-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1063.719', 'a10': [-0.5, -0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, 0.0], 'a6': [-0.5, 0.8660254037844386], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 4.9365512463040915, 'analytic_normalization': 0, 'bad_lfactors': [[1063, [1]]], 'bad_primes': [1063], 'central_character': '1063.719', 'coeff_info': ['x^3 - 1', '-0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{3}'], 'conductor': 1063, 'conductor_radical': 1063, 'conjugate': 'dirichlet_L_1063.343', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^2', 'a^1', 'a^0', 'a^1', 'a^2', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 'a^0', 'a^1', 'a^2', 'a^2', 'a^0', 'a^0', 'a^1', 'a^1', 'a^1', 'a^1', 'a^2', 'a^2', 'a^0', 'a^2', 'a^0', 'a^0', 'a^2', 'a^1', 'a^2', 'a^1', 'a^1', 'a^2', 'a^2', 'a^2', 'a^0', 'a^0', 'a^2', 'a^0', 'a^0', 'a^0', 'a^0', 'a^0', 'a^1', 'a^1', 'a^1', 'a^1', 'a^1', 'a^2', 'a^2', 'a^1', 'a^1', 'a^2', 'a^2', 'a^2', 'a^0', 'a^1', 'a^0', 'a^0', 'a^2', 'a^1', 'a^0', 'a^0', 'a^0', 'a^0', 'a^2', 'a^1', 'a^1', 'a^1', 'a^0', 'a^1', 'a^2', 'a^2', 'a^2', 'a^2', 'a^1', 'a^1', 'a^2', 'a^2', 'a^2', 'a^2', 'a^2', 'a^2', 'a^0', 'a^2', 'a^1', 'a^2', 'a^0', 'a^0', 'a^2', 'a^0', 'a^1', 'a^0', 'a^1', 'a^0', 'a^2', 'a^0', 'a^0', 'a^1'], 'euler_factors': [[1, 'a^2'], [1, 'a^2'], [1, 'a^0'], [1, 'a^2'], [1, 'a^2'], [1, 'a^0'], [1, 'a^0'], [1, 'a^1'], [1, 'a^2'], [1, 'a^2'], [1, 'a^2'], [1, 'a^0'], [1, 'a^0'], [1, 'a^0'], [1, 'a^1'], [1, 'a^1'], [1, 'a^0'], [1, 'a^2'], [1, 'a^2'], [1, 'a^0'], [1, 'a^2'], [1, 'a^2'], [1, 'a^2'], [1, 'a^0'], [1, 'a^2'], [1, 'a^2']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1063-1063.719-r0-0-0', 'leading_term': '0.0122352126637939618344581945980-0.920219071468304213160438576008*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/1063/719', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.920300407433854, -0.42987812793117103, 0.12084600725393291, 0.47853331746079286, 0.2600535274110732, -0.4359643625057857, -0.9487077781736853, -0.6069094742574644, 0.527029733854603, 1.46774113694788, 1.0614159833038863, -0.8219380624120646, -2.7975131604893373, -2.903848987103972, -0.3805887150575147, 3.338518217969143, 5.59247908873046, 4.797417749228467, 1.9760998787111173, -0.11224803510931397, 0.4134042414242589, 2.731479611700964, 4.2017414234476576, 3.1399328673115763, 0.5958087516276351, -0.804609967592475, 0.256395397410672, 2.3420910570736875, 2.886631837803584, 1.0756555359057909, -1.2944924219294125, -1.9399342340254069, -0.6723024283691068, 0.6046460169564986, 0.3877169480761561, -0.5846532081443262, -0.44293674414054973, 1.2156200052344943, 2.6598309946051475, 2.238920834881059, 0.5923828819333404, -0.17596602073425016, 0.6127384446403055, 1.2334278155809457, 0.18675992386172396, -0.8633617001920679, 1.773774439257562, 9.148049788958845, 17.05148953743503, 19.35991015479016, 14.192914034073224, 5.91800742169179, 0.5772569403101497, -0.007101885218527873, 1.1472212342221284, 0.8070262116146792, -0.7827346955922461, -1.3412203453893319, -0.3057875566835803, 0.5330998946523355, 0.01311955227304622, -0.5297097233205037, 0.619205288509503, 2.6377668867830817, 3.0070496121615813, 1.153619698202504, -0.45050595797116083, 0.3350685972369004, 2.139988781788236, 1.880448485176983, -0.746045079475963, -2.559301098440966, -1.3344651083789907, 0.8307670877791853, 0.3365716081864857, -2.5790779940969735, -3.695138772597336, -0.5543003645416246, 3.7528015254468987, 4.322315084948171, 0.8241522969391937, -2.229456949803738, -1.6794250801940984, 0.2783061788798451, -0.2799190663328166, -3.163937170666502, -4.376395246036808, -1.9052748730078803, 1.4442865349576448, 2.033044234599629, 0.1579987056066619, -1.0715441309115932, -0.43426420726832626, 0.30052487662707333, -0.14935195692651523, -0.6293194224310332, -0.16203064003464165, -0.24359799433116747, -2.3129492365542506, -4.289732374687578, -2.677313437305225, 