-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.13', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.3420201433256687, -0.9396926207859084], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.984807753012208, -0.17364817766693036], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.13', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.797', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^25', 0, 0, 0, 'a^19', 0, 'a^14', 0, 'a^24', 0, 'a^40', 0, 0, 0, 'a^32', 0, 'a^25', 0, 'a^44', 0, 'a^30', 0, 0, 0, 'a^39', 0, 'a^51', 0, 'a^27', 0, 'a^13', 0, 0, 0, 0, 0, 'a^29', 0, 'a^22', 0, 'a^0', 0, 0, 0, 'a^3', 0, 'a^2', 0, 'a^21', 0, 'a^35', 0, 0, 0, 'a^14', 0, 'a^53', 0, 'a^49', 0, 'a^33', 0, 0, 0, 'a^19', 0, 'a^19', 0, 'a^16', 0, 'a^27', 0, 0, 0, 'a^43', 0, 'a^19', 0, 'a^28', 0, 'a^23', 0, 0, 0, 'a^4', 0, 'a^17', 0, 'a^23', 0, 'a^52', 0, 0, 0, 'a^12', 0, 'a^38', 0], 'euler_factors': [[0], [1, 'a^25'], [0], [1, 'a^19'], [1, 'a^24'], [1, 'a^40'], [1, 'a^32'], [1, 'a^25'], [1, 'a^30'], [1, 'a^51'], [1, 'a^27'], [0], [1, 'a^22'], [1, 'a^0'], [1, 'a^3'], [1, 'a^35'], [1, 'a^53'], [1, 'a^49'], [1, 'a^19'], [1, 'a^16'], [1, 'a^27'], [1, 'a^19'], [1, 'a^23'], [1, 'a^17'], [1, 'a^12'], [1, 'a^48']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.13-r0-0-0', 'leading_term': '-0.0889296303878014312383105323439-0.507360736722431672433885046853*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/1480/13', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.515095521557351, 0.20220686578691202, 0.8047478613805974, 0.7506365942872604, -0.3005176728699978, -1.7856852663606393, -2.5160066741508382, -1.7369529941411068, -0.02376076361808251, 0.9984489807136127, 0.12051554608960752, -2.0876091260816456, -3.5122300193602913, -2.4065273677805945, 0.7701286719490748, 3.5609616954783343, 3.799043453022541, 1.7263656294855443, -0.33799030942701763, -0.5078726812410976, 0.7279422671815996, 1.3397816906025457, 0.3823028806863207, -0.7776557883070983, -0.22768091516853442, 1.8524037909499838, 3.107734013828762, 1.874934117152542, -0.4698237107040699, -0.8645853895054771, 1.7078745197933323, 4.68863653187607, 4.7779688414927035, 1.8644237288742456, -0.8318595598345804, -0.6775590710673809, 1.2845633064371973, 1.9544848959203827, 0.29540209214346724, -1.485647710442376, -1.1375444223777929, 0.5608441845345048, 1.1253605369601725, 0.1417029876730137, -0.04579333872810204, 2.035341948076894, 4.187221340148232, 2.9940823140083843, -1.3900360620754104, -4.791785369436104, -4.001907651453126, -0.7144554241785077, 0.9156507728193197, -0.2303176756211496, -1.1970710224905907, 0.41960112342691275, 2.935356790543878, 3.1193195470774135, 0.9018854494171658, -0.7192444666463599, -0.2688549414503782, 0.18794240976931076, -1.3034023458020982, -3.0006652675851635, -1.845860463932605, 1.4549188611150883, 2.6036862710353263, -0.39355255579219695, -4.016025381260962, -3.752816299232087, -0.1806827279233476, 2.0715081263651878, 0.8532704099110827, -1.004303444504785, -0.47228891155506647, 1.2292482984510493, 1.1521764933255807, -0.3222125698953269, -0.12522679652783153, 2.2479192648486634, 3.541896156979541, 1.8360641885954792, -0.1908907276876034, 0.57340411157264, 2.4146512814180943, 1.0984360199342091, -3.2999985778114067, -5.693439424333366, -3.051527785698979, 1.207576802304787, 2.1312933439376547, -0.021614857868381496, -1.1655009430685312, -0.02730483926987622, 0.5952830593405148, -0.7171166381162131, -1.4215123288582516, 0.3585987751802586, 2.067331979369878, 0.6501654758352509, -2.0810416814680837, -1.9406489903870292, 0.7899957556300875, 1.4298473889747794, -1.6503893429033698, -4.019555488592411, -1.8231087330994893, 2.2022033707194173, 2.860929798949404, 0.2200111087851896, -1.1447090038019394, 0.40518714107436543, 1.645891450726416, 0.5512955075175334, -0.39753186908932076, 0.9512476948532853, 2.328835769352488, 