-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6017.1015', 'a10': [0.32212044179849064, -0.946698695982806], 'a2': [0.8049393207604731, -0.5933571352007727], 'a3': [0.4738686624729987, -0.880595531856738], 'a4': [0.29585462021266384, -0.9552329787537804], 'a5': [0.8210178357710056, -0.5709025427740658], 'a6': [-0.14107212275242537, -0.9899993213038707], 'a7': [0.22924706283730373, -0.9733682675023206], 'a8': [-0.3286492866848144, -0.9444520349713704], 'a9': [-0.5508969814521025, -0.8345732537213026], 'algebraic': True, 'analytic_conductor': 27.942830525881202, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [547, [1]]], 'bad_primes': [11, 547], 'central_character': '6017.1015', 'coeff_info': ['x^455 - 1', '0.999904654533872 + 0.0138087595930395*I', '\\\\zeta_{455}'], 'conductor': 6017, 'conductor_radical': 6017, 'conjugate': 'dirichlet_L_6017.1731', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^409', 'a^377', 'a^363', 'a^411', 'a^331', 'a^358', 'a^317', 'a^299', 'a^365', 0, 'a^285', 'a^39', 'a^312', 'a^333', 'a^271', 'a^61', 'a^253', 'a^67', 'a^319', 'a^280', 0, 'a^445', 'a^239', 'a^367', 'a^448', 'a^221', 'a^266', 'a^23', 'a^287', 'a^349', 'a^225', 0, 'a^15', 'a^314', 'a^207', 'a^348', 'a^21', 'a^416', 'a^273', 'a^182', 'a^234', 'a^155', 0, 'a^255', 'a^399', 'a^322', 'a^193', 'a^261', 'a^321', 'a^438', 'a^402', 'a^424', 'a^175', 0, 'a^220', 'a^444', 'a^432', 'a^63', 'a^241', 'a^201', 'a^303', 'a^202', 'a^179', 'a^450', 0, 'a^285', 'a^424', 'a^367', 'a^268', 'a^236', 'a^161', 'a^213', 'a^302', 'a^289', 'a^430', 0, 'a^370', 'a^64', 'a^227', 'a^143', 'a^136', 'a^21', 'a^188', 'a^17', 'a^109', 'a^400', 0, 'a^345', 'a^209', 'a^397', 'a^353', 'a^271', 'a^276', 'a^23', 'a^147', 'a^74', 'a^215', 0, 'a^275'], 'euler_factors': [[1, 'a^409'], [1, 'a^377'], [1, 'a^411'], [1, 'a^358'], [0], [1, 'a^39'], [1, 'a^61'], [1, 'a^67'], [1, 'a^445'], [1, 'a^23'], [1, 'a^349'], [1, 'a^348'], [1, 'a^182'], [1, 'a^155'], [1, 'a^322'], [1, 'a^424'], [1, 'a^63'], [1, 'a^201'], [1, 'a^285'], [1, 'a^236'], [1, 'a^213'], [1, 'a^64'], [1, 'a^21'], [1, 'a^345'], [1, 'a^74'], [1, 'a^369']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-6017-6017.1015-r0-0-0', 'leading_term': '-0.189409656484662675421708455040-4.89552845759977872679656272961*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/6017/1015', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-4.899191249291958, -3.005155151276785, -1.059546620650878, 0.26237258599954777, 0.19907641607316306, -0.3185235944513449, 0.12961843936985254, 1.3218626458545413, 1.5498753637228355, 0.13693471971102297, -1.2377881182731718, -0.7206019677688293, 0.8537786694390785, 0.8659162412811497, -1.190388097451564, -2.5465075431049584, -1.0305451794538898, 1.484882711195946, 1.625873696746067, -0.3543798529062906, -0.9085590871069686, 1.0166393436371974, 1.857400745762855, -0.9252333858821843, -4.009106376534072, -2.6311600862172906, 1.7875631473767948, 3.0855765259000822, -0.4596123660201024, -3.3724590203592477, -1.3698672888724481, 2.1484974069337737, 1.8049419615878683, -1.1735500355304223, -1.3587876714225118, 1.8238202911324035, 3.44216867642373, 1.3680919997656564, -0.6837176409721502, 0.15567106445850368, 1.6044901814057515, 1.0778540763778837, 0.010984316820174906, 0.21466626556045362, 0.2878791763481249, -0.8066698761801614, -0.9204304935766052, 0.43443554529107786, -0.9499583176397882, -6.8110936726171065, -10.756469506757771, -6.784107946604875, 0.23089196643918047, 1.0046690302239472, -3.6702974042631533, -4.588019641501208, 0.526792558370374, 3.929174921127188, 1.5152735803878652, -1.005111543428941, 0.9150632543038796, 3.2429476571615146, 1.8191857286831066, -0.3258801280004928, 0.36910416503127774, 1.5294310786631395, 