-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1009.101', 'a10': [-0.8532908816321556, 0.5214352033794981], 'a2': [0.12434370464748518, 0.9922392066001721], 'a3': [0.7330518718298263, 0.6801727377709194], 'a4': [-0.969077286229078, 0.24675739769029365], 'a5': [0.41128710313061156, 0.9115058523116731], 'a6': [-0.5837436722347898, 0.8119380057158565], 'a7': [0.5425462638657594, -0.8400259231507714], 'a8': [-0.36534102436639504, -0.9308737486442042], 'a9': [0.07473009358642425, 0.9972037971811801], 'algebraic': True, 'analytic_conductor': 4.685776300584035, 'analytic_normalization': 0, 'bad_lfactors': [[1009, [1]]], 'bad_primes': [1009], 'central_character': '1009.101', 'coeff_info': ['x^252 - 1', '0.999689182000816 + 0.0249306917380729*I', '\\\\zeta_{252}'], 'conductor': 1009, 'conductor_radical': 1009, 'conjugate': 'dirichlet_L_1009.10', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^58', 'a^30', 'a^116', 'a^46', 'a^88', 'a^212', 'a^174', 'a^60', 'a^104', 'a^109', 'a^146', 'a^105', 'a^18', 'a^76', 'a^232', 'a^169', 'a^118', 'a^21', 'a^162', 'a^242', 'a^167', 'a^57', 'a^204', 'a^92', 'a^163', 'a^90', 'a^76', 'a^82', 'a^134', 'a^131', 'a^38', 'a^139', 'a^227', 'a^6', 'a^176', 'a^14', 'a^79', 'a^135', 'a^220', 'a^140', 'a^48', 'a^105', 'a^225', 'a^106', 'a^115', 'a^177', 'a^10', 'a^172', 'a^150', 'a^199', 'a^221', 'a^37', 'a^148', 'a^155', 'a^134', 'a^51', 'a^140', 'a^171', 'a^192', 'a^159', 'a^189', 'a^20', 'a^96', 'a^151', 'a^197', 'a^40', 'a^33', 'a^87', 'a^64', 'a^58', 'a^234', 'a^87', 'a^72', 'a^122', 'a^137', 'a^69', 'a^193', 'a^13', 'a^26', 'a^120', 'a^198', 'a^211', 'a^106', 'a^215', 'a^163', 'a^112', 'a^31', 'a^25', 'a^164', 'a^65', 'a^173', 'a^161', 'a^235', 'a^67', 'a^68', 'a^31', 'a^230', 'a^169', 'a^208'], 'euler_factors': [[1, 'a^58'], [1, 'a^30'], [1, 'a^46'], [1, 'a^212'], [1, 'a^109'], [1, 'a^105'], [1, 'a^169'], [1, 'a^21'], [1, 'a^57'], [1, 'a^82'], [1, 'a^131'], [1, 'a^14'], [1, 'a^140'], [1, 'a^105'], [1, 'a^177'], [1, 'a^37'], [1, 'a^171'], [1, 'a^159'], [1, 'a^40'], [1, 'a^58'], [1, 'a^87'], [1, 'a^13'], [1, 'a^211'], [1, 'a^25'], [1, 'a^31'], [1, 'a^148']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1009-1009.101-r0-0-0', 'leading_term': '-0.459256562383872415246462191974+1.34693711120600922486533095834*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/1009/101', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-1.4230798191375778, -2.766693537882512, -4.585983068700865, -5.837776995254114, -5.404754622416805, -3.037833832795791, 0.2648415489520646, 2.757808344936699, 3.1260093227839745, 1.5005980313636118, -0.5813754295971424, -1.3872248694849336, -0.42345184272279385, 1.1914842707278819, 1.8371109571206596, 0.997180137884261, -0.209081812816006, -0.17441524465688513, 1.4700585045800856, 3.352002421705997, 3.701773506399911, 2.1951634998545377, 0.29962035515493396, -0.3294741200034889, 0.32738993916989517, 0.6986381580850858, -0.4358298583534589, -2.338707932760225, -3.045303822300013, -1.724782313717144, 0.1424662769633766, 0.4099539065404106, -1.0181556702079526, -1.7638360712870353, 0.22925996587816141, 3.7251969862581307, 4.805666460619876, 0.9437456719103505, -5.812528338404351, -10.35503579974133, -9.411052787210936, -4.586489133788497, -0.3254949957725096, 0.7228129403320498, -0.28430850020679777, -0.7781731878100095, -0.10550470391135633, 0.3157320534881724, -0.3745205402460911, -1.0372921910358575, -0.29216379393502423, 1.1852664226276741, 1.349259978387902, -0.2692799210747014, -1.5504781453025465, -0.49560835042030466, 1.8470624539910316, 2.5054054358469497, 0.6588716332563817, -0.8409474794579063, 0.9646239371138512, 4.882811869381278, 6.497398655201954, 3.596596731185166, -0.7937997263982408, -1.936663277298093, 0.8727518527468646, 3.714630709330136, 3.25312399340719, 0.7928820915463719, -0.02050073305164582, 1.6215970644113995, 2.828964145741298, 1.4128499377674104, -0.8716922180326268, -0.8396726732734031, 1.536804410134676, 3.0508592686875704, 