-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_49.36', 'a10': [-0.2225209339563144, -0.9749279121818236], 'a2': [-0.9009688679024191, 0.4338837391175581], 'a3': [-0.2225209339563144, 0.9749279121818236], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [-0.2225209339563144, 0.9749279121818236], 'a6': [-0.2225209339563144, -0.9749279121818236], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.2225209339563144, 0.9749279121818236], 'a9': [-0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.36', 'coeff_info': ['x^7 - 1', '0.623489801858734 + 0.781831482468030*I', '\\\\zeta_{7}'], 'conductor': 49, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_49.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^2', 'a^6', 'a^2', 'a^5', 0, 'a^2', 'a^4', 'a^5', 'a^3', 'a^1', 'a^3', 0, 'a^4', 'a^5', 'a^1', 'a^0', 'a^0', 'a^1', 0, 'a^6', 'a^6', 'a^4', 'a^4', 'a^6', 'a^6', 0, 'a^1', 'a^0', 'a^0', 'a^1', 'a^5', 'a^4', 0, 'a^3', 'a^1', 'a^3', 'a^5', 'a^4', 'a^2', 0, 'a^5', 'a^2', 'a^6', 'a^2', 'a^3', 'a^0', 0, 'a^0', 'a^3', 'a^2', 'a^6', 'a^2', 'a^5', 0, 'a^2', 'a^4', 'a^5', 'a^3', 'a^1', 'a^3', 0, 'a^4', 'a^5', 'a^1', 'a^0', 'a^0', 'a^1', 0, 'a^6', 'a^6', 'a^4', 'a^4', 'a^6', 'a^6', 0, 'a^1', 'a^0', 'a^0', 'a^1', 'a^5', 'a^4', 0, 'a^3', 'a^1', 'a^3', 'a^5', 'a^4', 'a^2', 0, 'a^5', 'a^2', 'a^6', 'a^2', 'a^3', 'a^0', 0, 'a^0', 'a^3'], 'euler_factors': [[1, 'a^3'], [1, 'a^2'], [1, 'a^2'], [0], [1, 'a^3'], [1, 'a^3'], [1, 'a^1'], [1, 'a^0'], [1, 'a^6'], [1, 'a^1'], [1, 'a^0'], [1, 'a^1'], [1, 'a^2'], [1, 'a^5'], [1, 'a^3'], [1, 'a^6'], [1, 'a^5'], [1, 'a^1'], [1, 'a^0'], [1, 'a^6'], [1, 'a^4'], [1, 'a^0'], [1, 'a^4'], [1, 'a^4'], [1, 'a^0'], [1, 'a^2']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-7e2-49.36-r0-0-0', 'leading_term': '0.157080094892655861631156797779+0.426837362096014313076943194621*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/49/36', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.45482336119923494, 0.7085562446304358, 1.1468860822932554, 1.6750158995057227, 2.164192140459358, 2.474303925490717, 2.4736799367547686, 2.0715930222026593, 1.2541285009380911, 0.10960524465770755, -1.1700149217474036, -2.320120367025447, -3.0654412562411673, -3.1995960889678097, -2.6585950975329182, -1.561077766973113, -0.19423864140867542, 1.0595998799097526, 1.8391569575468834, 1.926889845910861, 1.3331477093206598, 0.3046569495514487, -0.75503297505141, -1.4313932695821223, -1.4589759106472424, -0.8311328004011906, 0.19124024105792695, 1.1842577689798692, 1.7422235777378992, 1.6601205308394889, 1.033419342789382, 0.22091416060643268, -0.3244248877435922, -0.28727615375983967, 0.3234959305579078, 1.132066803255107, 1.5357671141356488, 0.9810394344711404, -0.7450988465777839, -3.350366755944776, -6.0949097718072505, -8.067313097250047, -8.566915665515957, -7.41817463036028, -5.062592572973368, -2.3728541527690776, -0.2680177399588355, 0.6888748554306569, 0.5142672465252193, -0.2619884271062852, -0.9155179026667085, -0.9291620868290179, -0.2615005014071603, 0.6633086716928432, 1.2362246658068874, 1.0523429546435625, 0.17939008782219532, -0.8594141691178945, -1.3893430494033838, -1.0031467321557455, 0.15659580544421745, 1.4360554943769892, 2.0302308783403027, 1.4681549646355405, -0.06450583985805261, -1.7756228383794548, -2.688168498841994, -2.205770693138154, -0.4914539269417386, 1.5802760527181423, 2.895129165304251, 2.7359204114579927, 1.2130402442183117, -0.7761960060706845, -2.051275535860907, -1.8282397973481963, -0.17450998372052198, 2.0344523571186155, 3.6316729661749885, 3.835306271416243, 2.674665189179432, 0.9128499747140173, -0.4693561227839403, -0.8876226667180476, -0.46972186990956133, 0.1205324834767102, 0.21310904239350156, -0.3619517564201847, -1.1527150649929625, -1.4416532819632466, -0.8325389431076334, 0.35941653614563196, 1.2258892432634143, 0.8580371565016631, -0.967134150491322, -3.48996162741713, -5.3148165459257815, -5.230045308700861, -2.9932082950558403, 