-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5160.227', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 23.96293925769437, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [43, [1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '5160.227', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 5160, 'conductor_radical': 1290, 'conjugate': 'dirichlet_L_5160.1523', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^49', 0, 0, 0, 'a^66', 0, 'a^97', 0, 0, 0, 'a^43', 0, 'a^32', 0, 0, 0, 'a^59', 0, 0, 0, 0, 0, 'a^100', 0, 'a^86', 0, 0, 0, 0, 0, 'a^77', 0, 0, 0, 'a^30', 0, 0, 0, 0, 0, 'a^81', 0, 'a^14', 0, 0, 0, 'a^71', 0, 0, 0, 0, 0, 'a^36', 0, 'a^124', 0, 0, 0, 0, 0, 'a^53', 0, 0, 0, 'a^46', 0, 'a^13', 0, 0, 0, 'a^115', 0, 'a^112', 0, 0, 0, 'a^5', 0, 0, 0, 0, 0, 'a^26', 0, 'a^62', 0, 0, 0, 0, 0, 'a^45', 0, 0, 0], 'euler_factors': [[0], [0], [0], [1, 'a^49'], [1, 'a^66'], [1, 'a^97'], [1, 'a^43'], [1, 'a^32'], [1, 'a^59'], [1, 'a^100'], [1, 'a^86'], [1, 'a^77'], [1, 'a^30'], [0], [1, 'a^81'], [1, 'a^71'], [1, 'a^36'], [1, 'a^124'], [1, 'a^53'], [1, 'a^46'], [1, 'a^13'], [1, 'a^112'], [1, 'a^5'], [1, 'a^26'], [1, 'a^45'], [1, 'a^88']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-5160-5160.227-r0-0-0', 'leading_term': '1.28790341380607614213251183931-0.280921613285389402286975877732*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/5160/227', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.318185175195128, 0.8796986571452535, -0.36041202549454654, -1.7158579386787984, -1.5742753802039238, 0.46850954504207243, 2.5736448392642997, 2.445318339508483, 0.14203569087085946, -1.697072494273554, -0.9877568344308583, 1.0953530626030017, 1.6566692262343483, 0.14425856810885437, -0.6843384565637456, 1.3367191522838264, 4.304449707213622, 4.480911725982921, 1.4736251995652445, -1.1354282031644847, -0.9075870383706355, 0.08916178009387968, -1.138473564567937, -3.42704705827013, -3.0024476957074535, 0.4415891745861439, 2.7766569370150704, 1.545123186608061, -0.3417278929555206, 0.6228786018800678, 2.8367857214693295, 2.2882757506587623, -0.6726487837553614, -1.7767944227602879, 0.06955779460226715, 0.9639754871121983, -1.2415268845075307, -3.0213868950331646, -1.0602241877581828, 1.8779056175637607, 1.3208670502425117, -1.5132195351374398, -1.9561935128510677, 0.11726392535882005, 0.501077799818494, -1.4057735037985626, -1.284116628835083, 2.1135456625072013, 3.965723648637777, 1.295981145193863, -1.8545775878476898, -1.2323211111857784, 0.8174133181247867, 0.4490737363937636, -0.3609950469216897, 2.0959136057902805, 5.403172316673004, 4.483426245763079, 0.6796943849292613, -0.22792447925364046, 2.118993965173043, 2.6746788059266144, 0.5556086521894454, 0.2756691746365217, 2.598668363161747, 2.673845906928093, -0.6647721831478546, -2.1286061396668674, 0.49845765925834695, 2.2564220998455258, 0.22942814263435643, -1.2004958762815403, 1.066901875042276, 2.9128659747320693, 1.0544450636124896, -0.5837563274192156, 1.366189453658913, 2.945056509249377, 0.5560029767727915, -1.687255994897347, 0.4273466862143482, 3.0569555923929213, 1.4663977184517762, -1.2160175239844855, -0.4208454968086952, 1.165410146076104, -0.2922033848217899, -1.4297881530304906, 1.6994686221989819, 4.922249419670053, 2.995174362989239, -0.710758264846397, -0.709407438509465, 0.6472333036168347, -1.028771860438107, -2.9092498565411518, -1.0561285042026511, 0.8162942474069432, -1.6255527695862642, -4.244338623918234, -2.0083495444517245, 1.3245044710189604, 0.6183718874222064, -0.9567161069473467, 0.9165632140421877, 2.751012616023789, 0.804507008635709, -0.7575685777174158, 1.6177543896137143, 3.030867979695099, -0.34965022454525474, -3.2866634018057543, -1.41405168815348, 0.7336849310349564, -0.5559254157269938, -1.0546711217972087, 1.5697631914863441, 2.1419237891694234, -1.142332821617538, -2.0858632194656286, 1.4398912162818382, 3.1498473266864915, 0.8062985650864443, 0.05449187699214339, 2.1750561668723654, 1.5619258049379727, -2.00165002189081, -2.4027199192555093, 0.22909217592865155, 0.011965465521549042, -2.0035093905933765, 