0.5443742118422322, -0.25087799276083506, 0.6037727227844346, -0.31965387097711895, -4.206466863405659, -5.963394388616589, -2.7630793268493257, 0.5504341363589543, -0.021299452871588232, -1.230291596946627, -0.05369797931056487, 0.5166874245390773, -1.322441283959675, -1.7708132323246084, 0.2703482306122527, -0.1513940991037685, -3.552558428785603, -2.8841103249127102, 2.864968632080324, 3.898717988905281, -3.831760314561545, -9.672121303748185, -5.054120039029592, 2.703205132974047, 3.4428232231233467, -0.21948029160111565, -0.7886954012030967, 0.8719815018120622, 0.46769870829670784, -0.5474870368941167, 0.3026752428848337, 0.7334716596053471, -0.539560399815147, -0.5002335568015659, 1.1218807842388623, 0.5421813113521934, -1.7215534959261354, -1.2051302523370748, 1.0352963233639918, 0.36777273784704456, -1.2697539884598827, 0.4198383026067718, 0.9831644742353007, -5.381973484497406, -11.79264740085038, -8.07650306917996, 0.7339822267280165, 2.1508748568934126, -2.9334219428818957, -4.240537351882164, -1.0016572554409222, 0.0006918453676502144, -0.9839269079669763, 0.23570225164233152, 1.0668266836634839, -1.6285660004707545, -2.8509129425126187, 1.0078351946915918, 3.808370566709712, 1.0078845569176689, -1.8716381472928587, -0.42197833039735216, 1.204820623410462, 0.23322408325590616, 0.007631536585582707, 1.1320296506732521, 0.44936202617935894, -0.590912059544654, 1.203809591755629, 2.6567576035015854, 0.7517459061011341, 0.18046019428095258, 3.1683096336429015, 3.130766346747558, -0.6636429676674964, 2.3156968875057142, 13.48255155366196, 17.938914790398684, 8.948887227523432, -0.40936009337572216, -0.3463679465023511, 1.7683234287594314, -0.5475799633646835, -1.8744537760251607, 0.8432317802135989, 2.113054317678669, 0.2867725516651008, -0.27165675169726006, 0.5186716461781539, -0.14121579510171, -0.4671407929568862, 0.8848404670056826, 0.5424808188939152, -1.105899243566472, 0.8764568139457858, 4.148544973815658, 1.6615639664009931, -3.3468684635570183, -2.214910005975728, 2.304644427213508, 2.0813338842405384, -0.3966169983946207, 0.5000802979767492, 1.0511374407077148, -1.0126453921652234, 1.639228687329304, 9.665418047369588, 11.261141705659862, 3.432981048417628, -1.900184052368326, -0.09688047758119706, 0.43869585040711956, -2.2944220788940095, -1.5691343051945157, 1.5771892688940827, 0.7057862874254497, -1.7989823837661354, -0.8027262484559516, 0.17833332365691343, -2.2436561395147145, -3.417088964367255, -1.1324996481530663, 0.10031838424450315, -0.5429445784800925, -0.02084774604019668, 0.13344351531648388, -1.459844433630667, -0.7527964234056763, 1.8938750698167188, 0.853870946760124, 0.32065981712940567, 9.369112447662687, 19.8660211636853, 15.486147636446974, 1.4043668760795058, -3.5740842825802512, 0.8807357419853328, 1.155509045023291, -3.012514735850485, -2.786611515895768, 0.06647828817459556, -0.20594403972916497, -0.8888931664880044, 0.3610398990329161, 0.12222929925308369, -0.6786014638400742, 1.7687600894567381, 3.6329858412584293, 0.7477548170551412, -1.4927046070253402, 0.6320296875252297, 1.5360475266315503, -0.6201881121574973, -0.5185376663292713, 1.0502713261591738, -0.6537238332243326, -2.1071303811960074, 0.4698781632241196, 1.3551614150170164, -1.286998015016993, 0.43630543951848677, 6.0573276391206035, 5.426659959556868, -0.07016409327260274, -0.6288367718155085, 0.690757514813494, -3.4360265175514897, -5.418330729587689, 1.8421185010671253, 7.243426946006354, 1.792576359864308, -4.524688957130076, -2.985296616614165, 0.164819621136985, 0.020130097905339116, 0.10082162288667271, 0.7491847956563517, -0.26045665220561093, -0.45387792574725455, 0.8423046134537856, 0.0013222564152622594, -1.3840687802384966, 0.24809856655284585, 