1.1754596381380407, -0.22835837867617598, 1.7926067647208215, 5.489066105313206, 5.432049336347795, 0.9356092030682842, -2.4546232432354778, -1.2881531956184682, 0.8490902984352917, -0.42561263937328553, -3.2935143298310594, -3.2295751027685546, -0.5934485618564816, 0.429792713498874, -0.8761998584410224, -1.0029334444178564, 1.1191611289550654, 2.130097079514953, 0.4050980206054803, -0.9289535310750852, 0.06827933312061472, -0.13167641299274932, -4.631630025012285, -9.547113413068127, -8.750228315814812, -3.156501080818686, 0.537906734163004, -0.2517211955699612, -1.3985856793162295, -0.06675573365029588, 0.8616954207242495, -1.1185595299430935, -3.0982363723600645, -1.7930689115241658, 0.6460157812155647, 0.570957639209391, -0.7317971891910309, 0.10016304369470033, 1.6525596635478792, -0.08079302710909661, -3.7627137647447344, -3.6673786228046494, 0.8680882652460018, 3.5733386512089074, 0.9246234520789984, -2.4825764544712507, -1.683858471801961, 1.0501550727731959, 1.0697527149922328, -0.7198198827336166, -0.5120947415065775, 1.0660538863963092, 0.6049972482489072, -1.080266673830871, -0.21720207503903113, 2.469947803285954, 2.37926859845274, -0.5821762899744454, -1.1632469235923144, 2.12728016879707, 3.9992492428993875, 1.428920246779492, -0.8450407056877193, 1.6686310933203479, 5.418591126020839, 4.706301997103024, 0.8985280546463889, -0.6433904544289177, 0.45996222664049397, 0.5333540396991041, -0.497822372195014, 0.3886563370175044, 2.2432071514199667, 0.9959480387260826, -2.572414295534595, -3.10814349641817, 0.04342738133609208, 1.2968948999935945, -1.342704303252994, -2.4231279406615114, 1.4475790171373262, 5.324544913532905, 4.079068179787083, 0.6475983945558053, 0.2352889875911106, 1.498121859511789, 0.2037052074224786, -2.4407710364577775, -2.3342052648134874, -0.3485084891317705, -0.32904646254126346, -1.4820461674718333, -0.29219819891327214, 1.614543421887547, -0.3778519773527556, -4.5428206742527895, -4.158221945551237, 1.2109285486547303, 4.311900957654107, 1.8534449203374699, -0.8337086148095582, 0.3485764863050549, 1.936247029382201, 0.5411391321050059, -0.7742644841128897, 1.043038903446244, 2.838310175017028, 1.2526034908055839, -0.9043878476605074, -0.2295862435002919, 0.8064888586680996, -0.691370374550459, -1.4618213293715916, 1.851936764539794, 4.894704741400798, 1.9928624820413179, -3.504920139746171, -3.9924661623955595, 0.12134456047924505, 1.922813014090908, -0.14051300243790404, -1.2120956648114665, 0.036270263495271154, -0.1867463966822288, -2.2326458396747286, -1.947036974175218, 0.8627338983972428, 1.5580037547367451, -0.4571326438366013, -0.6041849770239512, 1.6036597987190164, 1.158255418662334, -2.3620782236760385, -2.6301986274838773, 2.198728009819056, 5.290814505169109, 2.5046402665928675, -0.8346500260617566, 0.31378190925157035, 2.510908644227648, 1.297613784668523, -0.8355968207929932, -0.35512121894666177, 0.415408514275558, -1.1393805658176068, -2.0094482188977962, 0.18193079860066613, 1.450520069805469, -1.1633155875988164, -2.9598117361634713, 0.2792143941845901, 3.893646635596989, 2.176396287232519, -1.4455046723464005, -0.8403592319588499, 1.740005952901015, 0.43766117684101846, -3.0436127580311885, -2.8299037759892456, 0.30631410391750064, 1.1184331227011037, -0.3003356564793975, -0.1348656482068488, 0.8066769127256325, -0.4306982590282297, -1.2634196482692448, 2.187698047927122, 6.227775055663142, 4.748341568482637, 0.3551279132344551, 0.15133760131888202, 3.093211086641788, 2.341533469863454, -1.86479595857043, -2.8961873798604882, -0.06011975007343459, 0.855051048879926, -1.2253523465341967, -1.6670133305861456, -0.025313631762899354, -0.5049069068467041, -2.724719866559002, -2.16690868067324, 0.5252882538319016, 0.7457964317240928, -0.41506810647188563, 1.7674240332111355, 4.917924465584413, 2.2177085340732297, -4.627292297595766, -6.71147756694272, -2.4273412400827215, 