-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4033.1734', 'a10': [-0.7273736415730487, -0.6862416378687336], 'a2': [0.5, -0.8660254037844386], 'a3': [-0.5971585917027862, -0.8021231927550437], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.23061587074244017, -0.9730448705798238], 'a6': [-0.993238357741943, 0.11609291412523023], 'a7': [-0.28680323271109026, -0.9579895123154889], 'a8': [-1.0, -1.4081532572346456e-30], 'a9': [-0.28680323271109026, 0.9579895123154889], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.1734', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.207', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^90', 'a^70', 'a^72', 'a^85', 'a^52', 'a^76', 'a^54', 'a^32', 'a^67', 'a^95', 'a^34', 'a^58', 'a^58', 'a^47', 'a^36', 'a^0', 'a^14', 'a^78', 'a^49', 'a^38', 'a^77', 'a^24', 'a^16', 'a^62', 'a^40', 'a^102', 'a^40', 'a^85', 'a^29', 'a^53', 'a^18', 'a^57', 'a^90', 'a^53', 'a^104', 0, 'a^60', 'a^20', 'a^31', 'a^21', 'a^20', 'a^75', 'a^59', 'a^9', 'a^6', 'a^83', 'a^106', 'a^44', 'a^44', 'a^70', 'a^22', 'a^43', 'a^84', 'a^72', 'a^22', 'a^40', 'a^67', 'a^74', 'a^11', 'a^37', 'a^35', 'a^0', 'a^0', 'a^35', 'a^39', 'a^47', 'a^72', 'a^94', 'a^35', 'a^18', 'a^86', 'a^50', 0, 'a^24', 'a^42', 'a^63', 'a^2', 'a^2', 'a^13', 'a^64', 'a^3', 'a^46', 'a^2', 'a^85', 'a^57', 'a^47', 'a^41', 'a^31', 'a^99', 'a^26', 'a^96', 'a^15', 'a^65', 'a^55', 'a^88', 'a^1', 'a^26', 'a^19', 'a^26'], 'euler_factors': [[1, 'a^90'], [1, 'a^70'], [1, 'a^85'], [1, 'a^76'], [1, 'a^95'], [1, 'a^58'], [1, 'a^0'], [1, 'a^78'], [1, 'a^24'], [1, 'a^85'], [1, 'a^53'], [0], [1, 'a^21'], [1, 'a^75'], [1, 'a^83'], [1, 'a^43'], [1, 'a^74'], [1, 'a^37'], [1, 'a^47'], [1, 'a^18'], [1, 'a^50'], [1, 'a^2'], [1, 'a^46'], [1, 'a^31'], [1, 'a^1'], [1, 'a^45']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.1734-r0-0-0', 'leading_term': '-0.575685801886184914443483075475-0.0832065123231700623896208265965*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/4033/1734', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.581667831486601, 0.35021091490913075, 0.5704138604566905, 0.0609827997458957, -0.3593083242459132, 0.2122997316746175, 1.372939927586736, 1.5744320175156696, 0.028282559472336856, -1.9241310970655445, -2.070666872679929, -0.07163495643928147, 1.8227878430031625, 1.4234795935316855, -0.5663700337022279, -1.4545282365491388, -0.2615855925473523, 0.8931930478510642, -0.02882241770888764, -1.6506123848321939, -0.9174033077481334, 2.0729544618679934, 3.3754886493784926, 0.5729321426613733, -3.093499654675269, -2.4686431411133287, 2.337838429085241, 5.5562689901332885, 3.3323919171832714, -1.151372230174745, -2.302037004964493, 0.21922224429109566, 1.773993147318913, -0.02365346607001494, -2.2145840794373144, -1.6385024806920625, 0.3297869614146366, 0.6186887921366189, -0.5172131089001675, -0.5921900869099175, 0.4796945699185029, 0.5575200198370972, -0.44101427998958936, -0.3990879056777244, 0.48383222952717947, -0.6207262831759921, -3.3633570708464298, -2.6558270235069443, 3.647196912779724, 9.338531194527615, 7.213723656009069, -0.4533501746382964, -4.70807170676574, -2.4042732316969286, 0.6352255007583341, -0.0993851643338658, -1.2770802010141502, 1.1440110233137302, 4.296235255214856, 3.29937955524397, -0.39441980244212355, -1.681924649318363, -0.2165999788755781, 0.21785143864308248, -0.7619807675024803, 0.10798112347371291, 2.722686074660783, 3.0219824542456584, 0.32811196633296563, -1.104285725597598, 0.4248252022431381, 1.208762037108115, -0.8281882671966868, -2.3381078872614784, -0.9636636989197181, 