0.6236705364689151, -2.7638627282323274, -2.8628417977072798, 1.3060318378592553, 0.8169092138526421, -2.7539608247864997, 0.8170930436331907, 6.530612398217391, 2.2433508337885164, -5.37569139913656, -3.5285736560507606, 1.5428702715697005, -0.44219628124126686, -3.4080254762043136, -0.9404142685818515, 0.9206109935546706, -0.32142292215291074, 0.5835254888082709, 2.1259446047415462, 0.023237714906226697, -1.2827435295750143, 1.005416482452142, 1.1342023270443682, -1.082835771099543, 0.6309106248397022, 3.5927642357222624, 1.3927580111741367, -1.700567271994615, -0.4222843543285364, 0.8936126198910654, -0.08911766715598338, 0.2771555875882337, 0.5877785442347466, -1.4227502360067383, -1.174730775664264, -0.03298781307149204, -6.502658063798474, -13.877989076038926, -6.3655994920210945, 8.496102047185841, 9.36314750069261, -0.9651511117527171, -4.049899383761819, -0.006625413543296442, 0.38350661066252595, -0.8782780051369767, 0.7878749379351917, 0.9581600475173102, -0.875880009468774, 0.41643681124956416, 2.440181919644331, 0.7503626474912611, -0.9029823559374083, -0.05244168619492584, -0.036766877283494113, -0.10459248884583977, 1.3593750787518561, -0.26975739959981715, -4.179827380275757, -1.9167221156237995, 3.731958640757303, 2.2098791422377846, -2.2999776537953136, -0.2934575879818265, 1.763685551834964, -2.8362504454643362, -4.727829178987256, 0.27066862711090395, 1.6992454647519095, -1.8776608839251159, -1.4998695426003656, 0.22662387185530822, -3.3016455088252736, -5.307951718551618, -1.0000079881026551, 1.2657796842356102, -0.4466951447915781, 1.7680356622496982, 5.669950628192428, 3.467980185250742, -0.6028359994177941, -0.3158372167657134, 0.49845344546183845, -0.32869885256938536, 0.42308789600030233, 0.9836298257362202, -0.5714960626820738, -0.10177999456792927, 1.5109849546069631, -0.9054073849321641, -2.969245603016165, 0.07597608117826377, 1.1111977325012246, -1.3054436198339934, 2.8705324356048876, 9.605429779755816, 4.3226996736165075, -5.3598950906752965, -1.2395126843483404, 9.090962309623345, 7.830374030334185, 0.3303288094044746, -0.8250327980200183, 0.7386982487431166, -0.15894756398973878, 0.00013423229317765958, 0.9433126946057939, -0.10367166578752919, -0.35763985837153744, 0.012728479381893962, -2.52923391632789, -3.381536166980255, 1.3073228377071886, 3.4205146932387276, -0.6566173465727125, -2.1508550291993416, 0.6031037845710217, 0.6299310843903911, -0.5139212211896858, 0.4769270096951794, -1.6471592007284535, -5.615819143681294, -2.793064242108484, 2.074294649818819, -0.1546934835525959, -1.7249287882846192, 3.8787886529786655, 5.373863615524051, -0.7973969131636296, -1.6782977770214924, 3.3956886590851227, 2.9076666987500244, -0.33074310619794006, 1.8580480438338198, 3.3048276735683455, -0.6141663211628661, -2.127764216636218, 0.4195446742222049, 0.6146887281015616, -0.3714584898424626, 0.5967257697457768, 0.07375380003426985, -1.648780078337973, -0.5754115683454157, 0.6243602828353341, -0.05150485130178417, 0.8407469595424437, 0.8187700738846573, -2.311026237676202, 1.2101365395269437, 12.149693624431093, 12.20054895626932, -1.2756228605278925, -6.768105118217029, 0.38382678669774745, 2.8112772317240635, -1.626857133602072, -1.682369952875629, 0.4171712339200313, -0.6274400279042046, 0.7310412178169131, 4.299257975756978, 2.830068097019202, -0.12193430406590028, 1.3349387735954625, 2.0851721188052603, 0.008157118016321888, 0.3923011716755957, 1.0813159958050829, -1.7515019533149334, -2.4464971867935614, 0.36707111874076326, -0.09670789388479219, -1.744501114991544, 1.1337027219595306, 2.9018885812942194, -0.11834835854105887, -1.1913851296780795, 0.07636550229809855, -0.9418344643123654, -0.2505170373642745, 