0.8606652610937517, 0.063677345967302, -0.27774555705520265, 1.333309371816621, 0.8465404210527898, -1.8850552389057627, -2.0859206675109854, 0.31293364152228387, 0.4238261007792954, -1.6627757999341075, -1.1376550524665525, 1.396369643567239, 0.9872560156066923, -0.85698604186338, 1.9197580388857334, 7.398403557307715, 7.249830765388638, 1.1503711869157716, -2.5007922044414683, -0.8326161154920693, 0.5411463771568727, -0.5863861218196639, -0.16715515859582333, 2.205124209618843, 2.0897363468470385, -0.3645714084340541, -0.6471841857947247, 0.5559438776774501, -1.1480271463667007, -3.8111316389798358, -1.907183692330991, 2.3023219117434577, 1.9630923898290686, -1.5115624219961972, -1.0245654758519525, 2.5638193098062176, 2.085313234379531, -2.1894388843206767, -3.2063520362113147, -0.2781900709535807, 0.7359701397626068, -0.9462146801319886, -0.9903928573881167, 0.26357050381503055, -0.7627624947982777, -2.1638497305001363, -0.16407083728308663, 2.025708784195562, -0.15342813303100708, -2.596731035991735, 0.5605116121285892, 5.147502656566605, 3.7958168545149236, -0.8108681662345251, -1.4514372094043184, 0.45424353139863893, -0.7918352653665521, -3.243098080731349, -1.6600069986702661, 1.643037794502392, 1.472241978480271, -0.3308618347168203, 0.24856012736127092, 1.0501464436961672, -0.45734888390273154, -0.5648690180354422, 2.6329179339045035, 3.2368620902880516, -1.6897029379749493, -4.905744836305169, -1.272527218540615, 2.9250182646274747, 1.6149353910912239, -0.7373026482967471, 0.9175889282199454, 2.705091983460139, 0.7011024726461477, -1.2162901934085013, -0.012783428457146293, 0.4107215587561487, -1.8465914711063198, -2.3369894965834943, 0.06535648356632397, 0.33974995314368334, -2.061818475403723, -1.7711112254264192, 0.6848515791139262, -1.2987027338195232, -6.73187768216647, -7.053007357854631, -1.6189493251122538, 0.9335287355076334, -1.7924109651716944, -3.109408852201989, -0.7515787375485703, 0.5086955538554223, -0.13713482388376502, 0.9430198670621517, 2.2710888915061287, -0.24449551597178243, -3.5989378698859564, -2.4245666208272865, 0.5368588601119625, 0.2453561702851719, -0.22030382634786633, 3.178894077786901, 5.203054050166001, 0.5118150848806806, -4.882286451431164, -3.5081902549074324, 0.6118366757696438, 0.45317935913367496, -1.5859854829460296, -0.6302934678838032, 0.7363904968475321, -0.6198102695225884, -1.2236150872854203, 0.9396753560362563, 1.4718702098819239, -0.8644738953200347, -1.0021292336660297, 1.2158890003188063, -0.5291320465136232, -5.731006235430872, -6.1516701174963, -1.0746308266238978, 1.1073506148538446, -1.510300360657026, -2.125504051576258, 0.378167618406494, -0.04875310045204571, -3.406039867319774, -3.551330343938354, -0.6152821351428878, 0.03513677002112358, -1.1453119179349094, -0.40208626376852463, 0.23274085626400923, -1.7669381089351983, -1.6633625795816287, 3.5645469569706294, 6.963728128023733, 3.406583176003368, -0.3902791734434498, 1.7358648814488695, 4.335441571336449, 1.8607709400506163, -0.9334561037677087, 0.4178871274157995, 1.5598473371960502, -0.4381727640376608, -0.9246765964766146, 1.8206629642557937, 2.655149666880903, 0.43288143116239847, -0.1289890998142869, 0.779950482998353, -1.107442364830863, -3.172831261077188, -0.025393171746647455, 4.0059849775717815, 1.3135370467905594, -4.218837193098476, -3.863360562610739, 0.09627239888743037, -0.05219364940817368, -2.7165040100880753, -1.9861686756624806, 0.2387722871455207, -0.12792419490336635, -0.2019119388168934, 2.520395683608626, 3.519130701613492, 0.7457406882151457, -0.5155908573959426, 1.1775997713771333, 0.2834093381876249, -3.2347238467984387, -2.7948661361971094, 0.6710070835293793, -0.7704527835648991, -6.089790026677846, -6.24764694795592, -1.0902419266389796, 1.072264006199378, -0.7225834898475925, -0.5041741200025306, 1.5008044381584054, 