0.08596848680655934, 4.138019979900389, 3.4638442949130246, -0.04343929043767962, -0.1302605490684605, 1.4980963239740754, 0.3655853007673825, -0.21505571920752597, 3.432326149618809, 5.8984923249631755, 2.5845199680094604, -0.9026382040849769, 0.26241977655284493, 1.2825858230056315, -1.1979549768540207, -2.228560963220922, -0.008813316747032285, -0.058099552167800494, -2.6935805849199665, -1.4028891842309732, 3.2373032506189694, 3.677295393999584, 0.12056999127477344, -0.6281008035828413, 0.9117521151525672, -0.2628282054188591, -1.502772776904086, 1.6050281964154296, 4.240927538611314, 1.3137169049035957, -1.9316763756771997, -0.5662935631901336, 0.5529059040531842, -1.7254196086612774, -1.831027562644647, 1.8818866856389613, 2.8145263582886124, -0.1144401138231467, -0.5751369702387534, 1.2282984687529241, -0.41680643132409884, -3.050472567434204, -0.447326926147782, 3.654007045990272, 2.494317443135178, -0.4679280292395091, 0.17242562003790537, 0.8969842555136801, -0.9231400377261408, 0.11408927097774016, 4.850353272471127, 5.480364846681402, 0.8526882047309217, -1.1002152988539349, 0.7942740730252924, 0.4379652688396273, -1.2326429930121108, 0.7135079597779808, 2.6963091263400796, -0.012931051690469757, -2.0246054294091613, 1.2472013615075355, 3.5757319846414704, 0.9579216229359485, -0.4942842694488262, 1.564198101740594, 1.2309256735423828, -1.4860383590257094, -0.46823058106974114, 2.2259444410899345, 0.40444015746663736, -2.256449607548994, 0.10928135621504119, 2.656338974290277, 0.29173155193958206, -1.6405061562598076, 0.24887584632801868, 0.19238705690071578, -2.919207147589376, -2.6253020068927193, 0.2639391642322455, -0.8989433986239298, -3.5264470921351294, -1.2779131894803195, 1.6543597132121834, -0.5039387465708826, -2.688725123995674, -0.4183510488380762, 1.0955907153582425, -0.02009968686668564, 1.9517238738000715, 5.696738224740521, 3.7699639747708975, -1.279633472158692, -1.5951174498417517, 0.19382617033350377, -1.5535714506899427, -2.6249525889406278, 0.47512735001232365, 1.8258398267788938, -0.36953799243196295, 0.4005051973413098, 3.4302152701369186, 1.3765844222134886, -3.219795498443985, -2.644603658433872, 0.15218428025180933, -0.6126440528096618, -0.9706348170472334, 1.8721261705878438, 1.904168953819985, -1.4213063073827956, -0.5312185006731894, 3.5677787711513163, 2.925718689682438, -0.3271945421423437, 0.6100827829644394, 2.389084757467732, 0.6089942505910584, 0.4082455614628679, 3.6022073364731515, 3.0829208642405277, -1.2152628710565663, -1.436901145188071, 1.0841183161278238, -0.5690313297248669, -3.061587116775443, -0.9255689974756037, 0.6976586662882521, -1.7961200071472039, -2.0745322647924542, 1.1570246307230518, 1.016082967020631, -1.3376417310966289, 0.6701092707724352, 3.1252668037794344, -0.20512258273996342, -3.605161627374804, -1.6156986320570326, 0.11472305992648789, -1.0483477477583616, 0.2048795745650326, 2.173779772472027, -1.3498582735638727, -5.382560105179501, -2.559421145352379, 1.49662846904827, 0.47037458317080494, -0.6740588244446647, 0.5223949247652118, -1.2569732482366898, -4.110699976121751, -1.3295461234690924, 2.7077250813451066, 1.093123299274046, -0.7976582701198026, 2.0351274652238076, 3.2901840853412905, 0.57891592775586, 0.44399545165919097, 2.1895092159213134, -0.23768009168809598, -2.7587911885954375, 0.2248401690548032, 2.504028714588297, -0.2613342470930243, -1.2259614934900838, 1.1903042731702131, -0.10494999690417035, -3.5771129025303736, -2.1720911977466164, 0.6124540664153307, -0.41899614922449835, -0.015347814929428563, 3.8192540603895986, 3.5623585774841375, -0.4330243560277266, 0.24035144665395114, 3.4839132659783587, 1.9843795214634832, -0.5052045875962612, 0.7649097752007461, 0.700072533087265, -1.562612085343279, 0.7640606817002404, 4.933713918596832, 2.4902970540705205, -2.366514385805725, -1.7385894823489936, 0.2609205945608507, -0.3066550085837201, 1.6049396741810706, 5.031051498238285, 2.7404521421684396, -1.654570765819801, -0.6079387183698403, 1.0237995367832564, -1.8999332865083014, -2.8963245117002274, 0.2979514875609336, 0.4339732890081043, -1.8167981562411721, 