1.9264732334015815, -3.3540609880732255, -9.667753700071032, -2.8343995260991712, 6.646657292722439, 1.843439143984675, -6.039029328043361, -2.15229881135177, 3.2747976924481956, 0.9661086137004705, -0.5519497706947112, 1.5877509150924314, 1.023312817628884, -0.533564257883574, 0.27642503010407593, 0.16490665668844992, -0.42598432861433405, 0.8524193488368372, 0.22142458598075754, -2.0520923338528787, -0.7259946334901043, 0.6362832069516329, -1.8258025679188579, -1.1866172100709225, 2.709608352381075, 0.2861305786308538, -4.529884710875642, -2.013880184637241, 0.9370420068165757, -0.6928223558858708, 4.106735114614198, 13.865246737812166, 12.012731845316017, 1.6212951873464092, -1.0448403601471083, 1.5037461784621768, 0.16196798607074403, -0.8655513257058473, 0.4240581992728451, -0.4602569169869616, 0.039987937198668506, 3.497247061166147, 1.0684692778985148, -5.96806796340479, -5.94552597562884, -0.9356593183985391, -0.07206640950937396, -0.5260832694127469, 1.1704319172794728, 0.9873761110021331, -0.22624082489253608, 0.31287440210755335, -0.32428018466916725, -0.49860236580713835, 3.091485243221708, 3.265772234625361, -1.6552110640994389, -0.15018773980995154, 5.143958676718155, -0.018315502680261612, -7.2665253334381275, -1.017181388739967, 6.490063562542797, 1.137045732311283, -4.130051395587833, 0.08628676222650962, 2.5867066120219646, 0.07784486604508273, 0.2363043067662651, 1.047204762856692, -0.9112039126110717, -0.9351840417899868, 0.5835507118410926, -0.1315939048401252, 0.17020042636035781, 1.740348509098534, 0.07393309672687291, -1.3044054233473703, 0.3809855759997436, -1.3002030354055263, -4.50918549120932, -0.800313256877986, 3.2833443639958277, -0.5058932388002195, -3.0698481887059184, 0.3418483646433897, 0.707428792078488, -0.7654453397616374, 2.514950225177764, 2.873330810455525, -2.7132472141686623, -2.6514558708543, 1.9626401840829728, 0.5330939969714403, 0.1264559100993262, 8.049958096476177, 11.202391804102724, 3.7695028719769033, -1.2055525582294329, -0.12427805701371065, -0.10156050073098895, 0.26971730101819413, 2.316462238365703, 1.1446247544176091, -0.6787852838279413, 1.2035947147857, 1.8120398064699703, -0.15351673488058032, 0.3224791469042604, 0.9077538852037603, -0.8134906893569034, -0.43108414457598404, -0.21185269308751364, -3.276351551605147, -1.3482000834394474, 3.2898649608940698, -5.549775451325183, -19.649926464551953, -14.31190423229942, 2.7064080266628943, 6.333672449873724, 0.44742923900685994, -0.08546183652482849, 0.7034854819829092, -0.9979690745738573, 0.23286975864477033, 1.7672666215554267, -0.1227280908682957, -0.44597570399379616, 0.3695634912376413, -1.670902150564358, -1.6542808757872693, 1.226303262445565, -0.4860932786597677, -3.621418655701912, -1.2659864840462773, 0.23608321414818448, -2.710469516500455, -2.6287370192138497, -0.04092258853722353, -0.19847699139526187, 0.5832271966758339, 1.7724522679761465, -2.018404769144627, -3.3774380331095055, 2.277821224686264, 1.934280413767633, -5.67649609918997, -4.945414875801178, 1.2258231548752714, -0.40151295670907794, -2.174906603911523, 3.163706825241277, 3.544086358166728, -2.664053613358054, -2.777188966606076, 0.5791704387939993, -1.4076447720341327, -2.9234124298205053, -0.17859592015413556, 0.639102000605321, -0.33184046283138513, 0.16476625015025942, 0.04128211087623133, 0.010098336921409611, 0.4626849582818807, -3.030463383117998, -6.10878869391601, -1.7658056617874103, 1.2226541320433502, -2.8871966831446603, -2.618609780472147, 2.1471940726614456, -1.3204015605392125, -6.568411450597087, -2.3908242649724722, 0.17193098785951066, -4.817323254670722, -4.055102656368942, 1.958694992247792, 0.7508533438719427, -2.603800158740327, -0.1822347130027016, 1.1329583470315627, -0.26388421883700103, 