0.8879459053254823, -0.5674459256030424, 0.3787583594754127, 0.33990417950421636, -2.8431813712713185, -3.5850828280446643, 0.4207862973903179, 2.3373841993905877, -0.5625468498519168, -1.4738256317053733, 1.5554452918799848, 1.257440428236382, -3.5125153622363454, -4.439157859906663, 0.22057435442335782, 2.6303118110526076, 0.5493126698011698, -0.4033325583754449, 0.47584307003964366, -0.8031490142610426, -2.387797686662845, -0.38434891868750826, 1.8018626042996189, 0.4487533832830199, -0.19303550066076178, 2.281277797032202, 1.4497383659461922, -4.826871109272388, -7.67531722445046, -2.8790666318330715, 1.4019244926373724, 0.19247533791473337, -0.7614714042645314, 1.2438690570258983, 0.9556572989728811, -2.082953233961647, -1.9272071403657467, 1.1110716785573742, 1.3317387095439415, -0.40120880803166936, 0.26560915922447587, 1.0188885571913213, -1.0424402807453075, -1.287278185690101, 2.3570784026690434, 2.3137302045102683, -4.450068666672617, -8.536214198047041, -4.405069316783754, 0.3444544773344526, 0.1414122992904512, -0.15138669084617024, 1.8443240153410074, 1.2358280261659997, -1.9916848066910529, -2.0228694529733717, 0.516308739411106, 0.33903099732872327, -0.9955067992728536, 0.4728266326396601, 1.2507019664403716, -1.752920427783906, -2.8148751923239304, 1.1133767878714211, 2.690292951758402, -1.4234858976234, -3.0615478267470166, 1.4563644978459933, 4.032877775867455, 0.8021907390072784, -1.4168148634690678, 0.366485358172218, 1.086496921859711, -0.048506246012973875, 0.9217516317678676, 2.132462092503444, -0.16847405233189724, -1.9556726140204472, 0.6703385374583819, 2.3563215822929293, -0.6304969437447602, -2.1784943841315383, 0.5870778567813483, 0.6159990551477914, -3.971668047839866, -4.7292741788328225, 0.40110121072621086, 2.803237113895481, -0.04724708138684212, -1.2677333766778829, 0.5111427738221352, 0.14118414689750744, -1.65280056540636, -0.724940743605006, 0.46994587314762565, -0.9232745321650997, -0.4594022316300464, 3.5079212679919816, 4.099571111905236, -0.2713250741410203, -1.330957898704658, 2.718321088487297, 3.4668312876523593, -0.49499107100058026, -1.1564391360811863, 2.0582991120872336, 1.8007739646308873, -1.4689061911669778, -1.2502213965042808, 1.0576043648754392, 0.27659277699290696, -1.133108657516714, 0.3399588415569762, 0.9765118535344566, -0.9746730682245832, -0.5060696301891308, 2.2020721567225077, 0.5059013725580258, -3.8255329601075094, -2.149264868866571, 3.495073830231325, 3.286326414572053, -1.6723635381191564, -2.512628991283269, 0.14745505514574606, 0.0485056835460833, -0.9799042654973247, 0.9316176964819436, 1.7897736411589176, -1.135567682062868, -2.427410443634108, -0.00010985871773066728, 0.7239533635570524, -0.8658985475104912, 0.0017106454240948562, 1.0691452225791744, -2.6648842462772064, -5.653693243842343, -0.7288384533421417, 5.543811271600772, 3.9102636661367582, -1.0331599351741054, -1.2538765247107997, 0.26965821859466305], 'positive_zeros': ['0.22362975713383038969436920656', '1.18188024646426329571011190512', '2.50447714228291463058815926386', '3.145287873930070421035695878787', '4.3059313893957049516632263046', '5.55415313638840286433404331287', '6.08094612519667294401209543852', '6.95805999577039465818361306311', '7.541876789640209451385987757098', '8.67839483524233918986336524893', '9.20196122274091648976042673114', '10.4981520481250825374727225909', '11.05292004583386000510338390625', '11.91621262948823949176034540671', '12.707139728789906398148430472025', '13.48235065966659308707765524048', '13.76363003380344011958292599667', '14.90948237618811726740358648245', '16.01848185137444965066291030683', '16.52027149838453922423447632335', '17.13609373071954059405074209906', '18.252420764547323740161204503863', '18.84091419470250125159957972876', '19.14018789154564154953041081922', '20.175991074335854738064687657988', '20.90815957471815275531622078610', '21