1.8057969108002687, 3.8472866295049686, 0.429398468880005, -4.330009640159991, -4.040850555144274, 1.4120040839621317, 5.5789529376095714, 4.0403249416467135, -0.07086536280813396, -1.027635048429898, 1.6398351126956858, 3.4599642495395333, 2.021720406564193, -0.1332242790318989, -0.21958801308853065, 0.6589703186235557, 0.18064624973678067, -0.9065699386526553, -0.26328852680123477, 1.486182849265103, 1.1973128860017255, -1.605707431874081, -3.3462292561272604, -1.600926537395161, 1.1378390653353276, 1.2417979872319973, -0.648034554391933, -1.1596635332892609, 0.06671880973934921, 0.0705126471115244, -1.7718541106409869, -1.9290350899202526, 1.4513443872309066, 4.44962375470314, 2.739319513319648, -1.1116819921856673, -0.37964854743413823, 5.956644623141212, 10.841674177975667, 8.385109430433122, 1.5664999334798235, -2.386155721236468, -1.4917286448892826, 0.2113167102986889, -0.05603206568976081, -0.5723136391207513, 0.3316266406756405, 0.9520270695340066, -0.3628646246755326, -1.7940994226268518, -1.0230777651257583, 0.6897415292772056, 0.7227469599552162, -0.235783445092054, 0.4197055705027978, 1.9625453461259286, 0.9732599971195162, -2.251303998504934, -2.740560686828487, 1.358406788965684, 4.324502526872877, 0.32833379299398735, -7.462574793545555, -10.40386991833739, -5.968990946887267, -0.40173253123121955, 0.7749434647927986, -0.5911899290312456, -0.5218511254845669, 0.16205286841873806, -1.4387840493148443, -3.8794232748254407, -3.108209001829307, 0.5124015828143658, 2.241615383757807, 0.36878506868747196, -1.3325782953179433, -0.02245927045201421, 1.8675811473087867, 1.3005239243817295, -0.24510032664915687, 0.1127837108774779, 1.3969132006310714, 0.8531769732371408, -0.7389153442414682, -0.5606952553902261, 0.5820396598353825, -0.6395137476798303, -3.33535703387634, -2.584839116907485, 1.9728113747809337, 3.599116805597368, -1.7684365411998098, -8.110920477744946, -7.143311746108074, -0.30662569541155926, 3.490239359689318, 0.7681955090828544, -2.76163044757734, -2.0204840121722003, 0.5399622473841246, 0.6288326681958528, -0.8667628447479926, -0.7759870124313106, 0.41718494258837613, 0.26063820016419215, -0.6998405568195036, -0.387063608723485, 0.28535338039985175, -0.7173013563063864, -1.4924000044277927, 1.5206952803851352, 6.535331348665441, 7.521135837516186, 3.24036929648131, -0.5984131741267388, -0.22612491400347567, 0.9724426127480212, -0.47707680210585846, -1.5375348494491434, 1.5166577530574963, 5.119932313668555, 3.1799100676275254, -2.587762083417119, -4.529855206658297, -0.7487007202312543, 2.476720392450349, 1.0652453751663085, -1.2813735250727474, -0.6710715465422723, 0.3858925169372801, -1.5405213192325693, -3.9783660455850107, -2.760748695252854, 0.5836200747857863, 1.4410717393187322, -0.2975290116790723, -1.0113340463250717, -0.11626069526109063, -0.22753745737714168, -1.3834755071836566, -0.9784871879953987, 0.6879990112720247, 0.7148936145066157, -0.2964780801897238, 1.0531720227775252, 3.0577156003868033, -0.851824357028185, -10.80841564625398, -16.778089281282767, -11.576193571878967, -1.6884782729575423, 1.6944514788434468, -2.0559272126530495, -4.5229453465175595, -2.069513024516968, 0.6490203316987619, 0.3693367085140549, -0.23785632276456598, 0.7748967619457521, 0.9677456996069593, -0.826889624144997, -1.5953667442575337, -0.028954728255144224, 0.41654967870943643, -2.165807919869742, -4.112643984857872, -2.4275762127674922, -0.002236684823178627, -0.14873456548751404, -0.7616302139110217, 0.8422293181357445, 1.8098116167709402, -1.2598660398272992, -5.001285401189389, -4.059432714643044, -0.36308937150475956, 0.07497327066754991, -2.3288220311112413, -1.9262855616247165, 1.1756331613628412, 0.6584676255973219, -4.251483056395721, -5.993623155413894, -0.9913117257357011, 3.870366869160643, 2.1030857845798177, -2.4620301458880505, -2.7797177364063357, 0.43707517392840156, 1.7641286241369156, 