0.43936575206459466, 3.4205767355537766, 4.56201445007958, 3.5304260058141965, 1.186257312130286, -1.01329271949991, -1.941994108869721, -1.4482563864464792, -0.30714176876177085, 0.4444111692183731, 0.29200316351980926, -0.41570133490660616, -0.7988265644870522, -0.183576883192766, 1.3191368882560965, 2.838549032591419, 3.365583968479974, 2.511370230895571, 0.8275447347778468, -0.5698597400606198, -0.8088167145347922, 0.10073650381956105, 1.2931973003611348, 1.7406666682827063, 1.1015389339634778, 0.06613962776327194, -0.10717208179519695, 1.4343294230692656, 4.366645922393556, 7.22840339634374, 8.3093936698076, 6.7985090209811005, 3.3804014038962573, -0.16303501004876955, -2.088431475096699, -1.7782438496186872, -0.03094471121653441, 1.6155175124023522, 2.0021195085878523, 1.0882981747175005, -0.19083707281491158, -0.7718967921963957, -0.3161771996710952, 0.5961587660390852, 1.0426989051534838, 0.5917835936188882, -0.321903940420919, -0.8043467654168917, -0.35297478335304944, 0.5842287614622741, 0.8676090691770675, -0.3977734431612283, -2.981824093028574, -5.461818077862698, -6.122753370210643, -4.207375025886341, -0.5683091076902771, 2.8207764574945573, 4.184791220025306, 3.140260522580328, 0.8788709558877981, -0.7845169494169678, -0.7645464785283513, 0.5701978847605923, 1.8251215581466056, 1.7777493925716317, 0.3728297957719504, -1.269067825871103, -1.8025541453431098, -0.7684304523538675, 1.0456022142257364, 2.27134159923071, 2.0799064060234134, 0.8175151168161658, -0.35886144861240027, -0.5120364161978587, 0.27420935196565666, 1.0146659113292065, 0.753393386683681, -0.5198472167234055, -1.8012273878394698, -1.9594267263662861, -0.8300420033267356, 0.4686033538043539, 0.36839837517911705, -1.7806072569017939, -4.9431917690106, -6.953841284879706, -6.06154951877325, -2.294323724763219, 2.4427316894884257, 5.652081684658132, 5.943512933402056, 3.8633127489468286, 1.274479622676757, -0.14019996101523838, -0.02945549166035058, 0.678339089327977, 0.8432670725036032, 0.184341100510232, -0.5811240476660442, -0.5782099658968429, 0.24773920426794593, 0.9678283720551439, 0.5082016298576202, -1.2692224849350928, -3.2708384301095266, -4.010718035310808, -2.900410918264625, -0.8409256462279918, 0.47357000277896966, 0.00549453864192799, -1.666382272322271, -2.7577625483858004, -1.7785805269380939, 1.1289909129006406, 4.180273732945864, 5.328972830867515, 3.9110489976557936, 1.1745144545267217, -0.7541561946181394, -0.5960081431235321, 1.1117816108225806, 2.5923971815047233, 2.411378771292621, 0.683514707314234, -1.109608262554474, -1.4716557194890303, -0.1871124236120675, 1.566410039376147, 2.326180510278971, 1.6246766224598488, 0.28738771204018854, -0.4616053371888918, -0.1850668028062994, 0.4376971478815576, 0.4387104369651394, -0.29157199239235626, -0.7256258827782351, 0.32787056490375927, 2.8500008622318256, 5.186853199853858, 5.158641145537625, 1.8922566658297422, -3.1963812277151384, -7.227394269697134, -7.92884609221907, -5.2937612107097864, -1.4678370603824453, 1.0087790843936573, 1.1135722934423768, -0.15333538972295305, -0.9621382983935123, -0.37074214126396404, 0.9713751819244155, 1.6552749977306798, 0.9767620214395043, -0.39476689437609463, -1.1428503631710245, -0.6626638674493442, 0.30976720895534127, 0.4330323147908113, -0.850252515973519, -2.645945469649291, -3.367253216196014, -2.241925005576301, -0.12289281909639024, 1.2280949403906665, 0.766254421226019, -0.8292881015922035, -1.768018045533178, -0.8649137331797809, 1.2418038111427998, 2.5765435698087034, 1.6529977985419002, -1.0156539621622116, -3.1680328341593476, -2.679060137631118, 0.5596625001288141, 4.4458756656497815, 6.355238878810597, 5.237810251546088, 2.313961981987598, -0.14767849075292108, -0.7784489579735989, -0.032381773532167375, 0.6119241879885191, 0.2402770074668336, -0.6986501287430888, -1.075805334700518, -0.42752666050313204, 0.48245251494857383, 