-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.469', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.17364817766693036, 0.984807753012208], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.766044443118978, 0.6427876096865394], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.469', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.669', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^22', 0, 0, 0, 'a^7', 0, 'a^8', 0, 'a^15', 0, 'a^19', 0, 0, 0, 'a^8', 0, 'a^22', 0, 'a^11', 0, 'a^12', 0, 0, 0, 'a^12', 0, 'a^24', 0, 'a^9', 0, 'a^1', 0, 0, 0, 0, 0, 'a^5', 0, 'a^10', 0, 'a^9', 0, 0, 0, 'a^3', 0, 'a^14', 0, 'a^12', 0, 'a^20', 0, 0, 0, 'a^8', 0, 'a^20', 0, 'a^10', 0, 'a^15', 0, 0, 0, 'a^16', 0, 'a^16', 0, 'a^4', 0, 'a^9', 0, 0, 0, 'a^22', 0, 'a^7', 0, 'a^16', 0, 'a^26', 0, 0, 0, 'a^10', 0, 'a^11', 0, 'a^26', 0, 'a^13', 0, 0, 0, 'a^12', 0, 'a^23', 0], 'euler_factors': [[0], [1, 'a^22'], [0], [1, 'a^7'], [1, 'a^15'], [1, 'a^19'], [1, 'a^8'], [1, 'a^22'], [1, 'a^12'], [1, 'a^24'], [1, 'a^9'], [0], [1, 'a^10'], [1, 'a^9'], [1, 'a^3'], [1, 'a^20'], [1, 'a^20'], [1, 'a^10'], [1, 'a^16'], [1, 'a^4'], [1, 'a^9'], [1, 'a^7'], [1, 'a^26'], [1, 'a^11'], [1, 'a^12'], [1, 'a^21']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.469-r0-0-0', 'leading_term': '-0.128672271960112682545736530929+0.452652501603253472327227941551*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/1480/469', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.47058563596763175, -1.5916741776974435, -2.9980471902151695, -3.77564203657038, -2.9861591588825527, -0.7092302923070649, 1.7617727438625512, 2.8152245891375607, 1.870468224234924, -0.04371807878778043, -1.1810643299319348, -0.7403945022379952, 0.3367439929978786, 0.3767152800792557, -1.1360221014110794, -2.8362931487502543, -2.8903314339761885, -1.1281339545481566, 0.5696358970316977, 0.3296897331483959, -1.3893157960708837, -2.016085693467689, 0.2863386257375419, 4.258457916945531, 6.559609876447576, 5.273405365919526, 1.9583362398863127, -0.19006943195811407, 0.07205141829347916, 0.9766585641697066, 0.38818946448261593, -1.3157347220232944, -1.872058229100039, -0.39495096136130736, 1.1881225885339939, 0.657218532204825, -1.30327424770357, -1.7374457600407867, 0.607352685427666, 3.211329481256576, 2.7201285059288955, -0.6639237780368894, -3.175879305243621, -2.1353487148798123, 0.7394361864762768, 1.7193201113633072, -0.06316569719544102, -1.7798576040469638, -1.0358156652481616, 0.9291963608850392, 1.353406897635437, 0.07606094336526574, -0.47360913686296957, 0.637264737625862, 0.9832265235306233, -1.663456244195742, -5.3974111770940185, -6.04461505705954, -2.7753934456728575, 0.4466318764706036, -0.0020312452357208882, -2.6777770935758958, -3.373007734261173, -1.1026565963244284, 0.7924424783775764, -0.22435844919004033, -2.2455745203527306, -2.023960020412912, 0.13158759133171632, 1.1311137694613314, 0.09639178346108701, -0.4270042972140714, 1.018699896496881, 1.9111023495429365, -0.43420954103113385, -3.9816211333546305, -4.068594654660466, -0.08230816416021529, 3.198822371618992, 2.033369392266937, -1.302969207103536, -2.189240573964619, -0.28920633307688204, 0.7090637663075283, -0.7477853601548798, -1.8994627486456468, -0.5782258968109302, 1.0844248207298552, 0.23236700345944616, -1.8478450014712087, -1.7706036837535502, 0.22273767034966027, 0.48953612810000624, -1.767660704321141, -2.467224005501414, 1.1606629937696529, 5.595595407821551, 5.54831547543378, 1.5338414018081163, -1.0336976351848473, 0.25587273915552505, 2.0504989159979314, 1.257037610773898, -0.30639928251598575, 0.2486107622906198, 1.6921675905464684, 1.0706749274901899, -0.6809417446654764, 0.03714448003136994, 3.12765173590004, 4.286764157430564, 1.869629642073929, -0.14825395429247235, 1.4561718639340238, 3.605834326241194, 1.6319134404196527, -3.0000150016805116, -4.500044545423344, -1.4120478930242986, 