-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4017.3470', 'a10': [-0.9324722294043558, -0.3612416661871529], 'a2': [0.8161969123562217, -0.5777738314082511], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.3323547994796597, -0.9431544344712774], 'a5': [-0.5523649729605058, -0.8336023852211195], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6961339459629267, 0.717911923064442], 'a8': [-0.2736629900720829, -0.961825643172819], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 18.654869573286486, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]], [103, [1]]], 'bad_primes': [3, 13, 103], 'central_character': '4017.3470', 'coeff_info': ['x^102 - 1', '0.998103328737044 + 0.0615609061339428*I', '\\\\zeta_{102}'], 'conductor': 4017, 'conductor_radical': 4017, 'conjugate': 'dirichlet_L_4017.3782', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^92', 0, 'a^82', 'a^67', 0, 'a^13', 'a^72', 0, 'a^57', 'a^7', 0, 0, 'a^3', 0, 'a^62', 'a^49', 0, 'a^5', 'a^47', 0, 'a^99', 'a^27', 0, 'a^32', 0, 0, 'a^95', 'a^101', 0, 'a^96', 'a^52', 0, 'a^39', 'a^80', 0, 'a^60', 'a^97', 0, 'a^37', 'a^86', 0, 'a^59', 'a^89', 0, 'a^17', 'a^85', 0, 'a^26', 'a^22', 0, 0, 'a^22', 0, 'a^74', 'a^85', 0, 'a^91', 'a^38', 0, 'a^66', 'a^86', 0, 'a^42', 0, 0, 'a^4', 'a^29', 0, 'a^70', 'a^1', 0, 'a^18', 'a^50', 0, 'a^87', 'a^20', 0, 'a^84', 'a^27', 0, 'a^76', 'a^98', 0, 'a^14', 'a^49', 0, 'a^79', 'a^3', 0, 0, 'a^7', 0, 'a^75', 'a^72', 0, 'a^53', 'a^16', 0, 'a^12'], 'euler_factors': [[1, 'a^92'], [0], [1, 'a^67'], [1, 'a^13'], [1, 'a^7'], [0], [1, 'a^49'], [1, 'a^5'], [1, 'a^27'], [1, 'a^101'], [1, 'a^96'], [1, 'a^60'], [1, 'a^86'], [1, 'a^59'], [1, 'a^85'], [1, 'a^22'], [1, 'a^38'], [1, 'a^66'], [1, 'a^4'], [1, 'a^1'], [1, 'a^18'], [1, 'a^84'], [1, 'a^98'], [1, 'a^3'], [1, 'a^53'], [1, 'a^92']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4017-4017.3470-r0-0-0', 'leading_term': '2.40303302289512505215812858867-1.88409173039128936631975984010*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/4017/3470', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.0535830359846656, 2.4939354332177954, 1.1703933354438474, -0.5523067521236881, -1.2232612500365416, -0.3342267271744466, 0.8014912482146641, 0.47282654913212885, -1.2920082020489103, -2.569229488030356, -1.831779946115582, 0.07139548017641746, 0.9380954299271533, 0.07580267560367632, -0.8623327770115379, -0.36979003404489535, 0.5942756263661026, 0.06566802225091993, -1.5547845281892174, -1.481235084295842, 1.3250961428916088, 3.7197081990874468, 2.0695413293035974, -2.313684952527572, -4.03955924447039, -0.6176766310552727, 3.8916842472183086, 4.167162451331435, 0.7996634898630144, -0.8775592828536443, 1.3396275545218173, 3.4730614180112394, 1.52707589564636, -2.4967990844405272, -3.665212880091339, -1.250877911773367, 0.8996756693142058, 0.5727588110167513, -0.22587800293408009, 0.2806578533145438, 0.45991734364940173, -1.2387368810480068, -2.774555604043476, -1.7455222819769427, 0.09846996418997706, -0.5464773188570382, -2.7765298741407287, -2.7471970536302446, -0.29842803944020957, 0.6831591452101535, -0.6251583564995847, 0.055452037046775295, 4.411469261466582, 7.056193221450132, 3.380084800847265, -2.2152499129063052, -2.113345721008285, 2.873918852637912, 4.736184797850329, 0.6595754774947963, -3.228213198930998, -2.064268943774655, 0.8779320831616854, 0.9313258343815299, -0.4879037205197912, 0.06177078813197082, 1.3651275932849545, 0.49309035755649655, -1.1517477035188048, -0.5313702128281221, 0.9689797794578281, 0.07149459738728307, -1.9311444901995194, -1.3847379622613354, 0.6958004612881663, 