.89044875782427731201518267069', '22.61747963798483079850618484028', '23.20720115383337001035996932794', '23.98571444241927038890377742900', '24.39796411443786360342162168265', '25.571115196492789587195994934172', '25.83312844020892065132621750537', '26.650637961175505785873074831915', '27.70992339673658923739247877555', '28.434561770653252024996153728897', '29.06843156313620999855060324673', '29.5493538609936220795012058334', '30.26655672962786238620879727368', '31.006477424058065428892145733024', '31.78529028502881834889255365528', '32.36015048620564421530480788143', '33.25689264769653783852645362060', '34.088075919685670475578232121592', '34.627121676401278680540340166158', '35.4250766126602172579499919247', '35.772908405289676380159363756098', '36.76476833169427704144906784311', '36.97821789881521408558882901139', '38.185135736658227380369872862347', '38.9016806386099855119602704262', '39.32623704337320256158497937048', '40.3998702232356577255915436645', '40.75549987991202555000884452960', '41.41505635680182776073182013300', '42.24608502240861913929157931560', '42.79624608460169585574935144165', '43.10629593670083116694970183223', '44.5997954455674046286610011687', '44.95739820985955502334312337389', '45.636106592596734338124150312677', '46.11697235608823895721080754447', '47.083590943082898074565068055667', '47.61783634774430082116920124266', '48.10842557864276641390972025979', '48.74285837365895194900510836790', '49.63297387047884761949032375153', '50.38044223989877522569317107116', '51.11483523305495300809231953491', '51.73858165298416633539491001962', '52.28317467089405004054007718286', '52.91330134882355307897472659832', '53.464088833126762501007031401872', '54.312390727637674881247256944286', '54.82225941775736915833167610729', '55.76011688363955437829367703293', '56.11052344149516504858961567606', '57.2860841635425419371287964760', '57.7002645430481967594043916062', '58.268713344898104168130929305939', '58.68484424326144718493588628565', '59.463835905204858853285773689602', '60.30829517407001370542557903089', '60.80498030952895109891448725870', '61.47271109064462069027571613404', '62.634471772003263842774042564001', '62.73316695676218572077940291488', '63.460451355916921543135207636594', '64.501446556897287536288579255306', '64.555814436835414438350393346368', '65.34997892787585788773248214435', '65.90778161539002864612015679039', '66.80940901501312958957926937370', '67.66789130789986372722517861851', '68.07767904247673630461345642778', '68.82825440747518008652968582599', '69.246770827553763873247532587158', '70.14616537677413713844093053260', '70.66794240394996943402988365076', '71.146211750571514837361853836076', '71.73817140998569268779441884757', '72.60539793750669231251288468247', '73.42813364559358038160379034334', '74.0445232220848793745768446458', '74.67783015005624421509436306208', '74.96159415564389399350181425608', '75.84116775487427397354902105851', '76.492462370906531912750069393019', '76.96822249707518136278805262051', '77.61041175263929810216716202978', '78.31313252711193131558605786984', '79.257044071327644168254912723409', '79.65105983933903552354871577928', '80.470878672844754375326073740051', '81.01828337456940886410936474222', '81.37806076641587606868242037755', '82.16682497547430021554665473983', '82.705769195406034764493669656971', '83.41922527135985608702685301433', '84.22721003853017075734489738922', '84.77632518892966511651466474857', '85.35070571672356947292090165054', '86.215605866768187332147522659385', '86.80148476128975284035122969906', '87.22159614409685246522996680535', '87.74283544835978158833186324199', '88.28527907677844345916594829173', '89.41534114204424795994520409939', '89.66719977313639792078820806224', '90.48642874854619521823755424089', '91.25679403585477572970375723177', '91.70815452317920301396794348225', '92.50694534548782852496913217795', '92.716524