0.3985007247558201, -0.42416240756396906, -0.5957173472486976, 1.4621326099829557, 1.7616494537659455, -1.3948830491586053, -1.5429153142009222, 6.075013292556114, 14.057934342357687, 11.870001521685595, 1.8879806957754086, -3.892274168408039, -1.434304632399326, 1.7646883854726003, 0.5771503871595727, -1.1582067020587266, 0.07820719968686672, 1.5011236934091938, 0.6534761521342618, -0.22752686048629828, 0.24770907200509315, -0.0009699863736889823, -0.9660032199931763, 0.4059863195863007, 3.409739426481248, 3.3642741964776928, 0.18063766126328165, -0.9106273132872214, 0.9880036852083942, 1.0098376016177064, -1.274691167265093, -0.34859931741671796, 3.7393532502943545, 3.394093410945613, -2.8556679806418654, -6.048079152232139, -1.5585984983841108, 3.0153184516750375, 1.142267513419134, -2.3532579979066264, -1.4962527549329827, 0.742148135262815, 0.3040237633080245, 0.17992667232602047, 2.7012903553568948, 2.9905888297950898, -1.8567507146745497, -5.756168965597223, -3.5036781893273097, 0.6108924100368025, 1.0864564991196137, -0.13216655945068362, 0.3057298615341008, 0.7135991089852138, -0.30691775383712955, -0.241040642253673, 1.1704031274362474, 0.6300889457430494, -0.9976451664985426, 0.6420599963186763, 3.5022210295951375, 1.4334155892103275, -2.857863613127069, -0.8355063462252977, 4.964986646578819, 2.7426569484325176, -7.7913058467909835, -13.034379964474667, -7.239556466897334, -0.23378680728231327, 0.5583664116131815, -0.1778060724642379, 1.6962362191502374, 2.4230930846463368, 0.18006033774755406, -0.8423190720788225, 0.5257907882793301, 0.7195002003541682, -0.24657829750543708, 0.6399826272921199, 1.8182940134481291, 0.4064369309829937, -0.5361273018066378, 1.9241007045308691, 3.008994749340936, -1.1016382084154188, -4.553969860636356, -1.969885015178219, 1.671401655594568, 1.0622747275699684, -0.029767670488545103, 1.4960150250787452, 1.077115634640452, -2.271571297758263, -1.4025911306080248, 4.452265000915122, 5.698355622186079, 0.0519994551572406, -2.1267731267428736, 3.1783849341737724, 6.379884080395147, 2.2413757696742405, -1.84596977196567, -0.9405869717522538, 0.2363528363060245, -0.9103854248637977, -0.8581003528278509, 0.290251972334208, -1.2780833953514188, -3.8450039979724417, -2.9551985490107775, -0.3950462132257264, 0.051911013065492506, -0.023235564509649514, 0.8988263911031835, 0.1636175511751969, -1.243048970522989, 1.466726726212185, 4.996116348680207, 1.0681971806635375, -6.09123950514835, -3.811095424678609, 5.913023874708372, 8.112646421938388, 0.6876909041268429, -3.2578263319099805, 0.6036572055422647, 3.1596441592483075, 0.9167231610604283, -0.4246731591199553, 0.1291286348457968, -1.0458956129036814, -2.008552326844019, 0.27708980353270984, 1.9428230294127993, 0.268576659771921, 0.06301656464560973, 3.126882700299243, 3.584308434745978, 0.0948496740817503, -1.110412283600335, 1.0591692920748859, 1.3211324602256438, -0.22419975786424576, 0.46472285876508745, 1.5023832457254263, 0.21421251512273692, 0.7452057711393536, 4.255122717654581, 3.213858023758698, -3.5344877610055017, -5.553174856014795, -0.004231236959550787, 2.696372246782639, -0.31598026078612773, 0.5502158558495371, 6.0411547257542555, 5.131288803661505, -2.762022056788509, -5.722145936656918, -1.1682030832340486, 1.729817111469829, 0.294505027328594, -0.1480608621560359, 0.8926050197414135, 0.46663624427406203, 0.018551823337730193, 0.7166230957365318, 0.033205726888087594, -1.0699145327956987, 0.8081688789485355, 2.5512591267264146, 0.19777801817029134, -0.8751298395971483, 3.8649464996180893, 7.001898657800342, 2.977081382387766, -0.6539632387229107, 