0.49972290444327006, -0.08057968447256496, 0.34768905240047004, -0.18082695690688544, -0.7261303201223086, 0.6961711382479705, 2.141769372717084, 0.7678461462926722, -1.3316820187981477, -0.6628138351225769, 0.7057646851079378, -1.0428395053927833, -2.942601850636838, 0.7962631590982288, 7.366640953753716, 7.662682085727335, 0.8018512886357839, -3.638911601488277, -0.5081309184549078, 3.578690467303701, 2.129818121571842, -1.1675941294761847, -0.40067194861491096, 2.3788213715711612, 2.177920592560547, 0.15619964510376189, 0.19251864659191611, 1.1810927712911692, 0.10806721655384421, -1.2254351628772548, 0.17977634383371432, 1.725670422028554, -0.6105423503748059, -4.332457006391451, -4.085440617018055, -0.7303532706710195, 0.679755695089975, -0.2385771774004034, 0.060974853729955175, 1.4368555085305244, 0.9989035682694324, -0.13883512989309282, 0.7441799381032881, 0.6376390106119553, -4.818216981023044, -10.7691874881531, -7.622605128806613, 3.289676405078752, 9.530164918222539, 5.4260214236118145, -0.6360041925570896, -0.5998103996300262, 2.1055629798246924, 1.4356627444480545, -0.7376290975897472, -0.16259131610618877, 1.247201567869252, -0.10402612917594281, -2.2522971196366184, -1.7617978498467004, -0.1437522247283584, -0.16834511066270666, -0.5615442552797149, 0.1547873237857006, -0.3010801708304819, -2.7469478088451105, -3.085454494742807, 0.21961173920494223, 1.486749851834818, -2.855126874204125, -6.836684325020613, -4.460332642432649, -0.16410745966461027, -0.8904627122855377, -3.6636568812387487, -1.3179455998941638, 4.143530965226128, 4.986738241403669, 1.2508275182907538, -0.36394173343292247, 1.0583151239874942, 0.4881984346873474, -1.9527784543824251, -0.8948271275852102, 3.303859437348219, 4.143756517547941, 0.3795976300839189, -2.0567698059854207, -0.6541635435207567, 0.5248227698388148, -0.43940179444917127, -0.4676196320772481, 1.206749925882199, 1.3748790539947082, -0.22216974724609456, -0.41532351393581224, 0.2958777103338651, -1.4979324968643684, -4.164749641318178, -2.885332793419719, 0.6917219406363095, 0.6935019309094244, -1.222417502643435, 2.0313432743049775, 8.24068731254758, 6.308914452287108, -5.396968810297081, -14.019366130681025, -10.71615594079831, -2.45872178737597, 0.7668455927247373, -0.31961380211065676, -0.3758255120064413, 0.39798332215340276, -0.2134085952271773, -0.487967576895853, 0.8700912135333351, 1.0593285868410123, -0.8125385273448351, -0.9062666890885621, 1.7671244312316194, 2.4958987955123666, -0.28150709369139354, -1.4774313744085166, 1.1389023145695865, 2.667781030696463, 0.6229715981842961, -0.4597036617936189, 1.5150562215287013, 1.887119124110611, -0.6826721164742342, -0.16083746988240064, 5.139854341624475, 7.413272263398587, 2.5228352867691255, -2.2154139091028893, -0.6996889309192565, 1.9357664579641052, 0.05462389308682567, -1.8713519572264197, 1.5092922523943086, 5.7097547747223345, 4.436806179080558, 0.49103741127207834, -0.4592078970741499, 0.12430060730090348, -1.5398045660324862, -3.3658823172178525, -2.059456235716292, 0.07758121821576261, -0.0504157782534733, -0.6931630299140642, -0.047984638517950554, -0.05499419666549703, -0.8466055611299274, 0.7227648930648293, 3.0884287826159684, 0.1814793029644441, -6.143973536412675, -5.2717030080113485, 4.9554719945471355, 12.245468149370312, 8.185399030102168, 0.5683484862267223, -0.7656710301062607, 1.3900937117520789, 0.4711534109754485, -1.2531706310494533, 0.7317587980232018, 3.170862878376718, 1.5509359383513237, -1.1444797642852438, -0.7901150765908244, 0.21278981488354284, -0.9776394720873198, -1.5525492648413226, 0.3938848686506368, 1.1864958569383688, -0.743572170998974, -0.9059718919955614, 2.3257786733411203, 3.7933715677760147, 1.2914709078133024, -0.20979905806261434, 1.6385725772947861, 2.465122299604719, 0.6185888717452611, 0.15383534768324306, 1.2209084065877809, -0.9807177929839335, -4.801330428330747, -2.5660697729413133, 