1.5786378365031417, 1.1247731421316292, -0.38795829162703105, 0.01240987519881356, 0.7783115120573705, -0.5944156074495368, -2.2897824698094777, -1.0410487645669093, 1.7516860317621554, 1.9055465539276217, -0.2331415070815776, 0.16787994208917692, 4.243329064186798, 6.7194104844385025, 3.8687829637201947, -0.5812058624139612, -1.3262367109293602, 0.5006328602628706, 0.11959140779445311, -2.5903707904869107, -3.328002339716433, -1.0699507318495651, 0.3777928155754247, -0.7675214400714089, -1.4841743070227, 0.050178196858789624, 0.9600425407478179, -0.6509207302308014, -1.2965538207214016, 2.0907063860145847, 5.703736507897418, 3.847937229935062, -1.8863240681417897, -4.586017541873666, -2.277769057557146, 0.15115779681157565, -0.24234212013651055, -0.30303180014395514, 2.3754387359302322, 4.531898183521173, 2.957789695423664, 0.22453261102777533, 0.09824222581696215, 1.1954037434459546, 0.41176602931025474, -0.58149756224102, 1.6283534980740775, 4.815095609459808, 3.6168885230858954, -1.193083733243227, -2.9917465276370865, 0.2678317470365742, 2.849462184125385, 0.727609561774436, -2.300236155382243, -1.6793139632807783, 0.5901058448783612, 0.599170060245155, -0.3672093468307307, 0.8441431688976591, 2.560000207755966, 1.2772947238468204, -1.2669699884283228, -0.7222752768075169, 1.8546895810465092, 1.6635250315710204, -0.8849355794383503, -0.43480559221700643, 3.480406514841488, 4.644630117268819, 0.44450501292640127, -3.4213280912303237, -2.150435796147845, 0.8852456430896924, 0.7543415978401864, -1.011777980088535, -0.6342668587859702, 0.6247132034908076, -0.26191435927045387, -1.4604221396187242, 0.28099972707643767, 2.6286486587072435, 1.2762985553418784, -1.7189293547596476, -0.860353642658584, 2.912098373476263, 3.4198240868317638, 0.0889925917603516, -0.8980395421535553, 2.528990728569905, 4.750482698790947, 2.350906522555341, -0.3606189854039354, 0.5189629936170177, 2.095874540609097, 1.0233580900760797, -0.3282836092051636, 0.7208097433820787, 1.5350207204254123, -0.3183712835908866, -1.4463699839163073, 1.1227372921103616, 3.18013925249875, 0.003713644074383941, -4.638407680273299, -4.10742508712585, -0.01587543725506759, 0.8102661487220129, -2.003126998221597, -2.7581629242417525, -0.41084445591714813, 0.28219328489262197, -1.7341130609292352, -2.139785347391292, 0.04100328876081444, 0.6201546065353069, -1.3753973350180182, -1.8109341839047846, 0.2305131058294557, 0.6212402251857683, -0.9815414808414068, 0.7633481307092103, 6.578611213120601, 9.128569265685984, 4.482389245764568, -1.1667641319965856, -1.605804275991331, 0.2853538239315729, -0.4309350888383707, -1.9197154482388104, -0.7347500637405622, 0.6361944857824288, -1.1599977310216054, -3.2143089135346696, -1.6758743204504423, 0.8451704383255361, 0.48855775864979045, -0.3439710258244339, 1.6064737123637394, 2.671655687553433, -1.5059782818847431, -6.516450972589083, -5.302630604884096, -0.053915463744323405, 1.6386197233428168, -0.504669023841411, -0.5431266037089302, 2.12728753791851, 2.5130813352420462, 0.08471635583187279, -0.7781791366991289, 0.27796351516604906, -0.32619887408527926, -1.7113121477345619, 0.23342220537631692, 3.7458160007535035, 3.0740650685595545, -0.8007432018328624, -1.3616267636781902, 1.5293212821707378, 1.4531611689204675, -2.223608093845011, -2.8009007085141393, 1.3397667191486609, 3.6165239506413935, 1.0194744875769421, -1.3455840200269993, -0.3609498225555281, 0.38161083931818673, -0.9997211961575934, -1.1657049412320808, 0.49898078660849543, -0.07055711318812259, -2.7295097198825182, -1.9812154716440569, 2.3503844191691887, 3.394330363168056, -0.5947368873714421, -2.7630663830972586, -0.07607769650960351, 1.450208493962881, -1.6319319589845482, -3.905566501878222, -1.5315539464019665, 1.0537807977224043, 0.2592249836757955, -0.384369617323427, 1.6250861795909444, 2.560357401227851, 