1.1268705035490736, 1.3607997300347536, -1.0897060825996467, 0.5725803849467727, 3.0048266887820336, -0.03803251534920226, -1.547148802279739, 1.560840228451169, 1.6484524756056886, -0.18749891178925643, 0.8591455404372907, 0.30859627052681726, -1.8462510197997777, -0.31183730355896944, 0.6640432454861742, -1.4019962128266732, -0.6653387529784899, -0.21774725986322158, -2.5211901650352897, 4.018531299453059, 15.006866487264293, 7.6480305072224635, -10.949888711394811, -12.148814062793143, -0.2185531348753252, 2.617002412093029], 'positive_zeros': ['0.84215103174053331626409078762', '1.350674364565874723061928681146', '1.83361042806282984415295402082', '2.83617772227677330268102570424', '3.57557603479660555710305496668', '4.21485848474823807432048749911', '5.11664028923158221177143993833', '5.881744308133265409639403292916', '6.42135002092475364664775015268', '7.11117196092078467870215294726', '7.99700194270192509433147415437', '8.71769721188487274833871684823', '9.48171538260524457195329365448', '10.18424074919573952476353015233', '10.774405530075417524484840281974', '11.72472745093676604397077487560', '12.160089958720440384243728703731', '13.13279545414850609096859634729', '13.3020517974613611969973498290', '13.85230596729161633753111115713', '14.577920344294565049728294910556', '14.90796508322647279860373691574', '16.235879376534178409529006949909', '16.64211885720143534320180869515', '17.47190715050903353811405094242', '18.258270884285242622808736210725', '18.657342296679129900788763367483', '19.607182969243459155847766448916', '19.92680881910712930555029329585', '20.75124947794153650007342238015', '21.05811126406718456151939629776', '21.52419450728806467155841767883', '22.72746777552710724051849092472', '23.12131669399253162321390834691', '23.760308869921676100222538138858', '24.17636499297526097329985729102', '24.95525124264085189728090904480', '25.29432147994592768834558532939', '26.10152796364489058021862836202', '26.74471495904900709856759959612', '27.68419888659767984543985723194', '28.41459534946031364179560617731', '28.88798157373010648223615320694', '29.477740491060847959009808643377', '29.92569015635160109642378112116', '30.50356375131295656470264038939', '31.03508308187111578324966784088', '31.63486932436759888722545281347', '32.33784531312518911598619901201', '32.86427130305488796917657056956', '33.38771684701968270036976751064', '33.82963394384597678942399267441', '34.96715897372033479675575885567', '35.45441823350114489976540001662', '36.40299608183549673932622157594', '36.56275672376702519346730888044', '37.15075945346037677968224175160', '37.65727179837545608511962068776', '38.37286474074113508761191256169', '39.13881840904176161920855456881', '39.73941718723426093175813043291', '40.378200245063052874925000056987', '40.62241685820167983579225698717', '41.33577453305638239414290108875', '41.71953205290321790067783945128', '42.62771209254942627394629077698', '42.77444948480251790657499932120', '43.680791679804886492003788539841', '43.955301128700581624610872185485', '45.287452798580497754307844133221', '45.65909908032041804254468168095', '46.19706503738603647677792827901', '46.79303963997633995124468236130', '47.55403849156269209813030584210', '47.90925542116974293703757373725', '48.3982458618187060464482283504', '48.87267695083096559125349996470', '49.46140145897396496030577895276', '49.92430122894657328764288351635', '50.71623539426947971211851961912', '51.39021752375456981352124011471', '52.10786747126797667034408124650', '52.41587237260738332914282829751', '52.96882337811198400185318192171', '53.34549374911718809013270738718', '54.51677630939528926510961036500', '55.01139711250069665589390030752', '55.37056426067562533206995956203