0.30774881323707476, -1.975562295187693, -2.04734773939173, -0.14266528048473834, -0.027864890435708656, -0.47504349499137, 3.6112047393975497, 10.213035641677083, 10.003423224285413, 0.7121740902546475, -7.532991747118017, -6.490823622921936, -0.9976564563418441, 0.5276651707981144, -1.1485360551893307, -0.7142426673964998, 1.0025056035174045, 0.06541013078419568, -1.7239354929356987, -0.09249020400745277, 3.086089393836263, 2.9178661403079236, 0.3097394330574838, -0.29245812958835515, 0.8593862073486852, 0.5627011560489931, -0.2988288383304327, 0.848969502979922, 1.9554615294316884, 0.12094790723928239, -1.849647655008733, -0.5932504102262597, 0.35133322339653067, -3.014117501069266, -5.982677842398397, -2.4912154992405844, 2.9972167965170646, 2.2942062629757447, -1.9725000449936947, -1.086097191686491, 3.806128410456366, 3.87664222770029, -1.2563727930114041, -3.237894848305613, -0.06678441669452137, 1.7390943603159057, 0.09390745723345814, -0.11755303601763697, 2.088593283306068, 2.1288601520090724, -0.41705582432293925, -1.0992848478925648, 0.43352614196030403, 0.5812506726532463, -0.22145558122293424, 0.9474139940274203, 2.29761274046205, 0.8965404224028147, -0.1913182141952611, 2.3652529834694436, 4.2820959724562515, 1.1814826517591035, -2.218539888600762, -0.5699814922574875, 1.8970645456155248, 0.3924009682489374, 0.04576800849151034, 5.396214681637983, 8.79152746830485, 2.608814245272066, -5.943371711921938, -5.9918458638530625, -0.432830484430935, 1.2745525829790403, -0.6205014857357981, -0.21717082270903026, 1.6086700924553474, 0.9757055149894417, -0.1726316151357606, 0.8180270026153462, 1.0394859124273361, -1.1104844999060568, -1.4536344240495207, 1.3128290287383377, 2.179556526309066, -0.3307467426186947, -1.448208938910958, -0.1261712251660329, -0.32828843434793764, -1.4954870910905362, -0.041576471743373554, 0.9509358669201367, -2.933955067819249, -5.8158674310960885, -0.28131097220162593, 7.126223993141286, 5.563488491935242, -0.8800738431574926, -0.8542192126645092, 3.972650016141096, 3.9844156164309434, 0.11500708504175028, 0.006013147046886739, 2.511260862070419, 1.7891283043329154, -0.32993799519926414, 0.42130281383791685, 1.2865572514523602, -0.6789671295903807, -1.6575649872742644, 0.45627064905435477, 1.1356372593576596, -1.1543350897497764, -1.8297891255844099, -0.05815456831731078, 0.26231513809457574, -0.24247322118619272, 1.401583137912807, 2.0254759372538325, -1.255997074096248, -2.510057225346601, 2.00949798674479, 4.045462890917288, -1.8928974420298634, -6.459790268136374, -2.0530355619480734, 3.0722228473392286, 0.8726804513354229, -2.2348568980053765, 0.1126765994643215, 2.2175127285369434, -0.01921057395043308, -0.4120059665387368, 3.596738266775864, 5.0406286141080185, 1.5586960768615037, -0.5819644427181825, 0.5927277069056591, 0.8221565465197125, -0.044340609414996235, 0.6656372588365221, 0.8777937554375972, -0.957386683984854, -0.58237677533046, 2.8872336586117546, 3.362735870843616, -0.05396197245188269, -0.901331832997915, 1.1627376266124103, 0.5476309198828534, -0.6671606283841467, 2.936552103291799, 5.826846460345599, 0.7125500219713465, -4.970448562273588, -1.553068074864799, 3.9248430478048175, 0.9453150351009019, -4.8047822732726395, -3.6531051125593996, 0.2758802052979914, -0.0321625644605581, -0.8915313019879323, 1.5834624016010252, 2.8436486504896283, 0.7210468475736247, -0.36854441069119614, 0.03035012303829151, -1.4996090247381788, -2.7189700829716497, -0.26935651179113657, 1.8152731447301185, 0.22463850296787533, -0.5844331117935984, 1.3014854863796876, 1.0284270862509246, -1.2123218087120933, 0.09040337582658634, 2.7808093858677276, 