0.6888275426039033, -0.9350402678406448, -7.649713144537547, -8.866599572697204, -2.2457096753315096, 0.9754847312023385, -2.3077393346787463, -3.0241354089797032, 0.4467150818207431, 1.0818624936491006, -0.4980711825593907, 0.9530173503329197, 2.336968259739928, -0.42141589857799094, -2.4151285678626557, -0.5201263868069811, -0.3301465582216545, -3.401916560244897, -3.6271714507849184, -0.6025399247356148, 0.08367918167935527, -0.8131636415662752, 0.6218305135652256, 1.6735472293271294, -0.17217649312709205, -0.767896005984238, 0.958730593184827, 0.7241589737131161, -0.20081278469443645, 0.6448014852152946, -4.823871850912148, -20.87954215639418, -31.120186066385163, -20.689589125252706, -2.4579973253528458, 3.4600511250764376, -0.16410134151693376, -0.5377957546192115, 1.4704988337688811, 0.30209224647862576, -0.8272263528504112, 0.37819043645111655, -0.030161656607728564, -1.567348418160262, -0.10668547657468468, 1.8308038770198218, 0.5267730972158738, -0.5787582143263632, 0.5402266939297893, -0.09711228003342309, -1.896250492669462, -0.24714710707507978, 1.7108660249272, -0.6993236280203026, -1.752361739239903, 2.8918771212479215, 4.9534196513438955, 0.030148465106509377, -2.6018308068459737, 0.8389859758519003, 1.7404167414476053, -1.2218656273772208, -0.18278694165861625, 2.7453838169695968, -0.2084875537665377, -4.014661798255319, -0.7968816294827296, 2.971616188186167, 0.19969987298324715, -2.3987464034958483, 0.007709591599746891, 0.4423028627813549, -3.329785837191489, -3.903506098618682, -0.4178540313428205, 0.8098480308129169, -0.15634667755133558, 0.21622329225854603, 0.3702506971672751, -0.16754790008977988, 1.5153895873544199, 2.9803225066371084, 0.5026711991408528, -1.2400423277551391, 0.9082297596803068, 0.5206040888191779, -2.702720106880524, 1.1016359695760871, 9.612038601213795, 8.225141410923577, -1.5136420031094724, -3.670533548474329, 1.4721131607377314, 0.4363558203336518, -5.217203067601727, -4.269485374495806, 0.7207175134407825, 1.1509288206497899, -0.5719328843929802, -0.030833800391101427, 0.02869981254978478, -0.913914637359175, -0.08850820441904308, 0.07934591727376034, -1.6689609135872865, 0.5085747779114274, 6.430389262208676, 6.82900398218799, 1.2241927906214982, -1.150573012301035, 0.4538034511284428, 0.11092596311448602, -0.7609052262807119, 0.21008969113490825, -1.1813074200087563, -3.9212442462190644, -1.4652585263944444, 1.9015111474144928, -1.8401088698959904, -5.113548639449506, 1.2410211297615568, 7.344695651933049, 3.3345934817347915, -0.9987882588800621, 2.401574073923067, 4.249274005447334, -0.35073528167407547, -2.413942727839992, 0.37826561916878876, 0.6313688412811433, -1.4139620401203672, -0.7194552299595246, 0.21415413017517987, -1.1679173988609888, -1.105399786142591, 0.5363746901917295, 0.058143454156667634, -0.560170646276249, 0.8197723858566403, 0.4835975013855854, -0.8670461237068834, 1.5310883577995293, 2.6964216693858845, -3.169647536451842, -6.074196843277264, 1.883967366820166, 7.428248880697043, 0.3249355394280806, -6.529903024980901, -2.9474641942856605, 1.1815433440384095, -0.678808951942371, -1.4310260140591557, 0.325999176549763, -0.6226470421611859, -1.3724361208155265, 1.1660001001851286, 0.6246738062591749, -4.156701897842932, -4.611180904251895, -0.38234543059958637, 0.7760801307939228, -0.4268078794633612, 0.4328269239735673, 0.1900635058157448, -2.311809061102755, -1.6907514395723702, 0.8681569068257008, -0.4003573872187572, -2.381461384382639, -0.7291485906835927, 0.06958736914674837, -1.3062122350089516, 0.2208815629074372, 1.4939383846270111, -2.678520649262931, -3.9692291218163445, 