0.4974148853868521, -0.5189724161628739, 1.0318877882478892, 0.8587312547824232, -1.6152560174718356, -0.5303497836963598, 4.950324789602332, 6.989497044128507, 2.140765348592362, -2.406270012360859, -1.2132965693994997, 1.1803213768472727, 0.22281130878238964, -0.8083677162714948, 0.9078988441682758, 1.528193078447302, -1.2057348304416224, -2.8536426886535726, -0.9766925070971202, 0.2975265439968998, -0.8157351729445617, -0.056652076743605145, 3.305032093573041, 3.680045756507513, 0.32268829974351565, 0.2099668772157241, 5.109614786137903, 7.189334179558309, 2.6130894373331692, -1.839522897654525, -0.9986155968898349, 0.9906353450304295, 0.3449053462597427, 0.05288340327084153, 1.6095595073923705, 1.021632178552778, -2.342622069510389, -3.262376367485154, -0.6816482110191807, 0.2978476200334092, -0.9273565071040974, 0.8388772068063882, 5.044374016223568, 4.755325617985729, -0.11992417218589449, -1.5670693933642137, 2.1833561342402996, 3.7674991746356548, 0.5270930699719079, -1.5041932943455771, 0.16704855085416068, 0.7210791795173825, -1.3611528232792995, -1.819909547921163, -0.206605957803992, -0.4780285223727317, -1.6735368138435631, 0.5099631784651539, 3.640943780918813, 1.9626448401172718, -1.800197093061005, -0.4792462229280855, 3.9479777558927456, 3.7010992793957493, -0.4750291666853088, -1.5077039310043805, 0.28984180968043666, -1.021842643853061, -4.379291402453877, -3.81054582526641, -0.269728918651021, 0.6788947864198188, -0.5224176272202008, -0.2138913376002657, -0.1406117267627319, -2.680391779105531, -3.5050031709112113, 0.5586838281276149, 3.4786069250379774, 0.14436942760490928, -3.62010018863114, -1.4990183559719168, 1.8605692159513378, 0.3052190841515506, -2.33560775913395, -0.6605435367976888, 1.8405111608418339, 0.6449564398085031, -0.8832050904395966, 0.6932791247636998, 1.7827353797228556, 0.07234614048238826, -0.2157678913206774, 2.3565799902342386, 2.768275456599984, 0.11710571056740354, -0.055997275898328015, 2.161547284288859, -0.14881407574973127, -6.540894265086442, -7.838400585235757, -2.1142689231146057, 2.0557515383322564, 0.8313860153885901, -0.4124408051503724, 0.5123766269020505, -0.33355668725510135, -2.641244003529395, -1.8848887272822612, 0.5058047807352087, -0.4625023818401979, -2.806257528428769, -1.5113841384306606, 0.9551819314117506, 0.13253746966816704, -0.2236396660624067, 4.24349001240828, 7.790277490264899, 4.10472912361062, -1.3313997685040297, -0.7870848679227087, 2.3382277068902346, 1.474933965594368, -0.9326585396795586, -0.25305089141119924, 0.8240848796190968, -0.6286333051063063, -1.09364144796171, 1.0222203566819053, 1.076045385513791, -1.6586064491277202, -1.4416186757222236, 1.9050028844527729, 1.6236198619535163, -2.2338437237200814, -2.034359087040852, 2.3953791962757487, 3.0547768096893027, -0.7157897377127858, -1.3791232976831131, 1.8480597331038524, 2.3708400734611623, -0.1820032526395216, -0.2677930929836359, 1.6498361750415331, 1.0046403720675299, -0.6943388524008081, 0.0879230173430596, 0.4254784274832072, -2.187296391403088, -2.487871832001775, 2.3041593512020495, 4.869640735536039, 0.662479769503026, -3.0677631682721187, -0.7054922284945017, 1.9396634016384036, 0.09194501164353017, -1.1932234781102378, 1.393306992525051, 2.7014603236165473, 0.4812431600837566, -0.10502635190704701, 2.1780809046248066, 2.2578889474570065, -0.1372566429145673, -0.3900777006204703, 0.47765535349540256, -1.2389667110848885, -1.6121862269889922, 4.134089304400414, 9.70174678240172, 7.005987814556241, 0.7165764266287116, -0.48881847530504624, 1.0809452139777964, -0.6094520932486772, -2.6319216740045763, -0.4833420769808158, 1.9012849327180472, 0.5762494787769729, -0.6582228834544589, 0.5382927900899008, -0.030585495071267704, -2.8475165901500947, -2.4501725752733985, 0.762921397474056, 0.571625877683432, -1.932859519191132, -0.39265085719149767, 