1.1616747416077875, -0.6619768206460714, 1.8441334607158062, 0.21848100292603584, -11.187277622896994, -19.47282868150354, -13.287983832852607, -2.53027807527332, 0.05295962140860675, -1.4833868849654477, 0.01146658121321768, 1.2309010137220877, -0.13104634392624837, 0.34442970781410615, 2.036730334347204, -0.14528363092600316, -3.4538061151410715, -2.201246737791478, 0.4062641819269178, -0.3870437350354449, -1.4170400595769588, -0.20927320087311366, -0.21512812197452236, -1.4289683510517008, -0.4418468409395546, -0.04182954759702727, -3.296014229703259, -4.204907297033339, 0.5268014278001312, 2.746388695088289, -0.39357103935248133, 0.9020056918392189, 8.172809922703962, 9.169914888128956, 1.7412841342900442, -1.9948522043094263, 0.2832922329723603, -0.9023031634138449, -5.111591238560583, -3.9218654170750624, 0.1475672181051394, -0.48532172036513654, -2.6728957182210307, -1.021804248053884, 0.7037165356661349, -0.3343520798696473, -0.015417858656802836, 1.7965126103832814, 0.6842898989591905, -1.4780335238731042, -0.6282492683652104, 0.36294037123665307, -0.5832281384669055, 0.4510595687928477, 2.410646666102464, -0.5195538476758323, -4.708201038903071, -2.529973629063149, 1.3019917386297621, -0.4838429981680344, -1.7772055686037758, 2.8184753669323173, 4.4979868905109255, -0.9928773771006135, -2.847582702615447, 2.246554580902218, 2.5107137203071157, -4.510331667927849, -6.994018509020583, -2.3375926521491075, 0.38286879988394734, -0.41028035173874455, 0.15245705461528716, 0.6231563079222536, -1.006278011294198, -0.7632845167827729, 1.5136995344970734, 1.021391621916027, -0.4572736913653432, 1.5039738093942112, 2.9054340697954966, -0.050303278699285886, -2.0006757971790137, -0.24175210928250507, 0.22177189860520147, -0.4744383864080918, 1.6683369658042042, 2.1332599611678678, -2.243233125191232, -1.3545309667088488, 9.00605456170409, 14.14411754022955, 6.131003604461482, -1.4528221861360733, 0.17271842739623355, 1.7175653511907463, -1.3363859756889744, -1.5690769219660596, 1.203020424718252, 0.2809591858221974, -1.972652680708336, -0.4559203299333262, 0.8899543821123663, -0.730182819696689, -0.6026513877798179, 1.387738618556573, 0.3925258380023295, -1.289555437100644, 0.5780230796467395, 2.035986493726522, 0.32684782747729435, -0.04446314026126354, 1.0720479237161213, -0.4589385212791978, -1.2366073874029606, 1.7934445108247097, 0.8273657156455488, -6.234784421259245, -6.976307135176796, 1.2651510250701956, 3.8754199916103373, -2.6339886766624963, -4.870720602454929, -0.30319105526901163, 0.7700805966142834, -1.2947099878337798, 0.5792659970622367, 2.376887260709041, -0.7808032172356805, -2.4751361922349107, 0.4077564860994789, 1.0265781370515614, -1.587681891183202, -1.4085035849690841, 0.5958907355005887, 0.3369065076690932, 0.0694751389663902, 0.7344410754087232, -0.7528218370157886, -1.4344659460246227, 2.5690024290777296, 4.895533752035126, 0.9760971961099354, -1.6948369610465763, 0.08091986302074344, -0.8161326329032565, -3.518271800120366, -0.9392216326133245, 0.9558496118338573, -5.674665967124558, -10.406184283865777, -3.5623304866388645, 3.5215027063474102, 1.0780722691114801, -1.6988257934360846, 1.2084424241694958, 1.971160666992625, -1.1279605851908174, -1.1908555480111858, 0.6523226813650529, -0.2731351784873238, -0.6542605013097864, 1.3794967114656247, 1.2040161254489807, -0.4904547370153503, 0.5480052570427679, 1.012028722043136, -1.8623377019548193, -2.5406361520728917, -0.08782817615200278, -0.6520018569612183, -2.5892663456967115, -0.6377625768251526, 0.5273728258566789, -2.2390558275762946, -1.4764104158690259, 