', 'a^55', 'a^67', 'a^83', 'a^57', 0, 'a^48', 'a^5', 'a^64', 'a^37', 'a^38', 'a^30', 0, 'a^12', 'a^29', 'a^52', 'a^49', 'a^77', 'a^3', 0, 'a^39', 'a^32', 'a^82', 'a^82', 'a^11', 'a^81', 0, 'a^24', 'a^35', 'a^70', 'a^52', 0, 'a^12', 0, 'a^51', 'a^80', 'a^58', 'a^1', 'a^47', 'a^6', 0, 'a^36', 'a^83', 'a^67', 'a^55', 'a^65', 'a^21', 0, 'a^21', 'a^44'], 'euler_factors': [[1, 'a^2'], [1, 'a^55'], [1, 'a^62'], [0], [1, 'a^79'], [1, 'a^51'], [1, 'a^73'], [1, 'a^77'], [1, 'a^32'], [1, 'a^3'], [1, 'a^28'], [1, 'a^80'], [0], [1, 'a^78'], [1, 'a^65'], [1, 'a^67'], [1, 'a^64'], [1, 'a^38'], [1, 'a^49'], [1, 'a^39'], [1, 'a^82'], [1, 'a^35'], [1, 'a^12'], [1, 'a^47'], [1, 'a^21'], [1, 'a^13']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-2009-2009.1836-r0-0-0', 'leading_term': '1.83745129768786683014502708731-2.03570781263772119599176612433*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/2009/1836', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.742322659682679, 1.931617772005958, 0.6808596387710221, -0.71733810601441, -1.1007422703974072, 0.044182532200578245, 1.7657486532087812, 2.34379252740027, 0.9605398394082595, -1.2973111084065554, -2.3226349983061763, -1.0792445467505678, 1.2539430494826989, 2.4526992206133174, 1.5871563541022198, -0.07421735073415434, -0.6772069294739507, -0.006984623854711502, 0.4201073656550136, -0.4628736460038326, -1.675026730544662, -1.4397147757238835, 0.22279272806359426, 1.190226664035661, 0.07213300345613032, -1.4383821148935085, -0.3319634366329903, 3.463434986509924, 5.936086216554379, 3.3091520173751867, -2.9495829951752452, -6.944124653403623, -4.715387724105941, 1.291420725632241, 5.135589416934993, 4.063109442444737, 0.8063855106792917, -0.7213813477866734, -0.1299490835827759, 0.25029132517107966, -0.49725704768208645, -0.8036249356733738, 0.2903921753054398, 1.2437135986267713, 0.546963179502433, -0.4212159626925305, 0.7899284569743467, 3.5620907988543347, 4.346194210487471, 1.5903136790716421, -1.6946278748783246, -1.9568360499063944, -0.053323873020235696, 0.33879093676068733, -1.4473672830868747, -2.051489855151077, 0.2306152686594866, 1.876721193301418, -1.0968494838782967, -6.647801553689456, -8.598309707948514, -4.880281456137182, -0.26436335894748314, 0.48695782490395595, -1.0514433484641303, -0.2838546540482393, 2.9764725430470893, 4.38472776906165, 1.9904760963560653, -0.8198373559959485, -0.6533254832026786, 1.033594875948944, 0.9383865754586876, -0.6997254619841183, -1.0571903452414408, 0.2483356506326516, 0.8052358687248536, -0.10616227195716951, -0.4329709022848626, 0.48564830410511906, 0.5194147346818074, -0.5700542072876961, 1.1345462572901956, 7.63308501464689, 13.454746507592974, 11.308033180219448, 2.5262274572668773, -3.531630840135459, -1.5738696789623678, 3.235001475809625, 3.5744611794788543, 0.007584743100922886, -1.7161305696361553, -0.14872554289473117, 0.8659844917851843, -0.3714639095114456, -0.969706892272292, 0.6244038230129295, 1.5854778341135312, -0.07362568898988735, -1.6855851789165603, -0.5356630621769848, 1.3442563524104283, 0.8700264113521881, -0.5115343159522519, 0.4750668913339926, 2.6644770204297368, 2.107464152502282, -0.8828674184794588, -1.900651555184694, 0.06353816092321288, 1.02073965924096, -0.6969824601866506, -1.3677265038234268, 0.9923812990320129, 2.1303983529132604, -1.185921629877853, -4.295539613539089, -1.3651129512191607, 4.312979460729226, 4.257418745787552, -2.1585276624036607, -6.436484517780966, -3.6108550236582126, 1.2912367884918938, 2.0987670579646274, 0.10003674372541932, -0.37168548766361237, 0.5369108660327209, 0.28122319124093653, -0.4727385481771339, 0.2575585048315944, 1.1450357253833223, 0.06602264647387047, -1.1579844455543666, 0.16351825661511435, 1.9768346525676, 0.7446814111246356, -1.5887423674575547, -0.5430228546243205, 2.2261414768239165, 0.9060843005763094, -3.721105743756253, -4.015195290359812, 