2.6238173171695403, -0.35282143402422417, -6.060056353642466, -5.38252500334381, 0.0051989767186157694, 1.7225733494219875, 0.021798484222382303, 0.31316831445253374, 1.3220121494338428, -0.06911390903552782, -0.5805471733626875, 1.7957676425281708, 2.0459288691744106, -1.3174627550048725, -2.0710084022221964, 1.0802596658129318, 1.692067942005989, -0.5231364962987339, 1.2853344698627156, 5.972852999030428, 5.151834563758209, -0.26674396435138004, -1.3704926438489897, 1.9971801249395793, 2.4110707689310447, -0.2131259472061989, -0.5552401004981236, 0.19795267605520386, -1.5027564403345446, -2.531659789611802, -0.2229066444347532, 0.7858354112925946, -1.4982437745978954, -1.521638692084842, 1.3436095398300065, -0.16849226750103, -6.046679174472238, -7.021407024234975, -1.7490583068734695, 0.9855271251711413, -0.8420069867123404, -0.7262406336398769, 1.485012077938362, 0.1147479535474765, -3.0759109638756748, -2.1434788875529, 0.8305585624707055, 0.7960205569404946, -0.07081707805232461, 0.9160527920131412, 0.05114144019802677, -3.173936946751573, -2.293321340002521, 2.631867172058535, 2.730249483473475, -2.8580304745800396, -4.589297832698639, -0.48824601698098635, 1.1865199713566132, -1.2809298748447167, -1.4535659758849466, 0.781819753059221, 0.18656728415498688, -1.4724019584909342, 0.43283786707546196, 2.6625367390511983, 1.0153172547148892, -0.6313441400892439, 0.7401037002547951, 0.7895136195139698, -1.2125844395535743, 0.8233229142645897, 5.8763743114251135, 5.113859111049845, -0.9630226951082852, -2.3988322548222123, 1.6729108838199176, 2.631419165821702, -0.37876117986173463, -0.776563719121601, 1.073769444329822, 0.4391925058829435, -0.511462563069676, 1.5537194617531227, 2.549691711373414, -0.11281458017049843, -1.2495458055095425, 0.6860909912833435, -0.17066649430158193, -3.655184383293185, -2.5586087963491337, 1.9713102450724564, 1.710252696871519, -1.8344391146122152, -0.3493621027866564, 4.124269059587056, 3.331083670498775, -0.8337046435681078, -1.2149284491781993, 0.609065200701814, 0.0529761024782495, -0.42307912055382757, 1.1443384795257017, 0.5955014981551827, -2.0730923537315915, -0.9371235693762225, 2.74487595951184, 1.7066054104744581, -2.099706187727071, -0.8843776866916968, 2.84999371398066, 1.6093803523258732, -1.2236970076723068, 1.3735036334739, 5.123453468363334, 3.235691180268016, -0.20204943765110764, 0.3315373354718115, 1.2655137260148572, -0.3196172624028931, -0.3861445118416038, 1.5613296100953744, 0.7573489492935328, -1.3002302193587059, 0.5451040562460309, 2.8106050020478643, 0.06639324661566615, -2.175396841211028, 2.2102374035083057, 6.33826953760243, 2.8631830440976835, -2.074883342228187, -1.446466233469749, 0.4531095101190292, -0.36820917559234434, 0.32457687258092244, 3.282722523530656, 2.7254630375161657, -0.8548732407778706, -1.2013373363560973, 0.8083597720018322, 0.4267907794491217, -0.03209544638554409], 'positive_zeros': ['1.64550308615103766849268349989', '2.804916767131143430401445359830', '3.64105510401770164679156538531', '4.16922892306844127367545274394', '5.49023080686934040526657287619', '6.00765360859611967139007228909', '6.84971991897531620062660572320', '8.383432036133659612992524209896', '8.727712992744117956923793860782', '9.45101530219047879645225905545', '10.374080480455598678709203561628', '11.046362669127083066566851008010', '11.813208679221733059157822047', '12.75692340800126693232016353164', '13.66440034255835533729793720612', '14.36664243920225089963451415840', '15.1581609301499556994489082780', '15.95554748604123779829020670970', '16.41453301694414615493124497161', '17.034034426420925649406880978628', '18.369920379710688928449863788223', '18.74971575190441790940411255349', '19.8226217858274041714330963111', '20.2787928049282944924858458511', '21.230495392846064601626936743111', '21.89856200347211615723724231196', '22.31709445762129011360173080