0.4802863416914646, -0.683712881942987, -1.9270620483510448, -1.8843683856616071, -0.42431423460511797, 0.9472362961488986, 0.37805312939122554, -2.4495020395559566, -5.668223280443113, -6.595416648872584, -4.0285638769546726, 0.5828391013040158, 4.208904607750188, 4.665795660265921, 2.278417409419204, -0.6357659510683701, -1.8927957457484403, -1.1972755499777825, -0.0032414561120483044, 0.1985746037090285, -0.6009374477383321, -1.0658215468571266, -0.06524830967440065, 2.0007971493043195, 3.4696832170794925, 3.0159033012083967, 0.971469715565535, -0.9642518912639179, -1.3386188084304607, -0.2717548510051552, 0.8145600291663426, 0.7473557616707641, -0.18912467353971157, -0.6531251039299806, 0.15663916828475313, 1.409981177594622, 1.3219247743023192, -0.9439105197735828, -4.048862002635209, -5.323928525589563, -3.099856040950105, 1.6047909150712465, 5.7057749660465475, 6.5480883475321345, 4.067787926493676, 0.69148492661173, -0.8747526657995132, 0.09552287906884512, 2.0451761645869535, 2.870616886919734, 1.8996262618897184, 0.24929740492930164, -0.5732883146216314, -0.24068243466659955, 0.26308044797599, -0.05470828498885136, -0.9813418088407384, -1.3458531003733534, -0.46620178453081085, 0.831977277418957, 0.8711379088070799, -1.0841028600351401, -3.7549035067693555, -4.771760457286407, -2.8695433691098264, 0.7668882633216649, 3.4304100615722466, 3.3228461956459574, 1.1885886391076277, -0.44644583028150975, 0.27924634012524086, 2.79172622065292, 4.6909398680528085, 4.11559921399218, 1.5335736562600286, -0.7698081047247174, -0.9410696274843132, 0.7067748054079338, 2.147093818995619, 1.7337711334588999, -0.2115730160850971, -1.865208631762796, -1.8339312655135145, -0.5154545671555707, 0.46822677565616616, 0.06746159124038666, -1.1193228268815658, -1.6067455704120117, -0.7345933683893988, 0.5757957263098672, 0.870469188108675, -0.13974363370762458, -1.1710830962768317, -0.83673851061367, 0.5153950614237301, 0.6935780084550252, -2.2983076600850745, -7.9527682711229755, -13.079821908210626, -14.21726005025103, -10.541904816468335, -4.590212330853106, -0.10704833262289207, 0.9751133274053595, -0.30650340013223376, -1.4884811447721558, -1.1772423355158235, -0.03401407779081976, 0.4649192263072983, -0.10074677318023764, -0.6707725344738884, -0.07638855961986843, 1.444530364065232, 2.3630559248003995, 1.5301660311418783, -0.4456724145589387, -1.7024482327011536, -1.056359109491456, 0.7052041780311311, 1.6275213534871107, 0.7059253126928686, -0.9483967615873782, -1.2312023948840225, 0.6379010765922268, 3.063574704312526, 3.523666347954694, 1.1425742521379052, -2.2586786750003474, -3.812699375151874, -2.374029278158138, 0.3748743697662486, 1.6156415850824422, 0.189232786373259, -2.3114374325507976, -3.2087120966228335, -1.4269695086501075, 1.5130334993442633, 3.0986857765560614, 2.281184807436537, 0.2828353399198255, -0.9011406965618078, -0.559372786484704, 0.2932776289957759, 0.3635266590384044, -0.3764998809353094, -0.824061589650899, -0.31465155959217805, 0.3274263568877777, -0.3535454118275502, -2.5327125245565205, -4.385842458466857, -3.678925074478994, -0.22448025754036993, 3.4316135535109353, 4.10527885866826, 0.9808179021210625, -3.4560362131984514, -5.60054457680588, -3.9720809453556307, -0.3886876575261082, 1.9801314336121436, 1.6368072216183884, -0.1400530227307744, -1.0021962942184244, -0.05529707015444299, 1.4538000738895982, 1.803542945084042, 0.7982338165866582, -0.13249267144967158, 0.26120886357671, 1.4823847389781857, 1.791215187405523, 0.23438955766770206, -2.109074418637468, -3.1355506867864795, -1.9277614868638469, 0.2667360910790737, 1.3963596642205043, 0.8121227864993154, -0.14526262862582778, 0.14802233226381037, 1.5325390879264191, 2.071772354374557, 0.2987078659123895, -2.7252470251957623, -3.9813990361993383, -1.4018423934135011, 3.7916568427521584, 7.847054568339175, 7.771686145545145, 3.9717828733000715, -0.31101638660944153, -2.0934801574105264, -1.1439513791702776, 0.439862228754155, 0.7764805448598698, 