1.7375382609016705, -0.5310828286395518, -0.891282935891654, 0.5572672464331234, 1.3585824018392991, 0.5648802036435002, -0.16750235294123036, 0.31536984819971214, 0.6562008077759173, -0.35821714741034233, -0.7108257861374208, 2.593888264562993, 8.249158188669876, 10.472693642930572, 5.801036448384564, -1.711619381946787, -4.578209280900007, -0.6850672617039603, 4.5438602692842975, 5.305924287812897, 2.1907589672675396, -0.013975676348978025, 0.6165247796616877, 1.3482715883195988, -0.16475562667819132, -2.2504357505183705, -2.15198875893589, -0.32779493190351605, 0.6128697587961107, 0.13193610542870818, 0.08977668650265781, 0.8847528583859772, 0.24336764468699665, -2.8140171977299433, -5.255920300983902, -3.7461090904599654, 0.2763353006081701, 2.16767710440871, 0.4834656539313045, -1.3303241420059513, -0.5659005517053528, 0.5580050832544723, -1.1861492791641561, -4.1610141225941195, -3.6906969412011943, 0.6693791457184252, 3.7250463491570596, 1.927271223115409, -1.336619092059977, -0.6294832407545042, 3.5397688870143336, 5.471158267313776, 2.5215111645950326, -1.4322677231241772, -1.940913372371328, 0.09531354046654454, 0.9554262527269173, 0.049260292713009884, -0.13338484075042015, 1.0730305459696527, 1.4573067404778193, 0.12175472354612352, -0.7844529808244319, 0.06699916499198456, 0.6429863262622342, -0.8093467467196969, -2.1252060403504034, -0.5317616275705972, 2.0780131672542277, 1.4555549041977371, -1.6047523570628888, -0.980049114855941, 5.736171201513535, 12.05860308173508, 10.262125706303294, 1.7434048508818436, -4.768984749284244, -4.4532751825407715, -1.0687015034379, 0.1713368938438924, -0.5279658602994708, -0.386306093193904, 0.22332340805615053, -0.861594134230323, -2.6020219177952306, -1.834596637811091, 1.0481069482902823, 1.943827188983299, -0.6015219166874417, -2.9300024610701247, -1.9732361641787073, 0.19575370552546908, 0.26689800939852143, -0.8907699389605517, -0.4551708349356625, 0.8334600039109135, -0.03614709379507075, -2.378549240663469, -2.19344802488363, 0.8237595254950029, 1.7872413815762112, -1.5523500891125166, -4.207504190122436, -1.242645518549946, 3.886514005856183, 3.769839936554013, -1.856558187661033, -5.551857666927403, -3.0985291219437716, 0.9476424630985786, 0.9322758214937361, -1.8166257356549038, -2.5083600391976892, -0.7517036645463223, 0.03423151083133366, -0.9669975251830656, -1.2802804009030075, -0.2679441055415679, -0.07923672997539366, -1.0931812338664768, -1.010472813471263, 0.41886084873322016, 0.3455414051791993, -1.549927057452943, -1.0401314422743666, 3.6945866131787652, 7.27530258043426, 4.139891454799867, -2.5763567233208904, -4.995757641035676, -1.8601639380378177, 0.5338254742972693, -1.0595040074905007, -2.2047818307910196, 0.7906521889742821, 4.130600016456038, 2.7804497454317074, -1.1791358615605365, -2.116026187367896, 0.15926316483896596, 1.064961565479458, -0.5259213206318335, -1.0566917661251611, 0.6226586231335706, 1.1019680356633037, -1.0997197442547708, -2.45829196966695, -0.5183744259125325, 1.7551709647864444, 1.1096292545625182, -0.6204193783674283, -0.28587525981338, 0.9377627756877753, 0.3155945106379674, -0.9374276501524272, -0.17115507917782435, 1.0129089899322594, -0.18943167295082017, -0.46218804898464866, 6.354297252242479, 17.8713297144828, 22.82561845571682, 15.474092734067218, 3.7646754136801754, -1.544614688509081, -0.3562089285043928, 0.1260622917014429, -2.2677251782729897, -3.3076360585550324, -1.3112348241264833, 0.31372390436595277, -0.25313292520214464, -0.7131457935915931, -0.04663038048566657, -0.5157425454365797, -2.467620763637451, -2.675181506622724, -0.2505640369368672, 1.0317126360430373, -0.7453443777899219, -1.9295342247255993, 0.20729671442680017, 2.289336475350576, 0.9073149830668267, -0.7804281433204066, 1.4350659786636375, 4.476114621833111, 2.4658956605348035, -2.7490722159961005, -3.654484811051067, 0.8935279549744525, 3.9651997496618123, 1.998745264127431, -0.25812573653858517, 0.9768163604501461, 