963', '23.08746432456331489909853032397', '24.0680734970112811563772480446', '24.87109575940307309524953843137', '25.6701989116404798080131769243', '26.12725034360282893921108622383', '26.95968571952931824052998557225', '27.53410603268437456972618493940', '28.39951281518943006654334399188', '28.8371523857612339843053474206', '29.613253550057914615010602659708', '30.755261396443078617805485490461', '31.215505704964970565496334018583', '32.09734257040595925207540218698', '32.44659996967285890558320246179', '33.29711461008130394168540783637', '33.74518146705854391749175057534', '34.93365497468229256273257169765', '35.10257398509332262628908792550', '36.04838936950154295674157781400', '36.990305728935318968330867214882', '37.70264818796414674440613149899', '38.121673267835690433689831806786', '38.66039866739523295701824179762', '39.48517657183669876024197724054', '40.27267123158194197149115220053', '40.60455819847806893495312367103', '41.82207498197982923953154219537', '42.40684991361157239475219292401', '42.82957417580990706578483206745', '43.906348263448079262682334569088', '44.220732604696222762123788720471', '44.99180667968262381254560916190', '45.52649275197463417735266780974', '46.096734385789907757768062047501', '47.084543130778760357098253956122', '48.08377909345534004138143815750', '48.36294541969870296336369299568', '48.80562144594990079640215023562', '50.04826045050874762687144339765', '50.28385429894257885960339709739', '51.01779112797437761331964511837', '51.393570360491491077490366289694', '52.42149887015309897286007184252', '53.10491948325442631166646997550', '53.811308583857992580643003250813', '54.5885118025130657674980289884', '55.150507447681800370234577938072', '55.483851314681740577099425677080', '56.38871479170917778033518179628', '56.96151338764557483781381226134', '57.696207821291647790813154490570', '58.168041517875915102058956418937', '59.08861376427857976567838824959', '59.88736250102472469610829873202', '60.433395535192339194403453363337', '61.06423155814369274127512634316', '61.51474935451891834473204875475', '62.15700941089321174589186040321', '62.93075420541416533549751466415', '63.51238163146397004909089975808', '64.38368807882777691504239406886', '64.7980204283879958879899850443', '65.86236744199422542046157902810', '66.166488068097812276838105669349', '67.055020768312927398393484249515', '67.35615920321417016422586410787', '68.08401464451154607479220987329', '68.64746022230035027443949108986', '69.37522192903158604587741848288', '70.31398052899145224023878458253', '70.73145665846803048169051052431', '71.62418944602835455763317042958', '71.93590799098975635515168634093', '72.80648739219399988071453164238', '73.2413661385324534763735047817', '74.026890232984850028086824520294', '74.494040098274660721754058211638', '74.94086208484230144453641400847', '76.162928498413083654093680372791', '76.80550365039174679695581985808', '77.110745998168465694160102248866', '77.92403987169987818586479188783', '78.2967367958528393787734766972', '79.241364874348184364091550580835', '79.793206167417321391393955301084', '80.098976288706317322955034678862', '80.856177523889018424564230541729', '81.87882081385547835074392978802', '82.4288690022897577592834028887', '82.88544027292552499991310918072', '83.76170108838559594572221194101', '84.28344099479889797589465703935', '84.62203319179263374814030872949', '85.292445017054412941079905202013', '86.17899712070663365714716667031', '86.71526188106718273251514637056', '87.31971866619092476084680432234', '88.035384346962468959887298719079', '88.843440356160726127574738503422', '89.44644933579535756152102060101', '89.80245687889393107008029815853', '90.52416975767413082054085375874', '90.92792407222309042971890807751', '91.71087297201520911859066408219', '92.458925422432627509094664654928', '93.1320178848457090059422716625', '93.61926010307539372163960474