1.962173579673822, 6.153312564194016, 2.8840781176136243, -2.261943577098859, -1.7577522430880588, 2.3256086111183984, 3.2196446341417624, 0.7139570899260497, -0.4602968317091102, 0.09548952169552126, -0.9214765973212965, -2.7528740778552976, -1.6638684581590424, 1.1708883043114149, 0.7995071975501798, -2.5872988077265875, -3.5158092784391846, -0.5616972280178512, 1.6045290206479663, 0.5962419477680645, -0.5264498375219167, -0.0026630564367351815, -0.09788339280327717, -1.204630807357481, -0.47389270675466844, 1.4825335152298487, 0.19029733225443368, -3.717144515626963, -3.5848385356931702, 1.3086041312953722, 1.9480483733156777, -6.308782613955352, -14.423881057581594, -12.365530016623852, -3.8262008589829724, 0.7672421807914037, -0.0330609267258235, 0.001848641805453672, 2.1134119512554803, 1.8518701476616826, -1.0750857578119795, -2.14022916144035, -0.4950630613751255, 0.34268321225929294, -0.3055321982722127, -0.058425035440354114, 0.5110543086190549, -0.8775057221487808, -2.2982472794338715, -0.6039269132706266, 1.4017096094708608, -0.9686297885533841, -4.905689607849165, -3.9447479237379373, 0.3879862343365323, 0.8426117409403124, -2.5821411735976674, -2.8325425801640653, 1.01242550467831, 2.2120003828819153, -0.7952995745775696, -1.6968455304725774, 1.2253782472326518, 1.5866006269740818, -2.6722671567160545, -4.684123714807956, -0.9983010030016524, 2.1447267970647466, 0.07911981417610008, -2.669654514434961, -1.6092027971859855, 0.10185454044077642, -0.9639928366897895, -1.969011075999207, -0.32151258900552826, 1.0266568067495372, -0.09388633921325046, -0.8303077464121625, 0.2988377536168111, 0.3037182566115709, -1.4199431498996857, -1.1964284621212093, 1.0183066950920445, 0.742853053260058, -1.6047615784218678, -0.8239200151509003, 0.9733894494474362, -5.175188374224818, -18.220178560264596, -23.941292529722112, -15.164900270941716, -2.7238147268861126, 1.2693938389733606, -0.6978747761032082, -0.6492327844303565, 1.0565183155091131, 0.39860229507054085, -1.027903274930444, -0.38202379271920917, 0.26779540037844357, -0.6907338188453515, -0.2483247235890665, 2.379844554515909, 2.733545712022415, -0.26765110340017506, -1.33120793134655, 1.3584978430529777, 2.5925792759076534, 0.22002851398135806, -1.11228534736616, 0.321940920087454, 0.33527631341000164, -1.5463386311515452, -0.6683868085140808, 2.042713843465931, 0.10572176454658423, -5.375136895393011, -5.638928134277371, 0.10281818284439784, 2.709699979036708, -0.4225982008089286, -1.3441020884003234, 2.675220322154769, 4.109047076591595, 0.08119928072077379, -2.0333166441718893, 1.3802221788774853, 3.9323452229233076, 1.5996734995179396, -0.9515227645578053, -0.4001501283246861, 0.13912033410819852, -0.9421042347292032, -0.9999759411332461, 0.06511328660761365, -0.33950747148412685, -1.195205880622493, -0.32465489822236726, -0.39462706343943404, -3.2421791580645003, -3.3053066087365894, 2.8921250116562303, 7.45927892266442, 3.140410336293072, -3.119751101288259, -1.6480165273692846, 3.187108990266576, 1.8899329047817053, -2.698754969940284, -1.9169527342441817, 2.2169269751986023, 1.96978605420479, -1.338496137414031, -1.4549216395894111, 0.3595774898177435, -0.5025264876286906, -2.0447964403059453, -0.817309640195519, 0.23081594224950852, -1.598512309292221, -2.3747779673967573, 0.2959477245384352, 1.8415006127883904, 0.01965147214997966, -0.4458412705697594, 2.1290247757574456, 2.6533127063208553, -0.2980400371994239, -1.679174188837437, -0.26170144694941866, -0.019007669073449546, -0.6509101749061853, 0.7907797130113232, 0.5101716788071823, -5.794235706475243, -10.727790993077654, -5.09130282031513, 4.21162592480035, 3.420750789533856, -5.262467993579911, -8.108459518513165, -2.9515124510934925, 0.2668671575097547, -1.549151270867262, -2.3437738602904026, -0.5183976591227386, 0.15834353027206857, -0.08159898782319804, 