2.144037780327039, -0.16061811424741734, -2.111615391513687, 0.8008463127510842, 5.281273855778849, 5.097933389488906, 0.9424718033867436, -1.408529751119693, -0.4276858831059083, 0.43189752759633193, -0.12143809694358895, -0.0365517714983999, 0.7454386935412218, 0.2087209974269023, -0.628388915620285, 1.1477328134284845, 4.006752849235172, 3.43479738823132, 0.19712450255169717, -0.27580067605357483, 1.8601816912102198, -0.41695778815760676, -8.687160500870352, -13.93620589025892, -9.402693797727727, -1.3413088990905144, 0.3341434394317688, -3.5663634947574683, -4.850883564534155, -1.5758849734927343, 0.834219337278501, 0.08632140894261586, -0.421108968594994, 0.6568975490388385, 0.5299727180322982, -1.236383538766431, -1.5045145988352984, -0.0412219909201046, -0.30291411075308805, -2.3703388944569546, -2.045996043416948, 1.151838456477809, 2.1589558894650485, -0.9190239047627178, -3.251747871298103, -1.672480890593652, 0.2898646375002697, -0.3398762420626839, -0.6636671486572079, 1.352141579348417, 1.7640410724641284, -1.7037198144016243, -3.5310771485711614, 0.6533991497487367, 4.842673705252818, 1.203470940185336, -6.564380995688897, -8.202342134515206, -2.5481937333165803, 1.8731112070415703, 0.8592099182291361, -0.9523542939190592, -0.1518408440658498, 0.497244267807726, -0.7088368437503582, -0.7671910164810425, 1.509316173507243, 2.597390658609353, 0.8187776107496423, -0.7145437701582263, -0.24061189130259078, -0.0367912826199574, -0.7939460956939031, -0.18595352655485178, 0.7207758387522101, -2.5978191306694383, -8.787316110505394, -9.747740531847125, -3.522207775387794, 0.6616931992647791, -3.7105047669974547, -9.829285580971256, -8.499877089326386, -2.2823871989589914, 0.3346650768798045, -1.1192617810276675, -0.9399057501798008, 1.2735879731774884, 1.219650903025911, -0.6553656442170224, -0.0935531302764792, 2.1186688240349336, 1.380708446173784, -1.641749110765533, -1.9286231153572553, 0.5614885314744074, 1.0360262954647312, -0.9936428979913453, -1.1829212044293185, 1.0317229040694005, 1.6051706970193644, -0.0868009668480035, -0.5381355750439087, 0.3802839531082163, -0.4967488072881134, -1.9843868867293522, 0.08646097123476605, 3.6065964426818145, 2.0826382778950494, -3.2937566496450312, -4.111674125052489, 0.7128497726432382, 2.2290431426702004, -3.001918974561204, -6.184505623486242, -0.9242793651080735, 5.997194752373505, 5.875020430832554, 1.126133192600075, -0.9667803665261141, -0.0642887046979862, -0.11102494750139347, -0.9329203317836745, -0.297832566055258, 0.5109024499484137, -0.15087631851958055, -0.2762214667983081, 1.0335833068894835, 0.26839836412381146, -3.6059285394371337, -5.227020429767573, -1.627995760023331, 1.7907263250768588, 0.40795298096282107, -1.7197851690715924, -0.21364734910179264, 1.0197581489605132, -2.039546468811202, -4.196461458960899, 0.29553916046476675, 6.247894303121073, 5.348919993786338, 0.044949146224125706, -1.3357285364633185, 1.2448009736652788, 1.4779153902831776, -0.8651573409016251, -0.8614351791140873, 0.8394253461204784, -0.6286133212345532, -4.012366955594034, -3.5305306416300666, 0.4216696451949563, 2.027368755058648, 0.37825700543286295, -0.2872620557109769, 0.5814373614825756, -0.18361377007524568, -1.983457514483506, -1.5406140371276251, 0.17056074916319375, 0.16969388397197557, -0.003383323496904171, 1.8017224222787598, 1.9313287594910642, -2.1221958965050773, -3.1525152906497005, 5.781429873163269, 16.853039252599153, 16.14488535316314, 4.460979205051742, -4.077739923984171, -3.095130802174442, 0.11807047701345938, -0.16786987428885342, -0.7802864421832649, 0.5234588666098161, 0.4003770372882468, -1.9226315039726625, -2.32867882452085, -0.07409562436187685, 0.8634403037306512, -0.04002253103189965, 0.7048595221931349, 2.6451074511253037, 1.9505493910232468, -0.38235961731825424, -0.15195514493534554, 1.2372878203210234, -0.6688424892563727, -3.551716752190614, -1.570905539912688, 3.1731012049274803, 3.504166885725695, -0.09195214986160499, -1.0645029529748036, 