646735838135692403591835', '93.67906860341840329575829491181', '94.2157168581289812881745908629', '94.50644351737693905238507121006', '95.41542289934792554281155120814', '96.42748150799290088659230080174', '96.88885026923810405938687242188', '97.25294506121880804655566427248', '97.91311425762482936856808127050', '98.70436563517395505312663058035', '99.12987688325895456786200729691', '99.81930949898584943712113599422', '100.443177208101247584337757145722', '100.80257371056289539422661330263', '101.93562371252605587937725098078', '102.61221545558559894869768042784', '102.98719304440410973825239033607', '103.46245705231628636074164263212', '104.32227002853714924920583355591', '104.82482181966276357502698428995', '105.18160076483059290343304712685', '106.06663832084819550624715688957', '106.72932515901387010641453714630', '107.27669795358703239322415722551', '107.967492865385941806298890722867', '108.78200002730296447874169826182', '109.21161160298601726254771952765', '109.90221267957309948477622440100', '110.178179533542476207964625837756', '110.953445615583532208971906251307', '111.54942986277466189884404682488', '112.1544036128460160457675599183', '113.05891199959346228074269096039', '113.65056134528654537436067311603', '113.96583005323151953761625168818', '114.826894100565258786115894626234', '115.54116813412731108158668889389', '115.88347645906505258957282716866', '116.485374613255099430740857196836', '116.947259783436026284454741966900', '117.722182882100027906309282133609', '118.50930027734742142511894608338', '119.22710998051589298544998334013', '119.58183438893764260308181880042', '120.38794153344152016223113376159', '120.93983015507362192332907265691', '121.32614970465996957065795773527', '122.178330141747616989618047824015', '122.55223050570879088107795644682', '123.326210586288222793246313165086', '123.6519574017550419811222580413', '124.79701891531356239272144157226', '125.14445055349279723366132672729', '126.04123480860129037949888617633', '126.47456913149713186270686171275', '126.68969701081425016516476097012', '127.481157680478998783383351537155', '128.35829989023029539046056495378', '128.801142239788095643645057438703', '129.10059290483375252925216256596', '130.02336229858386244935943808749', '130.874045467926829090152030844194', '131.30934339024355463761364173361', '131.97037222932920789891827273204', '132.3983889474874166308830209761', '133.00559888344571546977670491102', '133.63950814518627714779947931776', '134.19529344571564264620422688889', '134.64923458460155585345411437002', '135.69989071981833275156425821651', '136.096020408551005575719800246541', '136.8218526953002974718305962792', '137.18198491502654936116266671467', '138.22579996810320579570787763927', '138.44799463562776581438612542959', '139.15048684314367008494204726010', '139.435793517213349233669600167981', '140.123739415961201000181126511499', '141.17805363770051045874680045154', '141.400643679406224301789410558824', '142.34570071994872702177026815316', '142.75729021277776667026997974311', '143.37962215398515099608282253349', '143.87402488058452558173878572104', '144.763503295495902235225037339563', '145.038906788360660880474789004069', '145.50374399631703734953000842066', '146.251524642301686618440190164478', '146.942358886318462347189663256366', '147.80162748921425746777155467832', '148.11859073597356825174831025370', '149.00799178193003649982807435431', '149.33999512644248531728765650829', '149.722944032585905921887395039418', '150.711851210881557352696530237607', '151.05100254310658396089832557159', '151.58949826234471876087907963779', '152.42250372048468376388475972983', '152.755993718366672145933397122258', '153.82926369289459414632957003153', '154.25993703019870372583572466710', '154.76123473354507201178076460972', '155.45765762969108408901600942868', '155.85671635542010463342310927375', '156.2961990546091112669505