0.02366642706582403, -0.2918628034985512, 0.6390410508875825, 1.9163944119656826, 2.0894207228327466, 0.9611082584350525, -0.17180759290465136, -0.14337075481241346, 0.5627857302710731, 0.320285013090537, -1.5654132237518357, -3.6499696569226514, -3.6464010268788196, -1.033562016429511, 1.9132647642752403, 2.077997043220941, -1.35876166312502, -5.858983090609877, -7.787118809094796, -5.792418393734774, -1.9140381975901843, 0.6294642470506921, 0.5803831123738122, -0.5208892064890367, -0.4590741901782132, 1.071138419940246, 2.253313410693183, 1.40068183379454, -0.9660440620630407, -2.5696122481614583, -1.823007313059033, 0.4804247027511287, 2.083333168998464, 1.695544970182297, 0.20922675685780076, -0.5621253990786839, -0.03941599713475166, 0.6010257530480898, 0.07236021510832681, -1.2715440831690286, -1.7783772286775428, -0.6189210570707564, 0.8716117105902216, 0.46019869053980944, -2.299485860140668, -5.030092433629172, -4.637338882773136, -0.5938656120665384, 4.100094593616824, 5.528522349659006, 2.5456683673524334, -2.176391619586916, -4.767522022502764, -3.7301952154169893, -0.9090279755357823, 0.8248207372699572, 0.4717332377619574, -0.6153355059695709, -0.7722295189824477, 0.02551524094772414, 0.48822866312758806, -0.05985854782311407, -0.6884584293637361, -0.08075884610015101, 1.559126436431077, 2.3820410206321205, 0.9341617167346319, -1.9433801944400149, -3.7086614013850707, -2.7639543516077496, -0.24253277023708364, 1.1719105099190072, 0.19769523900097938, -1.6074394314596958, -1.6182003089046548, 0.7800743814944568, 3.272492675730678, 3.002133420654104, -0.27610644644607085, -3.7501935175602252, -4.370284722196826, -1.9209221728357686, 0.9299805915867116, 1.5621802832232867, 0.06600345830771677, -1.180726438392141, -0.3510838702648536, 1.8404086465259244, 3.1208477254737588, 2.3053428710554082, 0.5196049532414968, -0.277816789312238, 0.4169802637063729, 1.2656021592020341, 0.9216528280799601, -0.26492647112406514, -0.7869839888970488, -0.043746433046421625, 0.7601630870868921, 0.20875974659168767, -1.0658894349596204, -0.4159584094553075, 4.019061648233696, 10.647374684720717, 15.102577978988698, 14.035001122859533, 8.296373603650913, 2.1997122710096093, -0.4445565446254027, 0.5022797008962792, 2.1756668873162295, 2.122400727896995, 0.6403494262616525, -0.23098837392667732, 0.5254805649691872, 1.745037065850295, 1.7158247758668415, 0.4198257506727502, -0.4134345621744237, 0.5205481958917196, 2.3965780052993453, 3.1500018250601682, 1.9291223176806014, 0.14251755088214244, -0.21779667808728098, 0.9945839828288979, 1.849429993192, 0.6758714083024551, -1.7872951395796555, -3.081049413039829, -1.88570197520349, 0.2933067298247185, 0.7366678118981603, -1.291514509731675, -3.4728877246095724, -2.9140443041028616, 0.48017340653701923, 3.5780332601074853, 3.1890388078808805, -0.5474494467183786, -4.241082619157462, -4.699035494392206, -2.0087583117867727, 0.9355241301691637, 1.661680361006877, 0.43109788937470583, -0.6760851727757166, -0.42025583056214444, 0.4358610028632409, 0.5764863431692836, 0.06361811588513466, 0.20345910085115357, 1.5847203020713347, 2.9556253534598493], 'positive_zeros': ['2.83973610442772228754210029031', '5.044400320231324786207707825397', '6.64776176162004323808696295551', '8.06985933497139805237288880742', '9.78619198348865543619779416373', '10.48726256328192917339560235123', '11.7631775228370578818945767035', '14.4320396594566081730135319926', '15.215173683105178221869488634361', '16.33830144923573849041085251373', '17.55185138112648092126002908951', '18.71368516128555029382072606383', '19.98870248429834940166339868895', '21.32266906771563983246996079616', '22.68721944438723484399487505576', '23.77540328673930719136339140191', '25.49667130536254073774493272494', '26.484949728525398833522118732750', '27.02768989486612229440781973286', '28.346722925327816024040611171110', '29.23564306114711642774304216754', '30.89847796934645522520167015232', '32.34096247146