4.380730308964192, 4.990795312373672, -2.977277088281862, -8.086186586869784, -3.9717467805398696, 1.2309683396057565, 0.19316795099197226, -2.4752358821524547, -1.1199227971746275, 1.2000454319036014, 0.5974481477918272, -0.5424232655951536, 0.018057931635423612, 0.13707436851869337, -0.6854147583350274, 0.09475247648604948, 1.4899376845752141, 0.024766902627412928, -2.380738232181544, -1.124666513062212, 1.7238052015071932, 1.1215601890303453, -0.522360089744136, 1.876671603520938, 4.5271557951962835, 1.0220255230079676, -3.7714346116100588, -0.5059274365300205, 7.422394370425922, 8.565960573400506, 2.5105278383634566, -0.9234836592758644, 0.8172892716176597, 1.2961882940233065, -1.0401107942205359, -1.4956982016658622, 0.08636693799021553, 0.1331798407653082, 0.5529981242152375, 5.04657961313091, 9.448464510369062, 7.343625661012877, 1.579117432445806, -0.5949528072334004, 0.6418365378202806, 0.6610859410513954, -0.23775399750851955, 0.25642533551017355, 0.24075251522504879, -1.4905632716308115, -1.316026105793292, 1.570598661746087, 2.011795085114347, -0.8323579616250327, -0.8676577617990551, 1.8106695950588465, -1.5875462451904965, -11.518441072116989, -15.260168125823116, -6.979843555988298, 2.0837402928578816, 2.0843798171420915, -1.2750359458865848, -0.04031748202799684, 2.5195479119723716, 1.1657659480755838, -0.9938527662745914, -0.15209572993263215, 0.923547183996191, -0.029129049695468687, -0.257902841496496, 1.0121140745194188, 0.7038488297746279, -0.8281825544414536, -0.39777151522433996, 0.24783825841728951, -2.359581892570759, -4.549303632867446, -1.1865510591626056, 3.368018280088741, 2.1040008274238415, -1.5846394947191498, -0.44729408846022, 2.8161926153749386, 1.614639308574621, -1.2355300301465846, 0.11353162567954586, 2.1126457969713837, -0.5347532105136632, -2.7257199082229864, 1.7257242235908135, 6.915140605594101, 4.658174378987818, -0.8999069950872116, -1.5116904604542456, 0.9003281659666522, 0.4156981377360045, -1.125104679028535, 0.23642864699749772, 1.7068433262122429, 0.16268004596402846, -1.1062131668473012, 0.29790249902635674, 0.8402747103507864, -1.0461465785220239, -1.6118250372594485, 0.003800602847985171, 0.3004025028531496, -0.5324934245078865, 0.06069662085554782, -1.0118118407966554, -6.714887347889812, -9.680300023589211, -2.5219436190297193, 6.240523143396629, 3.290205922951691, -7.125103638720455, -9.769929046595632, -2.96049716448334, 1.6962541601758745, 0.23287165502405824, -0.8275453841506817, 0.5818677569749837, 0.4716458361234357, -0.7626964520828429, 0.11592915591371127, 1.107934333296833, -0.531439008974251, -1.5149699122467228, 0.6332218920978981, 1.7391436406121012, -0.2969874169611353, -0.466905419079037, 3.0729897856446926, 4.510121338105945, 1.5525566997506952, -0.5213411420001863, 0.2800712758843297, 0.19567525787692563, -0.15234575091341018, 3.227500705261493, 6.526023614668315, 2.751604214780068, -3.863238729779989, -3.643214404009667, 1.1748450696881465, 1.1669497261851736, -2.393192366216647, -1.5308487391737038, 1.4667798352270447, -1.2791242445173845, -6.572720432823986, -5.2900465669277885, 0.7401850920845575, 2.7050214118536617, 0.3240534284536861, -0.4824367677682808], 'positive_zeros': ['0.55615315327092306107304935081', '1.379947515424088261156904201474', '2.36847263575880451503833205114', '3.320072796926147290747870893679', '4.40809457439868200694589498539', '5.90390024173122798290051055135', '6.1630932840526864860895770034', '7.584967870628490398173637531398', '8.083324110991575269176594115603', '9.192838585594474185796975006012', '10.13329377346563030645720426904', '10.74451053769413274362347593846', '11.355167781776051760131093743598', '12.65325946485024607971678947161', '12.93345099418147311616426631485', '13.78591849112385565829201802406', '14.24023230163962250524553391198', '16.337937416904569658534234696333', '16.56471346906122045994025254300', '17.3484243724604