0.08919593665704666, 2.4339421047867984, 0.4577179898541075, 0.5149032981321658, 4.793105501379161, 4.763421751301342, 0.10822463427027174, -0.7488811971085712, 0.7447137739990493, -0.9884796520924592, -1.353382514462343, 2.1779638722808174, 2.0947334246904865, -1.8480034343690854, -1.372874369800649, 1.4529893021588107, -0.2754932587931153, -1.7539043303471977, 1.6934281735888226, 3.158966968221465, 0.37873367526203394, 0.28396146087860236, 1.6813278908592417, -1.02026321930186, -2.365384918662805, 2.133368665927, 4.21374051441067, 0.5499291104400241, -0.7161722989062893, 1.074590367919584, -0.20123942590315977, -1.1384700868559325, 2.187712254663484, 2.8464183602123274, -0.9561611033650854, -0.7541551558940754, 2.6056510793025596, 0.8600813490811093, -2.5871557740323428, -1.2201099356901763, 0.005865406930345193, -1.676457508596042, -0.1927503578440189, 2.543301560956014, -0.6203759703682431, -4.334603430512716, -1.5384024123275535, 1.201731824583863, -0.636171545082855, -0.5974518130727511, 1.3494113850953078, -0.8845329565154881, -2.926818060966776, 0.48061096664849534, 2.230759570532854, -0.8939928361956053, -1.0218140414890486, 1.6806813152859856, -0.07571091526069827, -2.4506773993260387, 0.3185907208673224, 1.8319979352719147, -1.1010503106534117, -1.3778710757299102, 0.48598043862514595, -1.6698401669915803, -2.8417200754764322, 1.8311300533214363, 3.9863936231867676, 0.05067172881323699, -1.420815489186829, 0.5794315450362308, 0.01644511955229082, 0.08798109665437932, 3.4528201689836155, 2.2908096675847505, -3.716570013249395, -4.328844620888552, -0.4276987234899143, -0.46603993668462607, -1.424911116943539, 1.0657743913419253, 1.2725996334676895, -0.9012426881589863, 1.810974329493905, 5.515868804816559, 2.8156548167056243, -0.020127151705932756, 2.2774862752742844, 2.619200368534332, -0.16767860793485695, 0.9506761025915645, 2.9913896386815346, 0.3989860753802477, -0.5553754106856003, 2.898315026499572, 2.6569607522915875, -0.7438154515632356, 0.4239057978796805, 2.0430886296228308, -1.6043386190493365, -3.492921889956258, -0.5367064611003591, -0.16774764676873194, -1.6610838738967435, 0.6638616770765623, 1.3597701480813171, -3.075144226294287, -3.758303039126843, 0.7164840922488326, 1.1998659675815027, -0.9816825484594218, 0.7635190058021515, 1.7892759289864577, -0.8233801902185898, -0.2585703905087821, 2.003803420210211, -1.5269742294716238, -5.2840615144023735, -2.2836434279410223, 0.2862345008046628, -1.5128495721152895, -0.742434010761868, 1.6590214675937878, -0.1193591411869028, -0.8264096628953008, 2.747415225539241, 2.200587802045467, -2.583715814728504, -2.2274996485617846, 0.8333289970021426, -0.37311929168591995, -0.7446710255843767, 2.3908004838947154, 1.7234680915252187, -1.3849005573659574, 0.18225433934238142, 1.4786527218951748, -1.9367001075105306, -1.9395142973627102, 2.6975360269451967, 2.7190216419659428, -0.388803516780306, 0.23719812775578086, 0.260876890084577, -2.37742300474044, -0.29992807128448906, 4.15020565485573, 2.222043152774527, -1.348170207832789, -0.2815079500747772, -0.9772742565303165, -4.679473797470402, -3.2950751950369885, 0.5879706368565186, -0.15192409232712661, -0.5560211378616275, 2.1175583607381623, 0.6784990784031418, -2.667443386464697, 0.26787906342242007, 3.72153745632852, 0.85533316644603, -1.1499678857869524, 0.8311347568703671, 0.45531280502790394, -0.01882144577401698, 3.5024566949584894, 3.269061750401658, -2.6831551053673763, -3.8584017862948325, -0.23045039692181918, -0.5628011609895549, -1.817435698810419, 0.5384507837518375, 0.4895256283107583, -1.5484830214334995, 1.719442996973626, 5.157752121619373, 1.8933715407911087, -0.561453803104764, 1.4952886675896875, 0.30793410280389, -2.737911421107202, -0.6818061561478559, 1.3057777865637343, -0.60631277295676, 0.7710916890140348, 4.290172227237265, 1.8775057718282258, -1.5201843321927926, 0.28581312059574115, 0.26688353130581877, -3.143460571904057, -1.7725877661897187, 1.5595453293898591, -0.1753998076453273, -1.4359784034600935, 0.6607182051591849, -0.7318942778503496, -2.791701730625488, 