1.0527050407600127, 1.2948895184991798, -1.1599012626390024, -2.5117349578909915, -0.7100071488231019, 0.37589621467934564, -0.5470537306244467, 0.17173540678107485, 1.6567969663017332, -1.0424282302325076, -5.359919740683998, -4.067442157924436, 0.23335895366856854, -0.9444537611899593, -4.970460382613529, -2.206837331443832, 5.1298670614218675, 6.279848161859881, 1.3978556794298416, -0.23251505385612573, 2.0590797251967006, 1.6545693710868543, -0.7684321675342675, -0.15303559292181676, 1.0903822703697252, -1.1931379032591398, -2.5249595012563453, 1.6670576210360089, 5.733721859814491, 3.707919250231211, -0.12303869893474839, -0.3220514498863965, 0.5712932122139006, -0.3127575963388495, -0.5292416051599725, 0.428853515997215, -0.4784957468133899, -2.0057423349981454, -0.6154793527886122, 1.0942134997071742, -0.16943290175106612, 0.2676077047806481, 5.443342649284658, 7.185685548901501, 0.32328991417870706, -4.794679162355899, 0.6696015465500536, 7.451936249021252, 4.600554845743471, -1.4519647218071183, -0.2861659254237357, 4.064093493559402, 3.2948515202219286, 0.05192824838936159, -0.17157536045540725, 0.28517686369095496, -1.2856066761162146, -1.8643234220182971, -0.39275452294273505, 0.05724512797749459, -0.050540105223578144, 1.5422372739016783, 1.4620013817521165, -3.1086033126689476, -6.230804774660136, -3.014355329633624, 0.6718312939752923, -0.6236075397226116, -2.060608045269437, 0.19488777277722108, 1.1508985658685273, -1.0348989125322245, -0.4525893234541808, 2.8359794526867326, 1.3844925396574492, -3.436704363702555, -2.402576128930782, 2.8144073256503668, 1.6986438588185877, -4.651857025283755, -5.420668376087654, -0.36635356056610746, 1.5036884998814453, -0.2870112571494974, 0.40161884221448346, 2.21671503401846, 0.41207520729309116, -2.0908947248986864, -1.0954502102193213, 0.22547768595257553, -0.9934645285415802, -1.4499077983589146, 0.0869711024036128, 0.26177967104075345, -0.523115258240189, 0.6577623536768092, 1.3454421554837068, -0.7698855816673272, -0.8469608791560599, 2.287407294042526, -0.20352032470866513, -9.686258573007319, -11.887584750757918, -0.26220254611061933, 10.391683966567317, 7.705967291969619, 0.11134068824666699, -1.3205928880255577, 0.18833129510811686, -0.5996628765194956, -0.6070476920436818, 1.264276363172209, 0.5742704011734783, -1.85855824496914, -1.034419319620566, 1.1636768788852552, 0.22181673313355377, -0.8690720193269613, 1.3471786142669853, 2.321657330006817, -0.8744634182227501, -2.781982997439655, -0.7503704913871946, 0.3599987929400941, -0.5144976799187365, 0.6099105219695182, 1.800814348682455, -1.3432264600226331, -4.414899867278562, -2.075159199720015, 0.2281654806045233, -2.4643059796164075, -3.5280290486529915, 0.7482644267131635, 1.5141727826117726, -4.4118323496822, -5.671081282518627, 2.161411637159615, 6.980354703827172, 2.2282530259677547, -2.6458333111728716, -1.3552532428930832, 0.2612208492490536, -1.02294788822573, -1.0394896306968986, 0.6071166176004663, 0.462402245031409, -0.37597104277753535, 0.1113654871533674, -0.27740991470468024, -1.324233182651685, 0.6674492119325918, 3.2387268134568306, 0.8451612194388401, -2.735264469504584, -0.9714590067812355, 1.2896491203252238, -2.4520012380261225, -5.688234036286356, -1.7451920373921466, 1.744319065191348, -1.5923974078865089, -3.162302655970474, 2.9452003614001425, 7.2645283220422945, 3.3681312531000254, -0.7853561348711378, 0.1653329545060246, 0.7275769045972655, -1.039641355753471, -0.4213957417756396, 1.4879481201016391, 0.19158973347646951, -1.0091297749808394, 1.98821622525587, 4.155968718776002, 1.6216199708515273, -0.006497005371922634, 2.3691814275471286, 3.3012653374798098, 0.9400456232021426, -0.06607841999424244, 0.5209982996399768, -0.4159371244529244, -0.8603425416998371, 0.5865953968103772, -0.38708520865774876, -2.592032855956446, 1.6272045038036242, 8.206549714360252, 