0.652603149435993, -0.10995525549157892, -1.6843367313315003, 2.0885193946840426, 8.430357447715734, 8.194562483406886, 1.8032579372564759, -0.9473611248709498, 2.426886942040455, 4.059623568522589, 0.6221515283646022, -1.8680101625284178, -0.19470761694740574, 1.195923989670486, -0.15394738305823508, -0.9530039580682695, 0.0599040694637792, 0.18267676847260794, -0.5384459881255381, 0.455692623111021, 1.754628923721881, 0.3516356150624349, -1.4237663064306378, -0.15966234796559983, 0.9202146585001896, -1.8570562012380851, -3.4884018249173208, 1.4628621893022706, 6.7835366403291495, 3.6192950612855874, -3.3479823408741307, -2.8271424401718055, 4.02920175966156, 6.298576704689645, 2.0854491784235734, -0.27042891501522653, 1.919680275083414, 2.8760215380215204, 0.683770788865171, -0.4423655632966524, 0.37632441580698495, 0.2529264103160517, 0.1000569289277534, 2.280494398128467, 3.338902265165926, -0.8270385418202262, -5.965276399727894, -5.496370342107823, -1.461706408327134, 0.013429058056018224, -0.7307943386039876, -0.1362064828522464, 0.4591790091530224, -1.0315382370213573, -1.5748505155684949, 0.2509119323163525, -0.62947568561443, -5.6070233468362485, -6.672767451664228, -0.002594998621669655, 5.1374641164561075, 1.2925633935065903, -4.146264132761993, -2.0711912025181345, 2.8126020178947417, 1.7858014213718754, -2.3480716721001142, -2.0788330397141523, 0.9510795779401736, 0.8636829824173373, -1.047692751771805, -0.46602089034581257, 1.1229327353838072, 0.6487569010727318, -0.1558127366467635, 0.42368493695308596, 0.04604635495121297, -1.7159781747681428, -1.4867445149706426, 0.2936939747405309, -0.6456125709345537, -2.602517045925935, 0.6107953669987504, 6.775241789662665, 6.879709311672038, 1.241474010092904, -0.27211775298858176, 4.008309859658179, 4.82707603827051, -0.5517595845558911, -3.737400790140078, -1.0540307377197426, 1.1485298320863437, 0.0017602095896665391, 0.30775736921749963, 2.6057801522819, 1.2273080922998028, -3.4676473502480967, -4.347481457520587, -0.5388701422717689, 1.429674381993576, -0.07079551855904886, -0.45620271028483916, 0.7344013737412078, -0.1098752685452708, -1.83186640650723, -0.6806331987695091, 1.3305956213942471, 0.3079389659901521, -1.416894217628836, -0.36650613441589186, 0.7155237402376311, -0.7496820587748362, -1.1308391418889547, 0.8758733051424108, -0.307854596235505, -4.691462838904514, -2.0724680022405346, 10.178051808162435, 18.03280545716655, 11.071393503665343, -1.0783012686088518, -4.546306474184757, -1.0244603908302148, 0.314284248908955, -1.0159266444042252, -0.7255823315206258, 0.16796186889465786, -0.4509090353460882, -0.1475970204435581, 1.973363352135543, 2.1768865417037047, -0.07450919129052401, -0.5818925483762807, 0.7318153157023041, -0.18378057226269287, -1.9474297728038308, 0.31387703653511223, 4.118278674533306, 3.012449003551909, -1.0556588069325585, -1.4256453106094251, 0.5820127330842085, -0.11956536282933174, -0.39508170880176086, 4.697004316560467, 9.274629209555613, 5.302474145410049, -2.1767437252589907, -3.2104243599541507, 0.37614647683967606, 0.8911572817600677, -0.18432896695516873, 2.4593323316960656, 5.299452854319474, 2.661765126725643, -1.4781962659229964, -0.9956260324807288, 0.9546530397490234, -0.8399342651673897, -3.384317507350094, -2.2197075155180683, 0.10280520820647454, 0.22507078857238452, -0.0479918207917617, 0.4536162005371404, -0.27872864770328354, -1.225802409991466, 0.30287086724464923, 0.9846073933336743, -3.1344712059255317, -5.945085045923795], 