786', '94.51691734937001709510079382602', '95.05143769714890949920811479954', '95.40216983629503547168997659971', '96.32162678433318433582821345904', '96.69222539226897279339685725531', '97.297938260505755290417401272237', '97.850004696444844809492380773317', '98.86129150229725093012280217724', '99.49819586307347535160101676834', '100.03607392595524441463162481055', '100.49420626842422051062606003660', '101.13432602240361901463906372004', '102.024712768560456787813325156649', '102.303642706723917920832845486164', '102.8189803843047085845529073583', '103.787004931135260907083826446191', '104.04005886779131939638047681342', '105.14475465504029974382559540296', '105.74645544963798239119039266858', '106.352570496704339519653464008818', '106.54457358198250464919079278870', '107.291489705689665136277257665576', '108.22102484907524297785761118461', '108.51996571959376449076513897371', '108.98814491072858701329173386061', '109.99171682177402117575011426815', '110.46578203784224692924155817117', '111.2949552839659788895528193725', '111.84999617410627265580059899514', '112.31331414547498065875338907531', '113.20124470391805811775366517096', '113.29793996563645568325386876408', '114.018994769422253956111595063335', '114.829596574925883955076051626747', '115.346660137773769620509814061751', '116.210382494130124364173166469700', '116.8074343367951002073836048761', '117.06969132291277789403652921026', '118.15596744762929684925848563350', '118.60589246992884749388315389915', '119.139764457675862346797743327364', '119.33738221322904460201244349374', '120.277953131157275953163787639336', '120.94617994126926703804301282035', '121.67172176037332212152565853385', '122.21493239723682078703245273644', '122.87487533582581166214383481201', '123.52315605120328973377140020915', '123.96648580854656436315523746754', '124.69970314402616235568259898878', '125.036427321565118047190111264536', '125.95408058237145513780458693089', '126.25868311190750201832442469087', '126.86652577764886243549513651936', '127.92352205275747575814448417100', '128.56417218318752653196009090941', '128.907943375261804983287397480741', '129.326236384156464386741641225649', '130.22125263503070397034093555987', '130.56687260048997943871448536405', '131.40803023594817746517783143951', '131.89796650376256198388442322676', '132.21680422527439209931182356383', '133.33489025289875345529007831626', '133.82004239142862653732432318157', '134.53651975547099118336051302488', '135.04378234302385073590491561252', '135.52145942673645541111854021717', '136.11085650342631986940146057250', '136.69120086852077905415074237137', '137.3229903530625565993776286093', '137.94503198891558458253188485532', '138.585066396684553446498340364985', '139.31444003747661960941435853910', '139.83065059272285660780771595559', '140.59878818867311772715028314846', '140.98169537589256561694804646506', '141.71247115632781279788525822382', '142.16908649686903672032867855409', '142.572010779450072381064839158624', '143.30697343621099683688031982253', '144.09910574768805142809279054458', '144.7428783506744638649621298641', '145.32271273733235522210717939682', '145.79995013662354768771277110148', '146.63533926507996094106419667489', '146.89583356558853142930455499898', '147.79082002848385865182738889706', '148.22118384778365094493448833779', '148.57766726080310874189803788839', '149.18523867800007644439453485781', '150.37046185781245387508441209618', '150.70934809049594584224868312114', '151.18484069560821028005335551615', '151.9190239865865861087782426201', '152.58407449665340701182346039824', '153.00473684799980091700248294067', '153.43349091410052347007883551515', '154.29011670520210074008473312230', '154.75328905683731055270261243214', '155.34488291682823866802541056807', '155.918801545637064538375875929602', '156.87464300872342456693705409257', '157.50562441055004415339972207333', '157.73768149062