1.5725974556722377, 4.950306891081831, 1.3219910986055095, -0.8132398934954426, 0.9883582620951891, 0.08305010444401403, -0.799657638835316, 1.4109214019570104, -0.8737675851298833, -6.6451525035923495, -5.126803992548769, 0.48240050435569093, 0.7524505773373537, -0.30257271315250717, 0.5070654702035028, -2.488834607013422, -5.729415405609844, -2.202390875324462, 1.0068633696010594, -1.0798184845999117, -0.5258974800471148, 2.4663376275928712, 0.14939095364813676, -2.4925510995427187, 0.4011063705031444, 1.677071201360989, -0.2293057728468217, 1.4631631487846772, 2.664129162489756, -1.6175969725238883, -2.9567490518948567, 0.9523328463527442, 0.9957739695651564, -1.038004584592093, 1.7144687113963335, 3.2093186744348765, -0.007161458279424312, -0.4018832020787034, 0.7741969130581382, -2.4400094144223137, -3.337028244588563, 1.5194304561975134, 2.3439991141289056, -1.2589072538138464, -0.5369771737656773, 1.0974893525995124, -1.241225679390225, -1.0387184160461087, 1.5668650068614227, -0.6072995513310843, -2.2662653866555535, 2.105077178515314, 3.5878635167354678, -0.2718717877395982, -0.317407505598971, 1.8942015198643476, 0.3211045668818413, 0.5432039952955252, 3.7977170422275237, 2.2794515209298183, -0.3453998274177633, 2.967521779319031, 4.552847355882072, 0.2613886980600891, -0.9201195663494598, 0.9915369789709616, -0.8648095122403227, -1.781967010171153, 0.9923705289105675, -0.29691609236224703, -3.443338262194855, -0.3162966353583545, 2.707618363650535, -0.15259665066304204, -0.8531454640468658, 1.52116923495654, -0.3931719848916831, -2.3451968622430885, 0.15104890218031608, -0.41231342734379584, -3.7593642861582985, -1.5485391323210063, 1.4047375908217716, -1.028912044441645, -1.1666052138964884, 2.405719048587983, 1.174890873596792, -1.5635165921989225, 0.5708272863549144, 1.2293363932962285, -1.1150419843611874, 0.5968355726284069, 1.8217702522215322, -3.2585735199505423, -5.34687711088287, -0.8622492296998074, 0.48457134499612936, -1.204571524283579, -0.08924864571941946, -0.9984246560311538, -4.248685849706036, -1.6175579136934437, 2.211142359849738, -1.1621676488093542, -3.9077305351342657, -0.6607205377413157, 0.5917068722931847], 'positive_zeros': ['0.55023699593166541307721355988', '1.50378377420183760942376331944', '2.5171710220279130895534507281', '3.271261172076777113060135776193', '4.088648210402762399249388106165', '4.5329801872840719386093727566', '5.766587409841416037363476119846', '6.49411700387211370477686229978', '6.65748695672135331089759981342', '7.77572251846465314524112748025', '8.65857924145480887223514926464', '8.96492213795580509522481615767', '9.92819855253117470020181991899', '10.61501309013883673351762115732', '11.11054733258681941001496790244', '11.97113780952668651604926587803', '12.64351363112550496631270997422', '13.41867295027488123766680304106', '13.84612932251862575185931526152', '14.511855834130692581232261360933', '15.41562841836909563723464358486', '16.1016687551467420389973224816', '16.66213104247482229376451435240', '16.96934763798997841180505350644', '18.20562797727660781027924954291', '18.48105775968868105846567877795', '19.50086829203364375061621005218', '19.61264229621653498634383822312', '20.56696954202886879530375221459', '21.20301883169449345653253652127', '21.901266898869338789481824053767', '22.39030512799026509414070159491', '23.25550203573585924516482090083', '23.58689552415949107302222216219', '24.4257950597381653035042800890', '24.96172561193517479610322351250', '25.765835224903523365476319862482', '26.30935478534677339916427726016', '26.836255632975243341260518290399', '27.37269401632792953231966836249', '28.357675502375333045427231661105', '28.87154802777497385862004906954', '29.2486912011648626997744169499', '30.11551186212267193194149967429', '30.47673394097437785330324007214', '31.40726092552372682510026070227', '31.95918057379642067048225566428', '32.39813059692378526448896861085', '33.21744080630259485710997157085', '33.58346798614717789625527250049', '34.35075718241610832149320170476', '35.149698957552258122527930240262', '35.536956588233585932678680736