', '56.07691405913620599552846622409', '56.634658238936108312750964425924', '57.320466685693926666215893188955', '57.54487595796063564924083223081', '58.63639041274189338238839000452', '58.8196127444851130917524418917', '59.38165652623828495343294431150', '59.72236236638597536599894033066', '60.39447863838106234717065111164', '61.04714845572739244635689166646', '61.21741843686891018577186651391', '62.5394138363183718593509363406', '63.06536346808367869293782777874', '63.52560695043029754507846978574', '64.36257249407229955119336692602', '64.640835741497044771633189763394', '65.22506028479503902423779539712', '65.65261453145169442109059389162', '66.07228734965353502110166809723', '66.936363626954320865085928079654', '67.42976959906227122702068155677', '68.03503537745978141822927493724', '68.5189443456010508201627484178', '68.9885189807899885019386907425', '69.64116614298213010016819555458', '70.1607400384139935264032212158', '70.59738268100105620257365086783', '71.5571222539408636357274381223', '71.95870413425039229141495243601', '72.280086255965884052545241064165', '73.06264997168951776576051235889', '73.81661789584115231068652869556', '74.65459811951104868107086457046', '75.00893822802342747711357171398', '75.27440722791033111464864064199', '75.87566609066466166162285793276', '76.356927089102507293745384423125', '76.87520508582037526814976830307', '77.46564808199499816501088128039', '77.88646167767787332871630561703', '78.645914403273311147617970146434', '79.12402457865888437753613996853', '79.650567986314196914426525851313', '80.38980570985529843511053266368', '81.11946339750061838202618716256', '81.53115076863756698756614707813', '82.277124117714411475718602183183', '82.72882438295666108230999015508', '83.036427703712778567890563457154', '83.75247101873748422844537007070', '84.25441876035020120040710496946', '84.82916443299720423826934286176', '85.25720759485487691522188249760', '86.04339032214197732026526227605', '86.61877111744788837449723410742', '87.15568674577185080495545827708', '87.41969756994750230299148318846', '87.9225458667903067808416187780', '88.61495323958803090571323250057', '88.744081706806607074243867680610', '89.81138800140377074280166240114', '90.59284671678175493087808794564', '91.25064164528584153303447211357', '91.62481624429730048661830477520', '92.07019092168960727031946977968', '92.6451369305242035402146462068', '93.07686710728897827413553033421', '93.841094389743822759909943760552', '94.39356013440887564865485185973', '94.67033777783705509387745173967', '95.028580218796377619070799893880', '95.60343162908012492807753225776', '96.344463697738772947750647520404', '97.00061886665643595217759777910', '97.52173405379667222371646598036', '97.966902567948120093983408618136', '98.7336372504114172971722598061', '99.21291146366118341526897214902', '99.86885272008769776241831467589', '100.05039731199279462691666896998', '101.00629135076105077496947474744', '101.46514162300720137270148570757', '101.727769895990220516690352826120', '102.74128392887626064986506114865', '103.18716643782696726094343696947', '103.616779304262104517778005170782', '103.96684919236647377964944366173', '104.577017250194174653485377416006', '105.01511959179221193909876955778', '105.54867853799597473096974838379', '106.243532721795700208440319970835', '106.6899119593527179918825334752', '107.05579116177185122769009369337', '107.92910448125303935017012015632', '108.47195523663761480832726510037', '109.39617359044373863366428527145', '109.81253178814312063405549295342', '110.26943099780524070420924354067', '110.62496678096271663750789021934', '111.22576288898791492119966320433', '111.691973133548747367741824143004', '111.878980255860496219700366888973', '112.73779459669668613282