2.2367144639456535, -1.9997059978916267, -10.158691821655564, -7.8588798632100545, -0.11023869183656741, -1.8576968772584619, -8.082683182217286, -6.026030004153995, -0.28526972829055697, 0.472265490598024, -0.18935974415873855, 0.5514594480071453, -0.504599681144085, -0.7199778848658985, 3.1326935143124346, 4.845522623344989, 1.314768158821129, -0.5923134663756127, 0.8322473845105225, 0.32588676639061287, -0.9532450525061198, 0.08887977475482937, -0.12643244416161356, -1.843299484166888, -0.4924191456119962, 0.21821454339747404, -4.034454794933863, -4.562490371549345, 2.8092269533358474, 5.308616392361653, -1.3832093583962033, -3.620873887330272, 1.165684164186202, 0.3965550716501898, -5.0823151707796095, -4.070558656941985, 0.0390596921662039, -1.0097331525249333, -1.9883088494969514, 1.107069333569866, 1.218867655096303, -2.3548864008187964, -2.313501694512278, 0.03709073703478108, -0.3817888101311739, -0.6963231811169076, 0.5451792042896982, -0.7197956089659465, -2.4484052049971083, -0.39801624456959783, 1.1829185131700273, -0.20845667011419397, 0.5411384198753759, 2.154308593356504, -0.6177862849962897, -1.7652875597552544, 3.689259972171076, 5.580816987069245, -0.3954009699529181, -2.197636826017125, 2.3139280860239584, 1.3885047197352827, -3.1426092164664685, -0.5628311736642808, 3.2039361070130328, -1.1524939239864316, -5.088270086845888, -1.1362596164045955, 2.184385099991879, 0.44431185954996155, 0.08096620280210877, 1.3907751398236368, 0.3507891805236057, -0.2435842791999239, 0.77241075372187, -0.4987073971813063, -1.5160106973028569, 1.6152648302167179, 3.161329157815068, 0.04511748489527335, -0.8996375689291195, 1.122617777282124, 0.2912773845440565, -0.5880968770273113, 1.989624939321562, 1.7518455747304968, -1.215966277913644, 1.469901583338884, 3.6213477742678144, -6.44610400318396, -17.300899038118917, -12.275327730893439, -0.8874650176115718, 1.3967889304598502, -0.4107728323930093, 0.6347654056902408, -0.3661811911990513, -2.943408915611269, -1.0376879950883358, 1.5230994213227103, 0.1365614534649344, -0.024672378904817972, 2.2644293058542733, 1.4770428650217693, -0.4717829216638355, 0.6008017762726537, 0.5608378837367975, -1.8000117468326546, -1.017152197157801, 1.0731301736632661, -0.38880518683520965, -1.2105834016314732, 0.294534738993899, -1.7641776645049512, -3.8554077493838586, 1.055295229888816, 3.223679010290531, -5.7855635421927, -11.606966568216745, -4.2591996910188055, 2.1659997324506035, -0.5714396826080487, -1.8492205612886492, 0.836649771661908, -0.32378205541293714, -2.3171150923652886, 0.12531143747175763, 0.918041709943411, -1.7984897255257175, -0.8639525591216537, 2.2224044126608877, 0.9783400133625074, -1.0930343806263458, -0.13221297533272885, -0.10993441779119147, -1.0981923138735643, -0.05699249269305836, -0.2895366905753784, -2.0010239743741804, 0.702841035903403, 4.022150908015299, 0.48646349441895465, -2.696973861541114, 1.4360193685901548, 3.772200058576935, 0.3834672622434367, 0.1330023431164412, 0.3586581413768887, -7.93979861281267, -14.642139618954792, -8.185241583843471, -0.2583910862988854, -1.6096023891508786, -3.0135576155275405, 0.3626218737010008, 0.6869006776358205, -1.487587662573602, -0.1651095452837854, 1.0781582917156887, -0.3747495707758134, 0.1858542088454388, 1.6177916230839458, -0.013238136584729152, -0.592804995609902, 1.3307675809680348, 0.1591933518790872, -2.1915066633071953, -0.4681689712992483, 0.476820999584487, -2.0362101796320746, -1.2012471915976757, 1.7666825979068164, 0.2195192843498157, 0.150628668867558, 5.777796998758133, 5.688991768143092, -1.4176157392436455, -0.1882548624091513, 7.986240010368251, 6.637965669455165, -1.0233365495279607, -1.1032411416280345, 