253219366137483', '18.20153660365390574194496089494', '18.754498700795538412681567990099', '19.26336665198539454520239150659', '20.49231839990058864881714000584', '20.87497688611315087259366938900', '21.79542899333255135674493540235', '22.67086661519470924549163878610', '23.16892789027539430991035542718', '24.09938695613885389918939987437', '25.06342678110265532352725299333', '25.875961509352866443830014412174', '26.206746422457472230900157138694', '27.3488189874212599721306625987', '28.149483588020951606483469476773', '28.88400383344494607149135398401', '29.31390575883817117591238096271', '30.1171719440965557386440921946', '30.193890488163524741957261843011', '31.4397187693513714915986687076', '32.21264265712213003881084131069', '33.05329383926266380843472838667', '34.05571772431119055294386391971', '34.521301171161898785431482364203', '35.59537324305995682761101071826', '36.00856497794498770790771021152', '36.60767716583430448710269179336', '37.23461161026912160879174243808', '37.96252349867902875919323448614', '38.91399601938663775127110133588', '39.58073560188049523690313945002', '40.29449317352327649470528957805', '40.64171842600202547853636874026', '41.45232146907191290879238880558', '42.39344971206687588543821435297', '42.839054229497232858305208136719', '44.14601560542921567666177055711', '44.934291872590058091126932179810', '45.292613049695296594508366873616', '45.85360062679429860861257461577', '46.50192579240942007904790822422', '47.35802029360787806656902455695', '48.02339551656140757238716325973', '48.343563521280608398565097395804', '49.161603048699669389998464299407', '49.91415021731070545859326358928', '50.63897460093753799928498471035', '51.91216010046780907634030167323', '52.3628141283955664196303794357', '52.98012171505780152220912018158', '53.20956037484918776856972540942', '54.330648729839047059268085921695', '55.04462774617965836125132308309', '55.62802053976497201164285195150', '56.49193979986346021786021186196', '56.84762408726177463407233868330', '57.65344294828200998871264661257', '58.253703442423672274533996151', '58.664665954340509499027668104177', '59.55994779010532459651273029009', '60.236649252333022430135748941079', '61.2643589053578939118040275294', '61.92872061417099440344844550893', '62.73072526771445200728573856412', '63.25188946708603794497241319645', '63.938962945849376463305928504679', '64.452483483180806059726732941', '65.12678326550208721408595037728', '65.46618989167923294472902474581', '66.14152930721041721991021640413', '67.420249051130857480315269245177', '67.85250292852657301915618006545', '68.36909470046119397277806571970', '68.95006785154672233707023636594', '69.85901181619175091478834609335', '70.67496991852811388118453452338', '71.36406541415841651925407181178', '72.00420985577090510382897214359', '72.30841185384917321772637257405', '73.375518549534202054485585862392', '74.012477381827451313976498969257', '74.743141802073946301334356843977', '74.9092879282563790357571208002', '75.800186201192953857828943732442', '76.43374228295926577551414398465', '76.71961011899734736777066907062', '77.4647061751389919584041507356', '78.825943359625913773099133987172', '79.236063015840595236341120090459', '80.20114525505875882486914991007', '80.73235241486036949908819958112', '81.04858639636314789562520938901', '81.7478265339270799109057367700', '82.505209158259595149210159326823', '82.8890500478889164105487520406', '84.063052228025924715933801313', '84.33040264523916771733914868853', '84.87552971826603521091441556473', '85.53296074686930663731687759753', '86.60809020543882572862396870832', '86.8873935428140303901187558547', '87.6874767029325556119770941501', '88.17720936199552508739728005536', '89.10988008873658963196901232116', '89.820647476935046155611514739085', '90.581633424287637196455359769375', '91.40015428682774811025141334561', '91.62952568152132930628867280659', '92.12878348041175042332039734328', '