'positive_zeros': ['1.84937398104984311600250929908', '3.02735058084224014542440513099', '3.83048208831743930330563146021', '4.930396806708529792226501350875', '5.36293266112586503875272191408', '6.94913140535766580837439577656', '7.377766157912451291300016146424', '8.04373148218290487409146808633', '9.34355401375698315256639908851', '9.80062256090819925556648111878', '10.60265583185428644625938980354', '11.609567407171027786490028832117', '13.165185808864485226579098856839', '13.6733802557288772785677564009', '14.41572469555113284628260184385', '14.87461575902392429717913298110', '15.68601995687094369625140843215', '16.519143734619400575935413652462', '17.255108993893578778045862771001', '18.2173792057222369074268760197', '18.650248795675073748432092757052', '19.93340810779610483489131438821', '20.54921231125010337941899387231', '21.72608091014272193274275701465', '21.883944535439646439726094828784', '22.98831270021732267472982450362', '23.56568031613825829013259182194', '24.60034224611596188986988849480', '25.204776311792483826807823903389', '26.11968961775123696457104832925', '26.42817000755049235557679779625', '27.10182506482325580541203452243', '27.61324759075112206335902345689', '28.98408346652251096215394277046', '29.72388168323632946931736491138', '30.93090432998894334289947224579', '31.07169648645546157994921680159', '31.852887601668212396105332481317', '32.87518225678502539717330101639', '33.5234533731287667666021772329', '33.69236751518382846060386966295', '34.409738965044501475054019135377', '35.60199066269705749470363084841', '36.310826249333035795136042047689', '36.98312810066817714710398890342', '37.35762551915066744426809534224', '38.394179183396441803827026158270', '39.22519207574714748860636372231', '39.74352610751239254480985148737', '40.80437199130851820062757879577', '41.547496981627437507917879386022', '42.20391217446897526546991712550', '42.54860052889531891761414260566', '43.46182687189865913481074308253', '44.045527487845122561092584883741', '44.55515668990527555274163100610', '45.36895090534478297588133283973', '46.0835292654341304521335273406', '46.62688727265295442507589289986', '47.874997548777852583058265858390', '48.920814046660859341336965764185', '49.16601397571845244832914465879', '49.8343880612140495943258925909', '50.13687926390721238443126785746', '51.13662735196484689761131902445', '51.817322984105681819474417858874', '52.7732879363578100879897990983', '53.19473894740972056556896879254', '53.84567778695249708411658068368', '54.36979554313401100386305485471', '55.23066111665147826084571928162', '55.820984334343832736816102282328', '56.63237101842651592867282331571', '57.40711431689440797139666276972', '58.34334084648771608898395269156', '58.86098999616810840542258111514', '59.874807628022606926981018973658', '60.02318632702824356341989896310', '61.05153466452931829609291835861', '61.20651639315386387518297502112', '62.09260089522150611272815433639', '62.56572905002170844894704040228', '63.21452657558560404643602032387', '64.249898565323271438398633592354', '65.17796516747998088891892399242', '65.48247839907006901238957754438', '66.19122275447757662755978137768', '67.08635019246898662029677856670', '67.79151534896579273802388740910', '68.34806833620518942903659655000', '68.960155426132305971229642437214', '69.555825164667590062668984409026', '70.368049367303739699004970274140', '71.11391900304015354080659458678', '71.62517819355540150459461632391', '72.25093968910675195412565484871', '72.84489389206501404394426441344', '73.406434496879066271277239349627', '73.79496105923799165137538898106', '75.46857677201625834607963019822', '76.00034127286155617912146101829', '76.27610839580815037629594869622', '77.388094444253634326714218042414', '77.73388193370597039533926027817', '78.469871305517563561529384121499', '78.5898436003301201420464196277', '79.718303185409052370400065153803', '80.21338726280023346536066074521', '80.91607751480804161472184746999', '81.67788829245315235519274325386', '82.0516608902970226456932292515', '82.95655066215642517712213432163', '83.69665184043795081526315022061', '84.608967934771161011171748444521', '84.84229828295837825386441857903', '85.60950262543651134461384488006', '86.196609509443603936041220693381', '87.2654957176882130600993344239', '87.9064942838227120562900947816', '88.37872224960254154579700555151', '88.76467435750281908053711747683', '89.42698817213090134654298964654', '89.86321992000364239676337396234', '90.96219926646868755326954029182', '91.2948098941546086494661611218', '91.85256223051936075655855635631', '93.213132599982493276112250546594', '93.476204930512672354906974830853', '94.5237255465934451819085800440', '95.02104812003156490798194272126', '95.45322345041167977718299241017', '96.03996162245225841085454348633', '96.886744120021687839086508313600', '97.12137795630324880479905401738', '98.01708780045197278638607470471', '98.67422830177712975541698600938', '99.60278180128741785334029047695', '99.91376991695788703303530190108', '100.4404459651995762067625278333', '101.11939725715628402521178118798', '101.84027899246685382862262308751', '102.54861151601615868928993999435', '103.572162103061930631848102925310', '104.17173345819782203102158701368', '104.72157236230198821872720212497', '105.15610557706489345901279066205', '105.74993620685694087196195561237', '106.68199536158144562158500336204', '107.300935613801230880575263469484', '107.47747333563250964371680890190', '108.16387042336705054403407675326', '108.56808855276688856809760039211', '109.88121837624805398699495370894', '110.11106170471089948625340030460', '111.43650241088806767811604666838', '111.67221135666664426088393296721', '112.31930135182169079416276676443', '113.00171233065704686974454013096', '113.45090753997540494250956781214', '114.20258009658576604080593589702', '114.92813991568690455472431891850', '115.47965974570917725589423420677', '116.11192809859654137594496746043', '116.85852403989880085972802083142', '117.3541332150343656517534136361', '117.72233140001069633449660419002', '118.43050424797540367578072416929', '119.184537285141058574761992289379', '119.955901549869091651535657307529', '120.47382347419958197832947498573', '121.28560839480914609659512011831', '122.28375575650712327207004540601', '122.836543839473790558831701917431', '123.08264858224583116865003490102', '123.8274489674756268998354872300', '124.32473358177327891513422989065', '124.76515887592385959755371055705', '125.34084579127981427996848751639', '126.36060114988083590272481000920', '126.91781552795258860342399923315', '127.52648030705883284662485368317', '127.95986619128170091851072566703', '128.7366144123414433106298316308', '129.690740121634537859993942926227', '130.17032569306823005231645280327', '130.81758565391540034001275857452', '131.38800909309009071081773400258', '131.811168410179923150992060494980', '132.777661282461554540192379977898', '133.511320151270767591418562220879', '133.8580059387380606617194285784', '134.34285753112388752633857842658', '135.269007405316069214428718678', '135.69905945146215794041313384008', '135.93866093536422787913311620106', '136.7320871591359730379885682256', '137.33797763672329255888787833561', '138.560395519920251261806129230189', '139.35318575586291389886724049809', '139.64727677051901615828246211618', '140.20114046819122756054062412046', '140.68906615683493291898671143360', '141.572985906639853622144247834225', '142.16767946417067009271921428040', '142.34603186944691455555271358099', '143.37131338512154522540296756478', '143.77758617870826589907260493418', '144.31168195928549480926700616874', '145.09892058690532916449143709552', '145.9285601972508620975713295081', '146.43539694903095020832267905655', '146.85964991843451173123274730418', '147.38667306492213728089404713948', '148.54663115671965534190488560750', '148.87441519792460777920071043893', '149.73514744557113773467927404426', '150.33715113938671785859773697714', '150.910465577839988825365202939739', '151.54442016170210395069801499946', '151.942838162363239669769986334698', '152.41541714828097659157889819410', '153.16981372852921212708271390944', '153.77273589634646116162089015831', '154.20879571503796769311029102032', '154.933850658346496190647180447684', '155.77295787909904435277626176195', '156.38538610797594744663397997399', '157.37510607611555285339035247409', '157.575811339905875170642003853830', '158.54207432783566933322906811136', '158.93216208901157364862742617336