2.5638368468301023, 3.120428368547021, -7.8882954712714195, -12.60054936798032, -2.790334121498135, 5.038008517708352, 1.8516043681544685, -1.6401670314415904, -0.2494767748120641, 0.34306050054273146, 0.04984170058531764, 1.4171033687971262, 1.2004602952022676, -0.8210313515922735, -0.47663928170609976, 0.5409997559020665, -0.35038132914070513, 0.6070261597305893, 3.0195050464677857, 1.329195070845757, -0.6740829954450843, 3.5664705779317583, 7.137419448249585, 3.1145181827786543, -0.6847165492941918, 0.4810300628156331, -0.5067659036526786, -2.709470414620968, 1.6027680165922737, 5.48306153986092, -0.9040432179620779, -7.806388363776395, -4.370022722403153, 0.889809413376615, 0.08358893768150324, -0.6516927522640427, 0.5840841028733054, -1.1018755598769112, -1.9026643393622509, 2.3453060389072373, 3.9933402587689706, -0.4455288027458756, -2.4095292096085323, 0.07191130047243366, 0.05013676620609497, -1.7115943163170149, -0.5044938007284246, 0.7954042247897342, -0.045314464015021344, -0.05440896794733967, 0.052115136613777494, -0.3096543478860682, 3.497370635692015, 8.007348788525501, 3.3968539765869856, -3.964617860926003, -0.7516721499493871, 4.432334577868155, -2.7867974498022274, -11.559977379016255, -7.028259311281503, 1.033720269726216, 0.8820260596635547, -0.203850487478196, 2.6965822306335796, 2.5315341622477048, -0.5863174117413058, -0.2859364607634155, 1.054945173016987, 0.08167899217058758, 0.38872083552442316, 1.6268878531872673, 0.2691663537963148, -0.01564423642284074, 2.7193235139404215, 2.249501778622221, -1.0727504603732694, -0.16242364503691928, 2.052516780623431, -0.0956321683250208, -0.6417657171827752, 3.4755110287668396, 3.7691983392080926, -0.24028775522901857, -0.09099152315004248, 1.3897688027298845, -1.881214937428155, -2.9301025943374923, 1.1998641073025138, 0.31912200996784845, -4.770280749197184, -2.12813222265831, 3.5136980155396964, -0.4899381410955947, -7.034594674242593, -4.3217876160087885, 0.8794465429509846, 0.42805728609637506, -0.5435054782613827, 0.6063725289819233, 0.03314557427958023, -0.7042411633067401, 0.27866796831961993, -0.584714931684042, -2.0768530876306457, -0.18382455187235286, 0.9607888253402669, -1.5034720121710152, -1.8454128607979192, 0.14069223656408278, -0.6164390797571457, -0.16030849652531529, 3.1023182320646647, -1.8314922859826428, -13.223904243100556, -11.088484269804491, 4.859045599746443, 11.500934182214985, 4.180324321456564, -0.6603037994902184, 0.23208985955285152, -0.7152603128945477, -0.9568988472146613, 2.0442861513406125, 2.2749891392234107, -0.0974889153381054, 0.03485912562363247, -0.02961046057590972, -1.4595136938174198, 1.659052383294195, 6.581802148507674, 4.7613128520715176, 0.239005616386592, 0.4160960487819731, 0.9618273639479327, -1.1781158142099084, -0.9886631087996571, 0.542580777935944, -0.6162708115417288, -0.4704645622209798, 1.6621509962005685, -0.32481528421546063, -2.6674971258082123, 0.7315087855557482, 0.4763129943777648, -8.103387591283399, -9.269231255454029, 1.740224023711325, 6.630004717567745, 0.32417645058153954, -2.3035627902162914, 0.8079317623585772, 0.46582242440455407, -0.060852200982577466, 3.967325523053189, 5.176711478086472, 1.206190794797248, -0.5688576280012954, 0.24288372891925553, -0.3997426094529111, -0.5632723579944078, 0.20860438712553067, -0.4468635685113507, 0.14755921700102953, 1.784689188535964, -1.334345406939219, -4.5935228568438955, 0.7800855570098134, 6.370840685351172, 2.0081600289793857, -2.660798934246487, -0.17484003362739492, -0.3132000119488173, -4.596257647518087, -2.7875971838000875, 