2.009930764250368, 0.028954149506945425, -1.3310332063609647, 0.7296746333820532, 0.664757140351206, -0.32457232274271464, 0.48779683667302687, -1.0625623465915544, -3.4337607315765455, -0.2874765158935774, 3.768154092636904, 2.17555925139908, -0.1507452197297887, 0.13910148633868105, -0.661782570955452, -0.8362217166809188, 1.3300835705724103, 0.05482294517148428, -2.5868828937058783, 1.4964850931328124, 4.620780317193965, -2.7818673501791364, -8.137200850298044, -1.4973098370167897, 3.019036730831243, -2.036456820999399, -3.7784341182002144, 0.44412401082028785, 0.7347380319759178], 'positive_zeros': ['0.829179900638887804179301697264', '1.63940257689042221498397455756', '2.2867587086390839808189405427', '3.424670821555825834227926946660', '4.08098443531521585897557578928', '4.78879361722261650709061231654', '5.32653376156187352113693973867', '6.12525079629783034584833437581', '7.025072319495135918235955425722', '7.850327651626979138719895725245', '8.83072887003003481574830373644', '9.23294806260853546145464347726', '10.11555699968405187029129287649', '11.07937584363950218443436078045', '11.735446357490422387397165043811', '12.07784091239604339460308068195', '12.61910905534500457664562557350', '13.72099229610351608267111346691', '13.959634663399452717976326488050', '15.04180629404137815918806281550', '15.49009928874545668089317923972', '15.93141775620422316030078183260', '17.04497308373512872883709943828', '17.642425102154481468924068767915', '18.47641797561528749538741486853', '19.2618020865141435594015795934', '19.8692229434179463984982951503', '20.29977853275092606743597062339', '21.01614268646481171420528830947', '21.65454994095455599544071106317', '22.19790920492086354661640518441', '23.00454461531306633091375407967', '23.48261504014067861830830593487', '24.40853990951732405914242352058', '24.67876178323137167007297553876', '25.07753237838126442472816344832', '26.2704020911691504372557839539', '27.274719200198262428979508290431', '27.60799883917474641072001763136', '28.23601717561288012522482961473', '28.759133274990707090385027424698', '29.383651900888430076824506483692', '30.3631513161216073759517434003', '30.71023240747600525628961343884', '31.400068190317991943543831875756', '31.71184380496931064959710036463', '32.513519787065108791641842721144', '33.21560367384914697950577538002', '33.50129966388781377080916160806', '34.498195584234105386100288271493', '35.155552794422445009421203027570', '35.69701392007619902963907668915', '36.487998720623116001617288357974', '37.193260738756444867065377431838', '37.82946940417322634301334103287', '38.1470728793379733219839601188', '39.00941488708896142033859369906', '39.59860615420593814482352814297', '40.178333785012532196871184107425', '40.444838863707084661544442854384', '41.39773185299219132828337134757', '41.61462587251092826170656507901', '42.580482442601341563565054858158', '43.17693572253465045540905409698', '43.80489281179355619357923201124', '44.057156379666580694702241985136', '45.08273081478351254649702833464', '45.967921521584381422722000166998', '46.45594591725184602482890453559', '46.90864761377903913499261670137', '47.70648070239962857151868615105', '47.92864842632012231572688426149', '48.60332571235862066371873852243', '49.23990065536041133159342566117', '49.962401861282436190630565237609', '50.66554252487674523839541791996', '50.847063407927644822956376634115', '51.56799899782341440714533587904', '51.992410053304806877934854144301', '52.822528718447250450308151313724', '53.69583201645819328767470407256', '54.121308367640988541923978810402', '55.01313343487479452909983503824', '55.311687236