92.70254647399688469026830057104', '93.53124756511826336263091476942', '94.17154257875634232700189811292', '94.56624869861522288863053503431', '95.273180565044239944755167809793', '96.284428800274019818299574201287', '96.904883722916581810913560479094', '97.67549850046833310524370017397', '98.1680627193228637895275250025', '99.10448846867022291337765350268', '99.31612015453509110492335329965', '100.01755889686633463582508313446', '100.601121077135502981353134430743', '101.200758875921185288459158402664', '102.273162795565384307863888084310', '102.73464573114907607752701789942', '103.11036394072738314680315975694', '103.98450751058004682625840279589', '104.194123545112078856174424796297', '104.74911897084132009248043639184', '105.846644929380328607964960905572', '106.82519201331728067141154610357', '107.25133865151183695248964024675', '107.992534341471652620215961028493', '108.4650666352838371556483610145', '109.04947136388779063654604072191', '110.060311928734663990215017205601', '110.22401442006687041655445373839', '110.87510912686009994163590954167', '111.18917585853005685419538274416', '112.16839367452923816141786190620', '112.64480793020709987054935016043', '113.77496913633620294488926495921', '113.95100313289125733973673099001', '114.76166800309933532476810813749', '115.76092065859663321278355363955', '116.04111172821802703830600075635', '116.62374365154431667082334097305', '117.25927332680559885423122128733', '118.15398146685537435186105847911', '118.85554982905381926939807046553', '119.2621406653236231751230090112', '119.78553220407991171646122305641', '120.57728250715831432087484432477', '121.069726479001519110685974306156', '121.36582868298893271715259376584', '122.426120878499555868565788657913', '122.9030908721284618982069995750', '123.318655551752183009911683578276', '124.24521242027437698409133520935', '125.46779170964709427968820443587', '125.860846615760045592673348805447', '126.36941575842495598644237826406', '126.80714488363096640733455201870', '127.32201958722246426580414749466', '127.9973060404677795228979378125', '128.559020460529895475530090691204', '129.34641761289834765942388811084', '129.88867711260116563182069867571', '130.71020662059839616375546330866', '131.0402624976862137557175297030', '131.79123865873404245518947225269', '132.200913402686489713456101956109', '133.25227554975386854638979213906', '133.810205118983015038564985467174', '134.38017401190842721762190088342', '134.90435630500350345709638364781', '135.99805340641044594126430805771', '136.42036502139827590339429816461', '136.62546999177260749627886586137', '137.79255518866307409888094069312', '138.10841665703270739185356514433', '138.7709509198810777700511895615', '139.040630983931991862622053280912', '139.602753652213614885220372206697', '140.32177268565423503539438358572', '141.115301100980140865184088612466', '142.22531267107225397948351442932', '142.60493819950468639487489700157', '143.18505913179850312859085838037', '143.678351046670143502846236741195', '144.5267329828165011309722003038', '145.176346703872883267338102967091', '145.42276298065233032243315385227', '146.1956524960979024600049273053', '146.7683749595828596030498814091', '147.29491408472557051612649734319', '148.29607040033657219818942612215', '148.50671992993466787950723164328', '149.53357876026166563382756023684', '149.6215096565820045105214083696', '150.23221368488699537944032436095', '151.053466251519943675319425056', '151.77247451735229299489732775400', '152.703678884070972269272920432465', '153.14303915786996939591260440144', '153.8710401088255843702321633066', '154.493816344065106693588065583625', '154.99313587536559607688655553887', '155.36612616393382885610016212947', '155.920105800981252052940066783050', '156.56522492608163038800587277902', '157.2953117620009822619819311984', '157.968182029929814209769237746851', '158.26091112516539366917496295825', '159.11492040803015075349031640527