1.1410685632274715, -2.183310606009322, -5.056646530157792, -0.9613725194258171, 0.6266667312511311, -2.7950760928166516, -2.2040050926474124, 0.826974313430398, -0.17947488447318144, -0.5657650879461641, 1.9654345282957024, 0.9220279716714657, -1.755645716826247, 0.5288924330465115, 2.9556018704401223, 0.7376577153203779, -0.6412385625239313, 0.06913527625927081, -1.338277302783494, -1.962340726484, 0.29899496922075663, 0.2946871805154867, -1.0425943247578207, 0.43862802714511623, -0.4791665421997952, -4.333034072950996, -1.4805154615377216, 2.6551852773322504, -6.467405065042922, -17.569578952928875, -10.495677059779435, 3.347886024063782, 3.3383777544706095, -3.0297723031130874, -2.1548646364974418, 0.5756285821689611], 'positive_zeros': ['0.167761324324720842066593155076', '0.966499867596301558953223079003', '1.49525886211072901841452147317', '2.50413447798768949742749263043', '3.44666685826702267536337403636', '4.28694698152111701827418248198', '5.04916312310794165463603566394', '5.61996943806375913480775723612', '6.356430430321414368130533083438', '7.229671402474957598306609895909', '7.9864959562556301359092352974', '8.97216479047591746125418039084', '9.66402567287484957409980858039', '10.3098174312006778201037027225', '11.18752265253187835069304160606', '11.73482259999142889168196568844', '12.361534225484450782648677008595', '12.986443257758712185299704131088', '13.56170389078399752818570188561', '13.97221144056198097256733301702', '14.84316546597683323502146989093', '15.91855203914549392276062517683', '16.77330009327567670271111438126', '17.171599793493514126252714285782', '17.711122652315494978186146523110', '18.71279690102669839660535128760', '19.42383847176916646332133512740', '19.763069244513554349288021642990', '20.29731294460598515170599682414', '21.287370324691298451426227902736', '21.808691954749289243885070156157', '22.39918441408867915966281738758', '23.286657799532978437527233855839', '23.64190979836924190022267353622', '24.173418938794886602773430800042', '24.8753379093295157693482989135', '25.40529960489320853316522056238', '26.62702279681728193531983515106', '27.29174837167985321784066125196', '27.88484070549824357174101481686', '28.425811895581223306729218509863', '29.227496295863810007034888837753', '29.56263625046528039202368105103', '29.99970577379413188945907838776', '30.577803303651321935786332439', '31.58200553589233599846253456620', '32.04022710633488699164941824839', '32.63647968600933454518781602012', '33.15498841876869410142416196594', '33.93247206202498529019629890038', '34.76572156893858287185395598639', '35.39600026594622481069206835665', '36.11374122798003107764720305214', '36.65515103019503466647545238168', '36.82847981109437398637330112008', '37.71313036651739169062856377482', '38.687646544800049532658731081042', '39.31835788350964084329945859492', '39.58419973768838252465092492549', '40.226257772284656137112285058755', '40.68157379853513234539174353767', '41.349495918816163918083791619802', '41.81089098470957761131842159714', '42.590718823476929967276670974815', '43.16850604541170335427768336832', '43.84228472538790945283437048906', '45.01956412619757564416322145336', '45.44386664323937419717253832641', '45.68142201733523714786030232355', '46.58644289500203120906224852739', '47.07969590088823412617568492371', '47.70130708447115849822918510718', '47.9925735703962220163380097280', '48.81287955865500919742830173922', '49.16735786982099522670826201951', '49.93513343300244888323669955355', '50.76228246861784149635696483492', '51.46580737356169190020763464228', '51.57901471090579427923242532856', '52.29230242131838422540289