698525010857871381253', '56.17204135283249312516877007342', '56.48295353960204327300289778805', '57.10209681954703113687029063748', '57.754078560210050803070009477614', '58.29597259672079617601130917602', '59.07443567781871821186165408286', '59.4704584991280611895994789557', '59.77363839284732179928420494597', '60.52449166857885196054826328494', '61.134325432523465937540615664922', '61.79710943202970965503105121178', '62.59304253440792400235169129100', '63.18521395644128772238418915697', '63.74061055671209218060169252439', '64.37275478723438135744780500041', '64.73293948110629392349225163717', '65.775843274368313607334240741152', '66.12770240559280353823505378106', '66.83556954642633605478804429541', '66.97377372376794162460848165782', '67.66074232762686267722571864526', '68.186566224516483089270171822915', '69.05716826001740746109223814796', '69.51123619836195606338553848630', '70.07858562239422126873498515938', '70.41649620733609689815639449597', '71.27865038276110387387997066925', '71.94412216864569190831844325500', '72.54390398889945078734417862604', '73.402036979007193335568497274457', '73.74453330670365131815244080387', '74.20882129801298207350409064173', '75.11378065382567875270222224209', '75.5256474114706423757354924857', '75.64952955057135831410201776630', '76.58755867444054070919022568510', '77.220105513227984969721081895087', '77.6149353652045927569821704865', '78.25354807516800826508972858626', '78.74116884547902198495083670553', '79.49620478514994475015497845145', '79.80884209358418908760675788812', '80.321785859673564244270839978180', '81.73351588157510783629430716721', '81.88726089466303897756981807166', '82.49852021541062076146237157260', '83.09311330385310227361368953899', '83.37736848433712776605831835697', '84.0510569792425875672157977212', '84.91971433925337269396191879558', '85.245249246046969188998742172690', '86.000363712936829837811476093004', '86.18581322013441704616003575212', '86.964388625736070175063668557654', '87.17942564851458234066112764399', '88.09403194103605892715726211208', '88.709401631176476413952970493791', '89.005825765692050290442468334109', '90.07984710913602102855031237233', '90.58445732050702483016976892740', '90.857679694215678520992900032865', '91.85627313666468379546558568960', '92.12850535221941582884628220479', '92.935861305314792625135730513487', '93.35729937616418195419268780914', '93.752668791700070389088063059085', '94.45426010468777532103887278984', '95.11702291185342852309018102399', '95.45132607866272026655761214006', '95.87705843469877077522568521868', '96.53049972430077621693373777003', '97.35336597784679292442169715673', '97.76807529178612069127294891989', '98.27509790477442560534735420193', '99.01174333483278996926933034995', '99.56109918384636941710135759017', '100.125402910091957803015554360211', '101.13494591457493456262835867201', '101.42583124332494571615660882186', '101.837943786783404335768526002544', '102.32549839930012055752706980725', '102.91425294500779821568523130390', '103.59361437714278506435310407596', '103.88498709295525295092029410326', '104.68327004272951113308763151623', '105.35451703296184500958830384496', '105.68815063337437975256669171263', '106.05106789431779751175516356919', '106.72779793892152798920881008910', '107.24194108893470372836533860062', '108.33497102743871246559231132289', '108.73533780545572089694669473386', '109.25152651435481114303325756833', '109.8505663997482398861794920401', '110.3425030961640318303088134679', '110.99423477208892802155687866303', '111.44179359852056728002197655924', '111.96250509057837749620591562896', '112.54957757218118505494884198751', '113.06005609036