', '159.49304262420437635723251389330', '159.64930496926569420910921073906', '160.581320014991931260034000124503', '161.794524897372908369186155690008', '161.88623944151418023972583593543', '162.53489262126218899419182159725', '162.94591079587902822468230447055', '163.70403358178085971852904788876', '163.99897015074297831312654992216', '165.00010043129724664408850884961', '165.68358486661643353238987479093', '166.36499946744980079123347101184', '166.99921786131658745442120285968', '167.700280573589714574287095387919', '168.25112513351508488559885993110', '168.82645178941639170680055018299', '169.560461263998451272982458060654', '169.820543415099938406692064550225', '170.32199567464409412211808021113', '171.17837975016372294253269439068', '171.46955219085123430171432578626', '172.15510781954038018425552402929', '173.21628675868347329362664340070', '173.46819583805321187257458311695', '174.34626690456639087650776942971', '175.095093593344773670771582200705', '175.62542411521334973851077406611', '175.883695591324596265563456939414', '176.647854241052465575921393326684', '177.54480724081703887349974051703', '178.11199720331834257326591241659', '178.55206660380848784857639309088', '179.04529260912974867349834248276', '179.77179663413081263149775991928', '180.35450432351483519116552166417', '180.99838295184849908861025346808', '181.43773480131105814607705991031', '182.05094295089534636464098251821', '182.474300116860743926426252605284', '183.191194783763898807137138224591', '184.34003827190207356000617153906', '185.115242273798018741747297937745', '185.39854813197366342517870873894', '186.13595711239882566573983965835', '186.39544469095171823384835557159', '186.90222138712956343689492779699', '187.801234937949613787428513215920', '188.25704681002031603842627469007', '188.723678523966032884021492772522', '189.35138810752380854601452242076', '190.21914356502075811958504799779', '190.82405166745790761369805708728', '191.22851941325898457565717107021', '191.606663902938000700353631487825', '192.70622464915490506462452091461', '193.39924478675244218725083773961', '193.93132814134884562823794293503', '194.123891019435061774482644477', '195.17369130742350155685030405153', '195.74662755761066520205077745621', '196.16382258229947826024257115732', '197.164881089914024786318608981346', '197.62147456124631365320284357760', '197.85029647774201178050548228470', '198.37367226043572777414546671230', '199.0197366981805685689439716660', '199.485494236533532202602858343743'], 'prelabel': '1-1009-1009.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.685776300584035, 'root_angle': -0.3954027260736262, 'root_number': '-0.791703382636215845109100635337-0.610905683327936967299386278554*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.395402726074', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(252)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.657952586112728531020712528985+1.00414527321402227821506000152*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.84937398105', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.02735058084', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.83048208832', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.685776300584035, 'bad_primes': [1009], 'central_character': '1009.101', 'conductor': 1009, 'conductor_radical': 1009, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1009/101'], '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': '1-1009-1009.101-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': '1-1009-1009.101-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.685776300584035, 'root_angle': -0.3954027260736262, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84937398105', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1009.101', 'Lhash_array': ['dirichlet_L_1009.101'], 'factors': ['1-1009-1009.101-r0-0-0'], 'label': '1-1009-1009.101-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1009/101'}
Lfunction data - 1-1009-1009.101-r0-0-0