284087', '52.896759257268452959917836984', '53.75277835073233728274037326093', '54.21778644297498458298991010241', '55.12973220574824638938433861186', '55.786319507163599620258119525653', '56.03782909829681499255175948804', '56.75404136225556719634533322994', '57.0161556467649146142735759692', '58.22074838523877764132257018154', '58.47425121284939510388461840345', '58.760913948949091065651167888559', '59.40144931853964406808460636660', '59.8908177078453044249860321925', '60.66709462681385472645051062069', '61.374950974371451110841445978801', '62.21539225068027872915560937628', '62.77470516232101245405124184489', '63.562057816073508881277087266141', '63.9557793261193483035358549334', '64.16255740113878560930586888720', '64.971432307098020683487398395787', '65.67091475349408987327835246370', '65.927286361036824378870728395752', '66.883849532263199269416917827457', '67.35930618230600617606669539109', '68.05927473087013949508881549451', '68.34338520367964427003929097261', '69.122496238619362352479291263456', '69.251395915995330338482802762798', '70.15651351570245438495952250608', '70.937719707085302356285388870198', '71.52879762409775650708463085818', '71.83401493646522643074926026019', '72.705817571479753344170958927390', '73.51247551353589497923333557496', '74.12180872535086640385645153917', '74.42138360458979331120883727083', '75.19956693586925959546642699726', '75.29487210185798856217507884219', '75.943991110422113175747800867', '76.4725249340335770129501971930', '77.20703450851146986551992945322', '77.58838738941189764425516888163', '78.63740708992523184723340434503', '78.94952500288339008904956293483', '79.310998697304458791713255717944', '80.435067672781255707655683488019', '80.7513590265836064236399595610', '81.51935759218580656230450372721', '82.0549639339624144481470977695', '82.3752985366915076406366928049', '83.0891800659602399212182858054', '83.843334171679785523594102294269', '84.00251535882541425192356213998', '85.09317719027995649909428656643', '85.33782895477142406435208239605', '85.846112384200010537169549999639', '86.537508071327204596549692250550', '87.019065314999170310762399453130', '87.65992129376281835217275212294', '87.89812200891286873275289077799', '88.237624662168140850332985646172', '89.74964017947437654726296280011', '90.2974520204729465468191182022', '90.69599152055187601254469329596', '91.29461395925208377329616014069', '91.78395740473488046720099141186', '92.18210600667698127244938949047', '92.82477249688453603825020031050', '93.51937789282418535380504662209', '93.92667768446636526014455297827', '94.36006425775486944509198965169', '95.02508932027541154278825573470', '95.56075448202651870444289870081', '96.08356867174134757694864837652', '96.876655071136622060095717004642', '97.43426092190648247483215873649', '97.989705053362125620103847073132', '98.45324171803543361498747050349', '99.05023245753151998417935901697', '99.73254081950905567213514505535', '100.32646507035393408275668681245', '100.93666648124613660211120681659', '101.29780269403490056888740879594', '102.231802484839353165612450241159', '102.743682273081733509274905954218', '103.04066794608759057666175699317', '103.585993475213969961183834242162', '103.82755920132341796763160386559', '104.73513704301458418437517666867', '105.20023725511838150092444929562', '105.67284935362671341026436510864', '106.20642631532252823627417660294', '107.13388526744977293929282605028', '107.715579155654354068955272526359', '108.14947218142013081144871566027', '109.00486021799043276658534870464', '109.549094094792330935397361216993', '110.0100332531402227390236798788', '110.32162602660306307039591575534', '110.95945792004472565991179079333', '111.26740321216204681376878032272', '111.84324471955825680002777362314', '112.89455795110528707484096449696', '113.34784112056032865151627738449', '113.773077916562470801111052639072', '114.299394547330837315931256501239', '114.53668920158307384587208124956', '115.40788390022749008355994601247', '115.83742801225845135809928400732', '116.519628530248903063846781912959', '117.36225875191341882278666581514', '117.6520667018880644762334912389', '118.416135670701152407642311764119', '119.02001712867378969589517230520', '119.46389986001109361708794588571', '120.14157855384113981828252004586', '120.390604685191903417651260809706', '121.1276340428950181078664828775', '121.57589829229941671378571587256', '122.02127976214316473513046309784', '122.57917618384060931187440979987', '122.98210241343637314443562180391', '123.6112514009682756599490510901', '124.317257222845593252930361662546', '125.0099405378087575822613837805', '125.78997978599092096623903273504', '126.17464959115039904909558159501', '126.795518833888170080378654794974', '127.085375187577216942801149312974', '127.682347873921660509584711007', '128.17256804505145354074835063700', '129.0977090159231714109562711875', '129.54432119733448223300563747133', '129.898076832487563287956178653186', '130.339951069325378357619925009557', '131.115056855670791111418371787820', '131.51782156305959219767703294306', '132.308911950875723116599896533516', '132.51954859601886339642871710090', '133.10076662665907965382672478404', '133.58440482982762312193014467490', '134.26497247953971360162749534393', '134.79619772190440990019804505284', '135.699555187653399114158510681763', '136.36189168326766606231519632162', '136.92018932178329524326590556793', '137.36310927135567549014474795454', '137.47044821267457866997152620323', '138.29744095296402619038601429047', '138.84586058809083887090051563055', '139.26758384214358696747035762675', '139.603823576382440111114840182170', '140.43800568865016422223196687424', '140.720902502198025363009940079', '141.763427827113957633852115866122', '142.095997226523352926192305276923', '142.444688265519023260154647520091', '143.04721466001274005471937353994', '143.72041339444439335833947808842', '144.59990812776756966258195817151', '145.01214881124675657115591927272', '145.45157876014940468857497391316', '145.80184211821477119133139032157', '146.414903329256824879766507225341', '147.15913006107633363226202205449', '147.80231014612011103972194114063', '148.132956406041152973180294522139', '148.82458588383135129121771001723', '149.35894583767773997464099499033', '149.71589209441456823022029668797', '150.02298852240099628982679917491', '150.37315784079059625487406176523', '151.36766733608663696178009005900', '151.90558176676053157099903432600', '152.422272030961701250425741315214', '153.37538792028432521645721473631', '153.86147028862567476745407770348', '154.09721207022484680368755329722', '154.92535264086900795615837150041', '155.35784110497291584791860504745', '155.96477826575047423075655357191', '156.15358929172320919291313877448', '156.92255115864795572055216236961', '157.19013087359907291170726874077', '158.005824302310932337197272529327', '158.45386559084441102367718185906', '159.05245620701158245724149087493', '159.43803396070716307743643347025', '160.28797872861672293721276520172', '160.6364215088083332871555529679', '161.107444816247854058058462138140', '161.78250628110344864690885451765', '162.2069650072696185451963221618', '162.90611752967032653462871128286', '163.41837324673485583798339681402', '164