780317388', '113.392720080846776659557481505334', '113.98975376536725422726305301302', '114.48764087944863516986090697288', '114.85770929115978003527635659396', '115.16836930619395646790836275481', '116.08057322298928948392093960611', '116.55128167404055081205599430324', '116.99853737177756522830382193314', '117.77119433850232966693838207151', '118.23112569392745037615889547768', '118.99515152555247302881002702361', '119.197024323774004835173518898', '119.95636191956052885998388348088', '120.570103100085933377836637876182', '121.07176101804854122406907043702', '121.405433486192467788008216142558', '121.88683771612217797529029520869', '122.59165330286894973126555841652', '123.08812888734652742348939896414', '123.23175494996771259349490412487', '123.83824408039760915157241860911', '124.3308538927086423531764563665', '125.28304210669303621342910916457', '125.921776762667446657412273929237', '126.44602408163769477278723410340', '127.07477490451348654942679718547', '127.360977604323614251631531183173', '127.743447530274918866760544038080', '128.714602905015917954267339741', '128.86867040369446820165991379440', '129.68924206984265450997977384386', '129.921494861700750861430270640886', '130.45928744504333870487016298476', '131.20117376206021784593373466322', '131.55006792349863068286062879002', '132.09794190676334662201712321193', '132.801212575713401086397762421744', '133.39129561388213206915230744882', '133.52947038631552246724858827956', '134.089479990999026303500585500307', '134.55184616103675661948795120948', '135.38459811605860373144012984686', '135.99285044764504369261707323330', '136.650931272123104900938210230069', '137.277555437003077356557429918590', '137.59352733137863909021231295523', '138.2776194686213824443233831316', '138.67143753655060576975373297034', '139.10984199082320385196472280451', '139.50536003982443098791939836173', '140.027847757965426020101583345647', '140.711607967202731240929051681872', '141.04727885181479367699917542129', '141.65012747030134852790508709841', '142.20264325469746819057365670379', '142.952335013066240646854390713873', '143.30221421514489796546621684737', '143.56926974508834101268392514280', '144.76043271291863312019860247193', '145.11584448727130595903757514834', '145.6455592073037689372579202631', '146.12737821248937235193518629600', '146.467304301348899014042322486486', '146.87070919268089405753397073760', '147.54759619287437825923419026342', '148.55525489515361402702008512946', '148.72804529395624482624105752527', '149.1761741715575646208320937949', '149.89271361967460147635890997228', '150.177142897730080681624745972353', '150.551128370372578286910792249524', '150.99962445341218874002750682616', '151.76249222896856143390899133424', '152.19524433382411232693190597406', '152.81192008700467765338050661230', '153.46658019193208052744657679066', '154.10359354283870988456109525680', '154.68270261743509668114371879601', '155.325194063769093676882254316780', '155.57941327357732640924267513291', '156.11971818037254295286957010090', '156.7201904530258551655601374739', '157.15041896393792236752660880624', '157.46741780526729354873645952549', '158.13336327681124780780229725068', '158.67229568939590453449527998645', '158.94255159405922833111257761', '159.72732777954653959749813091542', '160.28389076529263357792612713523', '160.90676298641681487842446362152', '161.34219408202664629850898279180', '161.676836285875263298002721080546', '162.35220776884103017041750457500', '162.97162825877933091180252109127', '163.48720925849259081572734537105', '163.74082516614514600879970184981', '164.85996005983623620399379902377', '165.34590611665089662930610433935', '165.581673117791153804072387790110', '165.88571844136001347778542905407', '166.696092