859905250697903599', '158.42593975962616905417245797912', '158.84804167770805088563486238844', '159.57250071140441845146129821675', '160.210681019110258101737905371603', '160.844979826540924415258006765589', '161.143258550337631200950213861975', '162.16944722096117160470992293302', '162.63654077882601021897511083108', '163.407200105280884321556094277533', '163.901372744554578960587332988872', '164.1408745366898622645718465664', '165.02648686084372524248646331386', '165.44203859713009561917976975366', '166.09685011539664482082136202970', '166.55154994278189568546487159253', '167.61860135257284422592122719536', '168.004664817643785558187676498665', '168.532095336243459487727979463426', '169.07286549248606441472765340827', '169.89244482952926272061926905085', '170.52310880576187678355635034641', '170.6757126457963389204986611261', '171.255629608990469843876140899474', '172.02079230012614896677183240975', '172.661689740192181404500120531783', '173.47523207503870507153113379194', '173.91563558183040664050430371634', '174.56392136765586121577154015369', '175.026409795779460092359964335976', '175.58215079779143603876469109675', '176.37599407455290451411904259745', '176.74584847094312004314923389525', '177.30278859502803274405502668792', '177.75427639708025291831357328020', '178.696756518147200158242256081187', '179.25454012939555501825224820653', '179.95752161875200133468691694424', '180.43408053535552267946714567082', '181.016755239708669942818437490163', '181.369318245752533958065867704213', '182.17576385728358140629506363755', '182.703232310100314675511136611172', '183.107914418211306126956038233040', '183.91641443565803598934670640438', '184.51232643804831898822399227035', '185.02371077550944668545598356041', '185.86277957011198344044179943091', '186.432730508347916880366856793067', '186.887242047490866537463044274654', '187.28982090825246007762972663139', '187.881069633783686213721245867762', '188.51207381800618396772492718535', '189.1878841122523959540191953705', '189.753038261819200786881472035108', '190.44880673501943321930080637995', '190.83978872420159266742869629644', '191.84123531824137603748452772410', '192.12796209280206290872475156318', '192.75633694017029269367728541582', '193.18951333897863937394075141103', '193.840448286686739746590594128795', '194.32369363700005390349533413663', '195.00494294879919996393755140746', '195.50949179463790314912715061571', '196.40026097040108538095666036590', '197.060749718374020204561252595927', '197.402388214198588042266702613008', '197.769198234576514109351007956817', '198.66649658542764325846031523673', '199.233109431031034861747883767892', '199.79519148484508650838191742442'], 'prelabel': '1-1480-1480.469-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.4118417805663195, 'root_number': '-0.850471973706385539559586267179-0.526020362666660522735393130566*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.411841780566', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.742063400251323210118415941411+0.381607598959275234383084467616*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.64550308615', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.80491676713', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.64105510402', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.469', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/469'], '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': '1-1480-1480.469-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': '1-1480-1480.469-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.4118417805663195, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64550308615', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.469', 'Lhash_array': ['dirichlet_L_1480.469'], 'factors': ['1-1480-1480.469-r0-0-0'], 'label': '1-1480-1480.469-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/469'}