301085', '157.157916391349400257097822546735', '157.76061184343527628183894042403', '158.28763555180364019398525974755', '158.84287538994922402233371056308', '159.67356732791062906807428113498', '160.39296023665529090681052386421', '160.7555289250097138812207920876', '161.13038691075955210366088333400', '161.91269265448772300229284444607', '162.57270320679551913934596755314', '162.84922549445914773766492705744', '163.52447936809645259421487685886', '164.535781552017527880869620661219', '165.02588784111638137284575076243', '165.450194814618020685765320241197', '166.03889303497114640672590996634', '166.75412363417097127012139729064', '167.40324608045358920101780680866', '167.76019625956194555980103630842', '168.30600593341402549718847762874', '168.87588140290879794030328955038', '169.503175804803141482668474400703', '170.582955660574243259864717800606', '170.96949621893609794501952133674', '171.28182279192890694754433170900', '171.99384495712755554236591737371', '172.73612701554647317191495455826', '173.18399506387206014123811758762', '173.68377458006955779920180824804', '174.220457721781798418670284052450', '174.9235824525896904060817809302', '175.53303027346435604174798317770', '176.16581913095536191644737994917', '176.93948185378067143743921081431', '177.449121924755486040430475517', '178.09988231152951483716353737881', '178.24868811433528201569859359477', '179.04638335822879198962806043981', '179.62886132362550427302522684666', '180.26002536830483209035406254544', '180.87719262612116019986242731045', '181.30297502958842218609546395623', '182.16434122559962524944560907788', '182.80791236138043585131172841245', '183.34541702069993374552379621117', '183.772164547605044464864707448139', '184.494519908240772458349540787314', '184.83301874499790088070166697630', '185.357619389316317456677433669648', '186.23028752963415447420138358367', '186.68226845557379743826836687084', '187.45936026464880083597802299582', '187.93099989575547171487589036802', '188.60069573434340163894430669455', '189.2105601582437135329697228832', '189.72801907641282573266705254872', '190.26090965736090773605898633850', '190.790465082415790307021857951553', '191.30641199672822288649453439330', '191.90924401397450662187976710216', '192.61346146451763569924138429253', '193.32690482849433813859903724274', '194.039454944924054149925101313786', '194.38443246865733930111464736239', '194.88512936382188519805285560858', '195.52180989383972117316221294505', '196.25001366102674083981410606378', '196.69998084242406560412198199951', '197.18724996676173406228548046400', '197.63497834211870061515989968172', '198.46672058810750433010966070214', '199.291265077654378630394654963014', '199.89308323432815793909159566001'], 'prelabel': '1-1480-1480.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.8895361159213503, 'root_number': '-0.940386115432344342019663497347+0.340108738350054073621500568018*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.444768057961', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.646189598619246437210121837384-0.341928205461423915336549337343*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.223629757134', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.18188024646', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.50447714228', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.13', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/13'], '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': '1-1480-1480.13-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': '1-1480-1480.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.44476805796067514, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.223629757134', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1480.13', 'Lhash_array': ['dirichlet_L_1480.13'], 'label': '1-1480-1480.13-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/13'}