002983887494634638244025', '167.036675977754430308076036163104', '167.77843823092228664383757956434', '168.05772250991082270570362478333', '168.60681176755030155929630413581', '169.158828256695902709358399672095', '169.335937567432871059555072719117', '170.06813321323542127854803570605', '170.49851309970376020720880939494', '171.50338867885226584432437007533', '172.22531299156420438502075659931', '172.514219096173008905361654562959', '172.94158737496055696004436100865', '173.40985372511480533507770779920', '174.044142891837906182005638483964', '174.47576085945412872599146079090', '174.77980367802639058782294573661', '175.475762284316301185976586565445', '175.89970483817479010340438295094', '176.689618452428818773018929569285', '176.91462310865983783408745189145', '177.82257640524753326925353033780', '178.04221766242207850933084780134', '178.33827346729895676061185303198', '178.93240634967141539950550717133', '179.57042791184162365252095840165', '180.08330503670667804208207303822', '180.85089479512210600879017284910', '181.22160398893407778328750199865', '181.71160341952354088655989076266', '182.36226628726546039787406945134', '183.033657177040357969242923581096', '183.3034260570814748706242981645', '184.083804393531681492814445008826', '184.543766669916809668297696415734', '184.926095939747134332267718854638', '185.3332845092280501115963776646', '185.62107250169987046921722158160', '186.02027384587701568606296498944', '186.97430049378487136932945520273', '187.31074158611322143027503462350', '187.96140671367467897986598695985', '188.378525561877390473615844876575', '189.210036027771085144494400385516', '189.39383555902896139638609932678', '190.191792922540374095335121739220', '190.67460258527015644399993091379', '191.266933494072005719219869176295', '191.78150912018341520632452234021', '192.01112298576159929331992085385', '192.65910530693622982281007992783', '193.07551070338328405859210081256', '193.74706454777172011389430530115', '194.22874940810150367498180629490', '194.928719597399934558703003807183', '195.12815005251747535258069244326', '195.66311165575196582087223991503', '196.288446059849071481707772157409', '196.6723088612150001343296372893', '197.30427304009411583769422813483', '197.46035332900581310620422192255', '198.00571772237954573842214705196', '198.87120853544443984099929614604', '199.69479823740114391521487133409'], 'prelabel': '1-6017-6017.1015-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.942830525881202, 'root_angle': 0.9753812444651122, 'root_number': '-0.997010590282433090151669407832+0.0772650170819520121133035259859*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(455)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.37847835342076127893036745411-1.98331267163675607975012184207*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.842151031741', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.35067436457', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.83361042806', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 27.942830525881202, 'bad_primes': [11, 547], 'central_character': '6017.1015', 'conductor': 6017, 'conductor_radical': 6017, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6017/1015'], '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': '1-6017-6017.1015-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': '1-6017-6017.1015-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.942830525881202, 'root_angle': 0.4876906222325561, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.842151031741', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_6017.1015', 'Lhash_array': ['dirichlet_L_6017.1015'], 'label': '1-6017-6017.1015-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6017/1015'}