3.395829203239295, -10.004016633922301, -13.529306523153688, -4.180623810113343, 2.131400858518175, -0.4067637813706038, -2.0070624876426404, 0.427046362225403, 0.5663146155613221, -1.3708521081574947, -0.6755990155476356, 0.5131371006068757, -0.7713460770534314, -1.1225875249632657, 0.6426890590188065, 0.47193145819389226, -1.121680659174022, -0.2590663106682444, 0.7728906362306802, -1.0342322121689038, -1.6347447079234727, 0.14342189298150654, -2.363722218736337, -8.744718394956704, -8.953529839743968, -2.4870506153725813, 0.2643717530129225, -1.6066538565819868, -0.18497097463814413, 2.3883926302603187, -1.103380887628063, -5.54308116805803, -2.995626467744524, 1.1011588537433072, 0.1679772678916217, -0.3355074719005963, 2.758580779504599, 1.7350100959505337, -4.8130719387731355, -6.874483189052644, -1.9993950782627148, 1.2207691734182542, 0.2946679095403659, 0.14058794355922757, 0.5801454786350451, -0.9373478947678149, -1.5796018146167274, -0.051369201610077485, -0.20675242690726264, -1.5520830893207385, 0.008883437722920474, 1.8753752667938528, 0.2627541312577908, -0.3966488230310021, 1.9030474071774999, 0.047061747184016296, -5.221156652967458, -1.609425854893499, 10.231943750591384, 13.435271712093959, 4.745637342510786, -0.10965436005717852, 4.01286230324986, 5.4756175166675725, 0.7939853082778752, -1.4560042150598125, 0.3088042562874107, 0.6334276804079937, -0.06888495962350817, 0.4722717815153435, -0.22022137858424953, -1.6452731785394206, 0.2826303933343269, 2.6475126454400986, 0.1421943792791164, -2.7990068874483907, -0.5895465006432677, 1.6547783737794433, -0.6718326683770185, -2.179012690903221, -0.14105885752573782, 0.24840898101851522, -1.0927047139728805, 0.42090907448151427, 1.6484302334894072, -0.9519092921696709, -0.058358312893953684, 7.622173374748542, 10.452959820091012, 3.020331134959261, -2.431629563005007, 0.40844916672685794, 1.4532036189746544, -3.050233662970208, -3.8707087771844138, 0.21216090093527862, 0.6497923442134207, -2.108852392436559, -1.2191888239220687, 1.1693228802820999, 0.0762123997732514, -1.2441138895693094, 0.16783966134659212, 0.7996463198235004, -0.13693220102445774, 0.18352756436208637, 0.19071608096456108, -1.5206044287160565, -1.1379722418501468, 0.4947298320877933, -2.5581394105472217, -6.135094901501281, -1.0600353447530209, 6.0748164918987575, 2.4121965017193223, -5.7120327418088905, -4.066446945555365, 2.713542100428655, 2.3578408798157873], 'positive_zeros': ['0.76634342407141543706250394852', '1.55435904575558733925742827196', '2.63109561975604571636808127704', '3.58175601218204676789177660193', '4.67081395577745088284844660382', '5.31506292608496757277180040528', '5.821302669557884264739696654679', '6.83570257556935699819367732595', '7.51217708685121510341681580030', '8.15948845901894005837186079710', '9.233391587602810172333987303196', '10.24602073739888747305697547790', '11.353136610199693736639457793', '11.92312607199768737053308774974', '12.325342689265701048840169363385', '13.06082007571321039051483313540', '13.8827338532843936978921074122', '14.253170517028004265253564832493', '15.44456119242931067158461014235', '16.26007091914351522011832566083', '16.64158396277767868218356148008', '17.47500725658219992411211868233', '18.05352160530607407159615551963', '19.40448940366511083423223361619', '19.78859092955649820222025569042', '20.34550394294811897473073316390', '21.4430940001901026614745362747', '21.99078001127924096558533735992', '22.67963000956061968730840220747', '23.382598702712414500570550257223', '24.03062695718698300117398939439', '24.5386506095575826917863839171', '25.13953190039823730262781739252', '25.52143964099156957303696237407', '26.968217582883367789041311466216', '27.59473750147630208981247659428', '28.43817727920898884537495534110', '29.085989195363581161130937277128', '29.61453289147997076263072040697', '30.213470925330400582