441889670034148592', '33.5317886314063611596578998506', '34.20071135563324623740035470969', '35.04690228327942121231572275481', '36.72375908385982720475632797569', '37.47432109854949575699474452693', '38.77666601603137728099252549321', '39.10683305152637815176861538332', '41.23304015814631049380259082191', '42.192441078832157120306767918127', '43.38464605230341741245396277645', '44.1718984391480030329843928462', '45.20152430761844641190903406960', '46.05611579289980012762868050517', '46.81039813443205473087325895394', '48.48364903185245661220207201421', '49.82135905726228625537966576509', '50.50907673102038163116455735544', '51.627723801911409985208507928600', '52.63518235697732686792420576192', '53.94404715021739426567890938166', '54.59756705196402151340218642210', '55.5140029341418847201946608634', '56.74158231782394227815371606318', '57.267890280807906406676843666443', '58.898751514825002272324231796738', '60.56566514321710715420265559724', '60.95189194770154998120143205434', '61.93987398598992853210867577793', '62.73330389006719874361188395313', '63.54727896358051030529483092956', '65.15476920565010836649823865099', '65.62631252554237027647068646272', '66.76759687265145120783350437193', '68.27985373641467072924499275375', '68.87719340039885159978695732915', '70.104769221040461062768475779714', '70.96978224289291591953499565454', '72.26792514611822947591817113973', '72.89932665556920769239065164427', '73.6408654626357335081057806779', '74.31761563022526254569209010932', '75.74558718054875316091467886474', '77.3371300171086925751743624574', '78.08938819751360752571153539289', '78.84012753221872949402954842497', '79.90824725993149014504385383930', '80.827994370166525961807801532018', '81.392573146507209712239479037829', '82.83172696274982064881738428953', '83.59489942009057628607067835874', '84.51005162193994852867673620610', '85.515141187766718726150618515317', '86.51850624109515004914064972974', '88.09799979020149582894266899978', '88.760746589331478889465812092596', '89.4582947219472262911257017324', '90.444720947125134544661633833451', '91.09399681402243990909808971395', '92.26399794968521601650087673903', '92.86981474851242138505789488522', '94.33620587460347462332051459741', '95.546715031325402157207779328119', '96.563692809689795639114032903697', '96.97651099798491016864232340389', '97.82404182184242231390813117706', '99.19910297950377315771128915021', '100.06338909816029565756339191054', '100.87709642203472189595533983706', '101.52383110741509716031338950782', '102.39770762510764522345613390744', '103.6500694436178985183085887850', '105.08612566258747309220188393857', '105.60855834787510292665082220169', '106.93358369373533516718302386082', '107.617999487957323848924843606331', '108.10214286605945300623442497985', '109.16645446421765467832038832820', '109.86037890526886389945128343880', '111.185222334934867957632425782718', '112.371710895001779876436665260638', '112.763119731548318849795391782697', '114.24460253338766261996311795056', '114.884854666697127519232400755352', '115.90676562158177742232096024855', '116.997512477449767900413923930479', '117.520099342707896245586880172544', '118.60146359458953816763553791002', '119.34165931932388791026916938439', '120.19441526960245137249930645570', '120.74045317356165340047098440839', '122.82455420059096631444157901072', '123.378751669254176627607297369506', '124.38546407220076591473310703873', '124.96127375171399206847910436978', '125.64372768017472991286953444698', '126.80571726216469548257417836412', '127.689300428905792745945536091621', '128.56457089654551137395414451839', '129.29405355844497574532269881275', '130.41443202626394992455234415280', '131.5160684336495633915878257337', '132.21158532126024182789842105853', '133.27475821684673609928284350778', '134.42443215780257496228457817911', '135.190826082928121734009828347519', '135.79567585097691045646758920694', '136.68181820486042999039431783298', '137.1058099786255435298