203216852147992774', '113.812336705352885740436618122428', '114.07418902957598679313914622983', '114.62714681743523329450821643620', '115.14595336896351863777748484574', '115.6695526409547422017311492938', '116.51569213440790569625096805968', '117.07420257110077153021848567326', '117.835894324658303991549206769022', '118.226956218254281718866777552185', '118.69544809942509097656081831614', '119.31497188538761164249930619160', '119.95936841836224489300882608109', '120.439338994066224587768694121680', '121.132489659191223229019989088023', '121.698920902301883414795877801156', '121.83644881004699148887177230', '122.3918437091764025710080883558', '122.9570442602398507033528800784', '123.81506469987538972153754788615', '124.35976335251215620733332523963', '124.59070186499397829256105566469', '125.38146845477528907668106005409', '125.70371468729514855073238501671', '126.6795303217064537512669114317', '127.25803781251802630280452805556', '127.70904199246936841657731446038', '128.32173495286922288671104940632', '128.91769168327808869498578634196', '129.32389545291455715541490974106', '129.79992285913608096929180345877', '130.49893874526083452089330347792', '130.84366530609924862832289367730', '131.38135240305610941423106853842', '132.20453379835502992921352862438', '132.39996640850749008877063149542', '133.19663689474180835840227011226', '133.51756223425338683100454357006', '134.167783476181220812520049847015', '134.60892227327481659400478894686', '135.63323158416898565768119461145', '135.83056313549426408434439667901', '136.90154881280862638412471465486', '137.31338118381921153603370363671', '137.5869140034625102981441030495', '138.03265771022222467084673525043', '138.518924456899232962299899234410', '139.49757220021627627088403576890', '139.83479370520600428759403528985', '140.367962333718335894390975653364', '140.91572552024171549760517384270', '141.22619822314569637123510965087', '141.94092391893590855755016511704', '142.21549749712004766796719487614', '143.017291942533353772580074282764', '143.691078096778220920367368935279', '144.29545709902185687765530543284', '144.71081850753517424082245543062', '145.61862295203866667431091175641', '145.8044835535048687183458403654', '146.45975705995295613081952254808', '146.98433797565231621091571616624', '147.80314103677099376655874674451', '148.02632622925004202568885839542', '148.59621012703533555288576035720', '148.96627270675075654192873518208', '149.73008289475584522458458569201', '150.26361471987109948759147017268', '150.54391148909755158499936585769', '151.20021321875510329339903104775', '151.690711565697077261965196643390', '152.48024750944741955002266438508', '152.96857640720098375743111027318', '153.51995749051103437430053832210', '154.0935265492810202788089804434', '154.63272494058538136198556709019', '155.378630640543532210212600293733', '156.01713864502536052035129343985', '156.23008774947411696618199640741', '156.94690012883463383794321218071', '157.2634394446325258505118696067', '157.74213013280921876353242342570', '158.30732158860713010004173337278', '159.06684740519609951610934724993', '159.50918807316037430447323823055', '160.043515691414436333185505263725', '160.40847406297346217573121446231', '161.094107834936869556918602751328', '161.4662498723696806734184184785', '162.0320406271475956362043761131', '163.16434845939214397335103098814', '163.63164457249129254462004051062', '163.92122772136260757424213609600', '164.33384037611042019106440835485', '165.08900050482674137676620338303', '165.64804670695805448249931627201', '165.941562184936983640337383683987', '166.75185343972391350495037191603', '167.074089524487635956038