269725461335', '30.92767616867601159019782700102', '31.63677778898380458627019141421', '32.351943545673677753237359812051', '32.73948259779117095354934799961', '33.6574150858767710482398337103', '34.366128807347624282051972324908', '34.896190216599350062101375425817', '35.51613526302343821246599635626', '36.166446038650280695044162512869', '36.94598612051007547708482993014', '37.71842792786903502241952460828', '38.650545375152045329525513553160', '39.39403618415587649514876096246', '39.81424145523339441579621599542', '40.40198185893510276755018125023', '40.87381534559706564302962316518', '41.57408789142605974024259871058', '42.165177366961857360651984107307', '42.89706427374590343130354232476', '43.49357155598938654093716185116', '44.12746838317548306332529795590', '44.91142485196379724594326430056', '45.77714445773830296616819832374', '46.38426987715065981265624159383', '47.2930823864304120480810809168', '47.73731673360578784949732768413', '47.929212653916109316970682851051', '48.920105694515177776117456277978', '49.45775329264806486461645295013', '50.36491395112258055692158770603', '51.0513368266696685021460393390', '51.56374630363732362538740340514', '51.84016212541256457224732555049', '52.56908433576491531024587543604', '53.14168451909799401258061173261', '53.98082702590391992401947920659', '54.47848728308304798935559708897', '55.83038179397577716157239414090', '56.24245926923723785770342754031', '56.56214602782831100377728691041', '57.388177711197979185517176861493', '58.22388273434132297298708380514', '58.61359881043676638523387955872', '59.083015337574304194487271592396', '59.54473338181415472281781387950', '60.378536387041346915492076831845', '60.862497280312798982890220182196', '61.8413216252757781496699496949', '62.27498297403462792091744384335', '63.045579512702708911137494075721', '63.675248943222059670834190650609', '64.255714584677564282570158945716', '64.824245322550377887923203536179', '65.691339372805897565713837444898', '66.25678045913708794896870010923', '67.13716420240820953101624928678', '67.30217352834277381007524137036', '68.17060843871959601128241080849', '68.73169096501575164748292675261', '69.30180290035550899760193067379', '69.75084403168171142445747604983', '70.47683576859637566755193987947', '71.03305441863118018689579753388', '71.65505472761386072566280733951', '71.9874595322481483653591492779', '73.556961961532854009294634449679', '73.96163187525069658131360632388', '74.48089558541479019187684259207', '75.06842640275417751110734056489', '75.725256686680092463876981033716', '76.05491159213661421551542896871', '76.598607510928070906109129899438', '77.47314940884931983870357315005', '77.99027516357146127873288204438', '78.77540271676135964563585195076', '79.3127806129434650825821205752', '79.74666075193181767464596394895', '80.38209992212009815330271112755', '80.94410840885668194298834700983', '81.869432801206780896342616472630', '82.46387757993105152790799826606', '82.93916471871114445742552761822', '83.755583251183057854843435950544', '84.27719719795555190277302619638', '85.15255967850822685645465927229', '85.73569890923279264583765374810', '85.99846041432428379196137391393', '86.84557431883868857281048772783', '87.08257935727350017345920075127', '87.93046960886908230075007515797', '88.01601061779638859495957824585', '88.93951836084942969528770325327', '89.818236587210398046213556528467', '90.40693495441049910488679892518', '91.05462242905860610286760224315', '91.69834581626240647675247628456', '92.36385173263211448279405573288', '93.036910454063286953989897048699', '93.354857220294938536905929422941', '94.20679114991112895383844858027', '94.449580583803191579656265583277', '95.28327875179931931772564708841', '95.94043094177081398189672262544', '96.32141346371925879867880163768', '97.15782423718227335383713565920', '97.88143249870619648148474153893', '98.11773910342455226