866823128', '138.45442168391065324739719462039', '139.44273335241555128861425823524', '140.66109149947283869235993987627', '141.53674187642453121471427497732', '142.19852777752807416420628213668', '143.35995167338459648142467126879', '143.65822197627493562905144377773', '144.71898170539879201188973403660', '145.896288934832539842810645425795', '146.805199428267469763121616632799', '147.13922108732899662958715551130', '148.15739693469115164134045883384', '149.15456307395184518210585045275', '150.59693700247969410999898698130', '151.46004556678428718696601457135', '152.1968715647787950811320886802', '152.64365753905616888012203580530', '153.99323112395340101463503510154', '154.44160186786892993224685702812', '155.07458680264900640074624699818', '156.34654850658481080939705075518', '157.09006051242598753398716254416', '158.63558030576176836461794949607', '159.219248553966523134629371160511', '159.8025484936211627124547589207', '160.81634756797864674591043858757', '161.81224395110990620774653088714', '162.862260990655315206691472597535', '163.45171584424600154001757290163', '164.08156191370147179571104103055', '165.111771427842461913989973009479', '165.6951605134613621117093690669', '166.91130416049453755869834752338', '167.97774032561327543638551996997', '169.18229786115690393947490762549', '169.81516280989460651050282975202', '170.61580366678148667484880004958', '171.22777207908442010336831175281', '171.893415629058359404325758081424', '172.9190155468754847877770651959', '174.09508852011900712403626866883', '174.720217434536662133569167158129', '175.5419899391882375107409650411', '176.540831168554205415623697704844', '177.69282953343112304627170461758', '178.44882169397960055471098695674', '179.11833545268741129977273012274', '180.43875286861250305649016155762', '180.80537678224336698232118520121', '181.80428861800301812804536629481', '182.512651194453597305673087836528', '183.17482411501210060247831881699', '183.79673472527316510724105639047', '185.82669211719901244639421448214', '186.15918103106722524288792541398', '187.34801694652605167114348273110', '187.66617557062725044822473191126', '188.85207394752588541862563552782', '189.26640506248526978783102313858', '190.66167075286918192845363306312', '191.01881918799963081483705985327', '191.96519256196832765729807540683', '193.075138884659841351093986933914', '193.58544655323533807230989590925', '194.6492480886698046083824209373', '195.58610199251508193459336239421', '196.75700395344766898328460040356', '197.59185033119292387732350446219', '198.27100439404103837716915753599', '199.12067734909097806510787282149', '199.26004406187985057562075763547'], 'prelabel': '1-7e2-49.36-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': 0.7755102040816327, 'root_number': '-0.761445958369134435405982779436+0.648228395307788401626567681892*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.387755102041', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(7)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.436684505744865138972824839571+0.382544101343815454711664931319*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.83973610443', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.04440032023', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.64776176162', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'bad_primes': [7], 'central_character': '49.36', 'conductor': 49, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/49/36'], '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': '1-7e2-49.36-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': '1-7e2-49.36-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': 0.38775510204081637, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.83973610443', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_49.36', 'Lhash_array': ['dirichlet_L_49.36'], 'label': '1-7e2-49.36-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/49/36'}
Lfunction data - 1-7e2-49.36-r0-0-0