', '159.70812865463861932048177943944', '160.77954052876271443002858037026', '161.142227878507738209693492269715', '161.74279671189221658040158621511', '162.477914069513767723409065099865', '162.8844235447241075788877634352', '163.00444166248610294516387174351', '164.50780632575746664074800096630', '164.85907248697105165426630823571', '165.504942408995906630592787527279', '165.84225722796349585324996875567', '166.30543783504520516254156082652', '167.02564357091381355910313684248', '167.72100225375891223539813226930', '168.21930214877480298562351901668', '168.680126921671890169122930307007', '169.900088521187691014698405664858', '170.47860778744275932836662525751', '170.94142808424387797006285189869', '171.69401532099621741955008087756', '172.21465854264138269637119395963', '172.80486390345818101293804356117', '173.1980511187853130595599834583', '173.87994346192775580258790733918', '174.46850796462213606728339504072', '174.748864209425304470632547390375', '175.691659320339106899510021289', '176.40497906561102728364287708108', '176.9128719002580170498023110032', '177.64580719271482138694850409464', '178.11316631771809152322045181889', '178.70835304043257636647172128596', '179.29091859497540474353599450186', '180.248593432693503171290868690615', '180.805500634317147077147402140841', '181.313453646360585394418303232329', '181.84309447273981159851278031439', '182.52253400016484634333990348769', '183.07396823780412739862672256261', '183.59626899974071140548280567238', '184.37419259675680796946322940917', '184.78401592778697938445002974774', '185.28905657482845464031529996422', '185.49708772431997021531163081188', '186.635688803664542927096389497235', '187.28783147071998971426540443344', '188.2655037308494215048788737582', '188.78068512713895524618679981234', '189.254474602585425933660442247829', '189.78762808025833181411820098011', '190.291157088226606788117568640695', '190.86311196493665601289643316862', '191.48853155061262994646184071652', '192.14640212994077811771310433363', '192.5560109104539839743845208268', '193.60470365165288057215175879348', '193.98114268457250290489920311590', '194.43486720471233220503326633718', '194.719615518339285989200645292418', '195.7417324483464254507706854953', '196.4756134023287346810548574165', '196.97350663043001260970999392485', '197.62962868612679316595689671181', '198.04796216072075464789076780203', '199.01983199444097332621886328290', '199.73438795028866897973985155315'], 'prelabel': '1-1063-1063.719-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9365512463040915, 'root_angle': 0.4957680080793412, 'root_number': '-0.999646496423716133173280794654+0.0265872561162164338485958196082*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.495768008079', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(3)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.514850346315208062480410607449-0.573068657238036032700229802237*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.556153153271', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.37994751542', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.36847263576', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.9365512463040915, 'bad_primes': [1063], 'central_character': '1063.719', 'conductor': 1063, 'conductor_radical': 1063, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1063/719'], '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': '1-1063-1063.719-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': '1-1063-1063.719-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.9365512463040915, 'root_angle': 0.4957680080793412, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.556153153271', 'prec': 47}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1063.719', 'Lhash_array': ['dirichlet_L_1063.719'], 'factors': ['1-1063-1063.719-r0-0-0'], 'label': '1-1063-1063.719-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1063/719'}