454484707579', '98.620011761075105513176421927868', '99.10361835503782567008409189786', '100.15246133996675411058343363736', '100.75399407643509606747054374788', '101.787305981078741129763896943826', '101.97601191993106728381214811292', '102.929829735603301268989315844739', '103.2392084787080078648412239879', '103.48504518894440422776654372064', '104.24842669175138476690616905008', '105.114878955133207881020684056993', '105.45680845744711089144914697763', '105.9089477949969402034083418130', '106.489982370369899852845446268809', '107.47334658765548185254880546726', '107.73270670991626222813901302299', '108.53027302864870350801529515243', '109.50001521978470928521255589365', '109.731386480284346113571464828774', '110.50413801216730175257033857876', '110.961101321774193870006293468922', '111.442181033810307815882311416574', '112.093863911419802255976623839113', '113.1087807059654255077649880997', '113.51493478020899087169313729617', '113.98006505249616347435292476369', '114.53087376870771015476078850610', '114.915814051639452333447394489272', '115.702259428813758491748726430001', '116.21951458257129009630734297880', '116.53483950249704252910270340267', '117.51186983950599396473871386421', '118.101065155142817836383729434347', '118.96140309783753256796129458124', '119.39419361602779884826724387060', '120.32069301091525215313518424635', '120.677575952135110365413050088926', '121.02351108713316637653031041808', '121.98958648873892474375626440381', '122.22979724013136428585449849933', '122.51931868845033597849757551918', '123.251172684445308457542336432331', '124.2771042669398328412281598393', '124.61271853512786954194783856194', '125.2905665455739190835038076308', '125.79794659306482008630430103888', '126.29376035964922833127220143922', '126.96055157373793518874196865800', '127.63545628199550914189997304563', '128.211777219093208821868785705885', '129.087848846506284472060689480289', '129.62879499537053835221324520157', '129.939753463634472893497024682492', '130.66430952455175506456836615280', '131.4384752891479323269991477134', '131.67331711368949665841904366312', '132.4807596695782913371896051815', '132.892189710753574640688470711119', '133.31810649577863450629223904468', '133.96344925246930582851654540989', '134.46452926741043860165639519232', '134.99127089684584446836600110346', '135.94312640999212753158902070214', '136.88181915849545015447071249585', '137.428435309069333396473013483099', '137.66275173085927688142827506781', '138.22866645876719170832945586157', '138.81777953451696905765263116077', '139.496098382145344524467159384', '140.03355450837550448370225928101', '140.47377747543284574219553594259', '141.17906013395042392251212739017', '141.98604952387724349950979267634', '142.31665714203265251099981343114', '142.71753996404470250664714259979', '143.34171411199559217100836233393', '144.26915142926197064743224155831', '144.44145548650165208009547021591', '145.26223189364934841215721990450', '145.72371508646013836550388679626', '146.48827961218254423677311869678', '147.2925526284861862925051509975', '147.995531604558713997451229111', '148.2310978032334164668671377034', '148.93570615794552716678801884205', '149.50223408340162616476465167239', '149.943512847932105567087254774056', '150.236173559678261501217166770788', '150.87366852006915727289501500897', '151.62028616982332576250150823890', '152.27004137806791014625903008559', '152.66055033398729464196117556343', '153.53732930661227439255991935412', '153.95573517938942227678346049246', '154.564281519208437612045270870783', '155.52230078215424572679632206415', '155.91118713736489669366179211688', '156.38297591546909551888583411119', '156.93155975929061120061242425996', '157.524703241721406972640102267282', '157.95954565332497796821822528568', '158.96561177720283274806937932812', '159.06500660181165781750902421560', '160.176680355470879015796457358473', '160