693', '36.08364259023221379064014666570', '36.77610104168836166149332672351', '37.388856607218371733210959642061', '38.252689399037210748961557759205', '38.424093411370368529481834573763', '39.20039454968228823618867449668', '39.96643685112063459721140913248', '40.31422903995553549054589487509', '40.9312326007213742244420145914', '41.869402289409856079091351862563', '42.209376738569950449131257440807', '42.87316067992243624003388448417', '43.159295926636063215885734956709', '44.24851832938916059047774495761', '44.65239655647446069352504339097', '45.18714313600686965737813955257', '45.93885720884574494941082767023', '46.24169730894733754831112083515', '46.97025671114767393542199922743', '47.82533710594156517543394510888', '48.239852959338008090242077375517', '48.71446823826104854709235292300', '49.254257563335861240528117661109', '50.09204483269296425160098994288', '50.69976831745373527241338018157', '51.04250219402292534067880042285', '51.72648253874261686810348249279', '52.486716691837505167800539582', '52.90373908500164965243956011727', '53.39829922088032834177686050745', '54.09085474551207900525062841950', '54.92283180579319826635321646493', '55.28190043123812674069010074051', '55.79095282615376751188097143005', '56.24043176617592193556159915320', '57.25193809956416110006468255665', '57.68920605749442437719977634883', '58.18815566331544241751945699008', '58.67974908889753678590525893906', '59.37395453216784408863827957926', '59.9104238562134485993311259659', '60.7276719439077190717498798207', '61.0364927175756741756548515295', '61.69325321549281742667252445803', '62.2323765627375326837302628097', '62.84625543384132630930539793085', '63.42889421594476442118939204636', '64.088665398904549663626676183548', '64.65183876914189671432620836476', '65.023373775012611676245168914986', '65.893545422287147779725590292', '66.150608537018264065610508569218', '66.97279474565346450788356535439', '67.45648139104585473052006690702', '68.16907815579187622446996417003', '68.73749178905688430664856074103', '68.82302750342695869184861986630', '69.9048241175534843450091254524', '70.54686427891711067811464915413', '70.728193417573092245266598942469', '71.52129361867802724939346689884', '72.13044360686305741719788901983', '72.45663301990060758597063300627', '73.20860533180469461277993305777', '74.0297138994817321569916684835', '74.26193346009494778513211197892', '74.810643917832088882365807538662', '75.484704382056857164576787558337', '75.97810997476692630390046611652', '76.824893039525393888952481008935', '77.11067352649278955392983359730', '77.92520401098235347871821516693', '78.049061944237865626982602849923', '78.965978084373064293672481123444', '79.528263163555445124055654373828', '79.94743962441198255729057737745', '80.71946846107770939772007508681', '81.05792841676758324289437662571', '81.75959936364829926975031930400', '82.29931399318120540276561731152', '82.75592194238577136150856902245', '83.424840135042796537379059764362', '84.2759210843998868094485607976', '84.431004443065943367274595892', '84.9774072597293418693044862624', '85.546375814184161546036719067639', '86.40845952193502739550726359171', '86.939273600564109618108826720703', '87.35582379770533339020104274102', '87.68477891534940618993189371734', '88.51738224588170787245235863568', '89.16807505541984361096168012970', '89.50515752004714057774683484177', '90.418059470340112776852570573287', '90.53165400360035075935326877712', '91.23153531151878142083956912704', '91.858719962889775239923915925289', '92.47555520234167473994090612832', '92.96857110442358347135553584254', '93.4287050445350348751645002908', '94.26340958286717572724858236665', '94.613371122503633626757370660891', '95.001618996075004317404944468309', '95.89292163247279143983674220255', '96.22768534674703871647978480006', '97.07227811101358644364350084138', '97.37407575838351224967347552464', '97.90061103507464189644841165900', '98.38619300549925302630123718318', '99.19905080503556250260138949976', '99.91167875476761677693932329083', '100.179139619386820142544997088663', '100.454883822754975391258565865192', '101.415326