290835511', '167.57687261102366493112111540914', '168.24090321105586371128929012730', '168.69831283886919700126579821425', '169.28612423520662394237399084821', '169.50898413479318949704068376603', '170.261756576479751455221206561361', '170.76974307883570680078594709398', '171.71137718927724475333649450632', '172.14480233824625126475485823133', '172.70181995875773151151871408451', '173.091861000282831494767924683892', '173.737312456952280315590002196155', '174.1742858833863413118614622038', '174.76229247634177376988894883330', '175.41745322657419887759776948317', '175.97305855768049521083395366681', '176.21920514891307055040250045860', '176.88968658086238906259101155158', '177.13179633081171792848352464140', '177.76521913989622133760644992188', '178.46478659166054605321222216499', '178.98102851772624536055454648968', '179.73128014051570830396214249378', '179.97889570704402523349809827038', '180.33900145984713139556667954415', '181.5944210099594717070570054143', '181.71014750548967825553819772330', '182.465403576709054470393556577589', '182.89778151853461411749198415685', '183.45850220687040044699650376216', '183.9818788498679732536387151098', '184.34472459928298119166419820739', '184.998106328547530120153232511350', '185.412725742682671206171783650233', '185.95372423174275683524342938280', '186.61933931271099180380754696530', '186.94946137648889608876652332993', '187.60394665133065792658741732642', '188.15106023864030574594756688868', '188.42411231098627003460321515628', '189.30384627341511285808973173586', '189.69534766054610105460517584130', '190.5703915364057949418539165253', '191.023335776057298692893430718006', '191.565338634883367395253505347908', '192.080239415124560670089214458831', '192.64005679218714562503675679038', '192.95470525458738766499841954007', '193.31540691521303351069865398713', '194.07928098032182801578476779767', '194.9492363135230862050436580559', '195.21528221959467582167920652600', '195.4569372769623545855241993047', '196.06169422728253627849695418276', '196.56725171904521799302552724909', '197.11208054760812623460982718687', '197.72379406364115789638257499560', '198.49280804086744717698726564657', '198.96036166280391710674936829326', '199.64987339741080655687888135454'], 'prelabel': '1-4017-4017.3470-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.654869573286486, 'root_angle': -0.42331252318946483, 'root_number': '0.238596946909828218861914973111-0.971118683233572957275455521846*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(102)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.57174803428479566267674755911-0.758773016517668157359612993252*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.829179900639', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.63940257689', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.28675870864', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.654869573286486, 'bad_primes': [3, 13, 103], 'central_character': '4017.3470', 'conductor': 4017, 'conductor_radical': 4017, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4017/3470'], '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': '1-4017-4017.3470-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': '1-4017-4017.3470-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.654869573286486, 'root_angle': -0.21165626159473241, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.829179900639', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4017.3470', 'Lhash_array': ['dirichlet_L_4017.3470'], 'label': '1-4017-4017.3470-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4017/3470'}
Lfunction data - 1-4017-4017.3470-r0-0-0