.352454668250673236320668234436', '160.84526586770190091668741089210', '161.43463255649160863180301151233', '161.82859411158043261406091026241', '162.42846504190158950749040694351', '163.20722476371503709517678050694', '164.20722451020272675957070683258', '164.65513503340835170166409519335', '165.257973450735784956665510417012', '165.71003674703872886337687138591', '166.366871734546069868191571377729', '166.73260593676908816812939162526', '167.38559367101081046105025022154', '167.89406048860859570476205406251', '168.4810337330320093089800555786', '168.9203831883362433926689499459', '169.64570054009082557739591301181', '169.80676049074591901112144316569', '171.117514858446829074735112706816', '171.31347711365126917080530983679', '171.89124974912734729314328707454', '172.43919722254778669288469213462', '173.31610879461093502684769883118', '173.77423627820781817503101932001', '174.10824661156599503984440053407', '174.78053254064901938445723796830', '175.75691561961201333048811549091', '176.35085714388383150900287848700', '176.49618575695009877600639355179', '177.03064368473381045634210161686', '177.82532087713329355968070455173', '178.07780303095218178467822593870', '178.748996656668086478605584294536', '179.41226427564355463195342432756', '179.7526776693927718348225473481', '180.315316623660682353217985260276', '180.984829514990917706516988421008', '182.11659302636047209633925180688', '182.21447109558959608308400699092', '183.1799714521409426152136221933', '183.698294603978628882774776568139', '184.29091680169811526670133332755', '184.46069587341783122000914512325', '184.9590463920540932600581925800', '185.59847426860447356051421411489', '186.260516354346487141782256695699', '186.9252516278774707711799594031', '187.43543709302033096369137134320', '188.146904988177050989842095217167', '188.489671533662369031490924633921', '189.011045423870345997247878561872', '189.5882650579029162987461854403', '190.00346090791188795331166503086', '191.05327886778702620193891605194', '191.53145403548531600551624214669', '191.993431135141545587378792681547', '192.79391250012366459411113096559', '193.198196954873826042991126607877', '193.878467858138991296483521189048', '194.385629706393715836735712974454', '194.97065768188487835106967439235', '195.56549489034816448445099770284', '195.865881040524133892540716677741', '196.29429120106388162174667246108', '197.038860610772460323046147285169', '197.30574438917783611603615437476', '198.16228825642598945036350443000', '198.83170304131678547445868144859', '199.54555239543845762943442854051'], 'prelabel': '1-2009-2009.1836-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': -0.5325584242885723, 'root_number': '-0.102107043514949262086364000263-0.994773417248689983228431642108*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.266279212144', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.59017330963922199728761448972-0.689479669342350907663274309840*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.766343424071', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.55435904576', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.63109561976', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.329756776881393, 'bad_primes': [7, 41], 'central_character': '2009.1836', 'conductor': 2009, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2009/1836'], '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': '1-2009-2009.1836-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': '1-2009-2009.1836-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.329756776881393, 'root_angle': -0.2662792121442861, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.766343424071', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_2009.1836', 'Lhash_array': ['dirichlet_L_2009.1836'], 'label': '1-2009-2009.1836-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2009/1836'}