061835617040991851323978', '101.9385861651633001787979345297', '102.334304301719243988092251621131', '103.09345416137134162496780607552', '103.490869242274339770404590553955', '104.0547528266155225413743653958', '104.75585405377912598485434056175', '104.93543372520072945325366169306', '105.94667195987060551688634083261', '106.37002188692615876097755651247', '106.74947088029745899052642378321', '107.31921839005431904750367536397', '107.97203727102595017252037098876', '108.561130208169793110658375508458', '109.035771521908041674953534391011', '109.5609674415317511160666877571', '110.370944289326021847959658610958', '110.57313818151310745625853125236', '111.164925539288007094878316526998', '111.75033688291633880285404410394', '112.54882635517619773917467624362', '112.93046037356405232897573858680', '113.41219684566999255888175096516', '113.88368240853524904651966691608', '114.60519037369703734197939563246', '115.06507448121645390477468938888', '115.68633946795009371654740081473', '116.43720617678266729340952977521', '116.56453034742859113065500734670', '117.20407590046002309730694084089', '117.77590780870058573840166042815', '118.55123476241304915700191136425', '118.977276057033683108890326337179', '119.45315186911190141507144730302', '119.92458992757801249915740792744', '120.59063241334848685779834339967', '121.16644198768483135942189522123', '121.6672683380913182923263125355', '122.181110298116947678065326752570', '122.78638185498370980072365875006', '123.32996170337857594788426471605', '123.93457089310781114964082961372', '124.20457352247385740007295098806', '124.89706907749939180542389960821', '125.62882998384040501835790453638', '126.14630422402272335518073563988', '126.565903780603952203785053896010', '126.86302743263655125871831490821', '127.62045740939262836378806782044', '128.50233189868679137266246537282', '128.662247082171518354950749762220', '129.259162362019345958023051348595', '129.83893096218474810437318244814', '130.183585489697005477841129915545', '131.217553071956524732961627049501', '131.26791246467200432170084320948', '132.15857786712555674648823808706', '132.38870459219636336286029284712', '133.16380964223396038989402854261', '133.502230225810607207828728862248', '134.283848609075053169584482950690', '134.64373610351669609617133980859', '135.20368260458272642401606586797', '136.01046088669821306331783393299', '136.21924581591994629160883290220', '136.8110448381953106799810587864', '137.3022151283835965232029221265', '138.07035833227175649151335150720', '138.57630343328823305829681370511', '138.97839296660315869990827646666', '139.58934820882822551437650641112', '140.02672085107993389006297953922', '140.53687679142215257414230126785', '141.44986035472968192538094035695', '141.64868554133530275380370934318', '142.26291166303788748179884077696', '142.79936473185949914284882907901', '143.21285664611917672085251158690', '143.888226714651217517535742998378', '144.56773867742847854075618778445', '144.95001065583197569695568727511', '145.39665233701799536310571240585', '146.08259031655920726143143445738', '146.54435333246810310089877716642', '147.03181875975985628063802654693', '147.63247128718503285248249360426', '148.3774886598632255031765834563', '148.706778311603778111064008263987', '149.09660548054480779737964455748', '149.7058583424478334007491857954', '150.46498106140411360882463423699', '151.00429858499984087049421392051', '151.11407729714627642429771581086', '152.114650261023047048348998880188', '152.47725709315192466805857037903', '152.88502449022612374782274277933', '153.48719868394137965877433735101', '154.046482383783191506795642131746', '154.75600585513682016807924767031', '155.189596275605755375749619016353', '155.70801169410502728354902107420', '155.94053701139982221002181188171', '156.73793221817544951567870178865', '157.533575095045252047924346744', '157.725596446705817692470416842034', '158.37300382512830265485436165564', '158.80865618903766947295184755770', '159.2674219805840213245278666157', '160.149033432368483887999095591662', '160.42473380769486827826934495906', '160.96326785761987300392997