.293550470108731585744167751957', '164.75529746930338154209082431452', '165.151407574298452102850811532690', '165.63221683004458677729988671867', '166.15636777372761705347354273180', '166.46311985151880747319001438552', '167.20875902758414692456296568960', '167.64551055349698038215910565983', '168.39930282788249464873966391808', '168.62034363098623042749082283392', '169.07868172810075952286284357949', '169.62998967694496235470720784076', '170.531582749951409941818422017714', '171.45811413420470847466476597436', '171.80096145724692501172717392314', '172.05600386450783758942444501842', '172.61326680690695170562896584705', '173.41792439671049409176635270176', '173.73904802593650191942706860357', '174.05616702261848163179343076259', '174.58521795200376755201034937594', '175.66084329545046955998888770882', '175.85524990305626776050434588728', '176.40018480306742572184200646715', '177.03022673192193924216015281734', '177.384802321208505091942964198440', '177.87611772545274032200400586745', '178.41111639931919448812998903012', '179.008886672271366735317001434788', '179.39922369537863825986569009927', '180.26618409482376761000739422926', '180.95264367749357074361003820142', '181.47452005100385223319729864473', '181.94850006442012912706560967913', '182.1960282221854590511540986749', '183.241553129510066909639980264223', '183.63539415741743998970130804595', '183.94204178798689026698086003120', '184.559678530202948470165566393786', '184.84542718000107821587665071147', '185.28873796760193140894392120970', '185.85288820780752662041684374706', '186.532782371530997869033579262052', '187.27770267320200405219282487808', '187.83049464629006596712312777489', '188.09704746699872291261110875840', '188.92197076060139550518138941428', '189.24104505144475916901194618782', '190.06966707406613371401055613365', '190.38261839693289605625376954494', '191.131823269820602701266684245571', '191.53567487224719272587798570604', '191.952160757523480573138376728005', '192.58264061494562430797906108692', '193.08276227186657300939909752217', '193.83720644240861358336375426966', '194.30042593469031506116709206816', '194.43440601389597316255940218636', '195.26879110644579710669103011589', '195.67511428143194633936805872657', '196.175746217281182174439385312159', '196.51823813516361272061355836080', '197.258289336540174779575508656831', '197.65060648580241779494142383014', '198.65320878710503714867038654343', '199.20607802523534419329048542047', '199.88610630744694030183899801985'], 'prelabel': '1-4033-4033.1734-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.09138076310370839, 'root_number': '0.959074448531968892084405031292+0.283154025528685981736363417369*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.325643132242964556389723643588-0.828068181004718672964618558475*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.167761324325', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.966499867596', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.49525886211', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.1734', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/1734'], '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': '1-4033-4033.1734-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': '1-4033-4033.1734-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.045690381551854196, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.167761324325', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_4033.1734', 'Lhash_array': ['dirichlet_L_4033.1734'], 'label': '1-4033-4033.1734-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/1734'}