359215', '161.62203273619817366921901500735', '162.09256945030220945560657853948', '162.433092598950892628133901998583', '163.25024342770840073778521138678', '163.71561851568519219944808744418', '164.08951374292363362867967206327', '164.81850300825577046061772005586', '165.29478386023357519771096281937', '165.83062478476071740799754974534', '166.17853059155758620716449572684', '166.79330103078159031509478113224', '167.601730966612437524697437992722', '167.96043030653479951162841376952', '168.449182944325323893934316349996', '168.87249640017580332484855005427', '169.32387810143339713632259963646', '170.27417804143913344664218585887', '170.75392813523536090139883091627', '171.03956654094972611665951105066', '171.364527195343496292958112301181', '172.33184382764197974498501709907', '172.68451300382358565058307667832', '173.17247897196103377868218901701', '173.760687961215747151032304423306', '174.34151227539041145061781244406', '174.93927992680748058055745223347', '175.1416760347078399160542097156', '175.836522766403476641751757171978', '176.48344275180337578325808997178', '176.98349941563510082968257332721', '177.35861301011077865322720378332', '178.12424392786145020174910333603', '178.500428974349592213001084457025', '178.86634116240245743878363785087', '179.59448695533658192955048638906', '180.19042835025076296492498716803', '180.684039890427076079921287872427', '181.11073232047450823937478841013', '181.66625782711286548782653894945', '182.137752790830054402126210877513', '182.68611585234093508287614950283', '183.41225643599629166618669673324', '183.78594842341081883981704800578', '184.42955337139734100923169886338', '184.61441529954248653506404940330', '185.51417201668052175849538551040', '185.70436377331962910134375916359', '186.58255616946574580972528444784', '187.00110687865054958603282873731', '187.40788571889392716280725738937', '188.00849617780132858135462482691', '188.41358911988324807669757092072', '189.08174189660617862176166990294', '189.67360579857346774145720625404', '190.10121781662958198123852677423', '190.59073503283882573911635305755', '191.231070084590520644226287509172', '191.522139767346876030797573705907', '192.29727822871770247685709841369', '192.71347579031083454468039160769', '193.22498796242572074327248817510', '193.84534985912219809004958901073', '194.31659578228081045560260135713', '194.83525201737599250311279916779', '195.2561217104098873727705963830', '195.7663512544649957335403842667', '196.633427784553012419100633782494', '196.954568917194429910945584719618', '197.52185639788743128176876383793', '197.68532042923827079026057544021', '198.530824325460721276588536555570', '198.99308982351247994463139692087', '199.75125711522466042047736823954'], 'prelabel': '1-5160-5160.227-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.96293925769437, 'root_angle': -0.06836005439795685, 'root_number': '0.909166205434703534459224588269-0.416433441134909876683117134657*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.937141211287241631335406772364-0.0730209962763484358791478879076*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.550236995932', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.5037837742', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.51717102203', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 23.96293925769437, 'bad_primes': [2, 3, 5, 43], 'central_character': '5160.227', 'conductor': 5160, 'conductor_radical': 1290, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5160/227'], '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': '1-5160-5160.227-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': '1-5160-5160.227-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.96293925769437, 'root_angle': -0.06836005439795685, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.550236995932', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5160.227', 'Lhash_array': ['dirichlet_L_5160.227'], 'factors': ['1-5160-5160.227-r0-0-0'], 'label': '1-5160-5160.227-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5160/227'}
Lfunction data - 1-5160-5160.227-r0-0-0