Formats: - HTML - YAML - JSON - 2026-08-09T10:35:08.771871
  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_648.59', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9730448705798238, -0.23061587074244017], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5971585917027862, -0.8021231927550437], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.0092993486406883, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '648.59', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 648, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_648.11', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^52', 0, 'a^35', 0, 0, 0, 'a^47', 0, 'a^31', 0, 0, 0, 'a^3', 0, 'a^24', 0, 0, 0, 'a^46', 0, 'a^50', 0, 0, 0, 'a^32', 0, 'a^37', 0, 0, 0, 'a^33', 0, 'a^75', 0, 0, 0, 'a^13', 0, 'a^38', 0, 0, 0, 'a^44', 0, 'a^16', 0, 0, 0, 'a^36', 0, 'a^45', 0, 0, 0, 'a^7', 0, 'a^53', 0, 0, 0, 'a^29', 0, 'a^22', 0, 0, 0, 'a^66', 0, 'a^42', 0, 0, 0, 'a^28', 0, 'a^41', 0, 0, 0, 'a^41', 0, 'a^55', 0, 0, 0, 'a^15', 0, 'a^12', 0, 0, 0, 'a^76', 0, 'a^2', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^52'], [1, 'a^35'], [1, 'a^47'], [1, 'a^31'], [1, 'a^3'], [1, 'a^24'], [1, 'a^46'], [1, 'a^32'], [1, 'a^37'], [1, 'a^75'], [1, 'a^13'], [1, 'a^38'], [1, 'a^44'], [1, 'a^36'], [1, 'a^7'], [1, 'a^53'], [1, 'a^22'], [1, 'a^66'], [1, 'a^42'], [1, 'a^41'], [1, 'a^41'], [1, 'a^15'], [1, 'a^2'], [1, 'a^80']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-648-648.59-r0-0-0', 'leading_term': '1.03593375300836807997151621782-0.958539122365918688832892300708*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/648/59', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 14}, 'plot_values': [1.41136670986956, 0.9590641188633129, 0.20648527867125058, -0.8590075162692323, -1.6513494939024551, -1.5326857788221169, -0.3752630306929634, 1.2021862945091155, 2.150231768228608, 1.727611726384341, 0.14523613575539676, -1.4520526241099638, -1.785797999166926, -0.47967191910329776, 1.5330017912469045, 2.6813954108467364, 2.0522963498116504, 0.21332458482870692, -1.2375474791672567, -1.098070800872771, 0.2978536435309926, 1.3456084374996349, 0.7009411268521898, -1.3304660479808603, -2.9472024591360633, -2.5276948962536965, -0.2588307990184132, 1.9346739098889745, 2.1977383383822318, 0.5394887166938789, -1.2270974481161865, -1.3980088331335665, -0.17763990783745134, 0.5741148483310511, -0.5495214190064033, -2.788865354446858, -3.8460619355931733, -2.3084350753977985, 0.7237986929107307, 2.661833681430311, 2.0953826698901206, 0.21229626198372145, -0.619855636208501, 0.46182774043648406, 1.9170149449752785, 1.7449923220258483, 0.021496511269539102, -1.0041073264529283, 0.4992458351274619, 3.631786390362052, 5.523427409570565, 4.430153113547497, 1.619750123646496, -0.17461606789936684, 0.07742621302098104, 0.6848802071242022, -0.42587875293571154, -2.904696877929713, -4.227684369098239, -2.796364646287802, -0.07846293721850386, 0.9692538085802557, -0.6078596968476218, -2.6323691416723523, -2.483300571631128, -0.32096646436680126, 1.1653945133473622, 0.17852676950176696, -1.9207545441987077, -2.3981065676275612, -0.7062976264741879, 0.7879215375017359, -0.08154263604808636, -2.3280975254049414, -2.9348439448323203, -0.7272076830195136, 1.9911588741969435, 2.2466536897683715, 0.099601037322775, -1.5369601073423886, -0.7193348033004618, 1.0806967124255467, 1.1116099806161581, -0.8297343248131615, -2.0631104967679654, -0.7018490819859993, 1.6113839454786894, 1.7284792597809742, -0.7858216916389212, -2.895815163388607, -1.9403699753621229, 0.9532344377793189, 2.4084380047649727, 1.1823896482977496, -0.5209835809641953, -0.47419593405166194, 0.287733929221147, -0.9963225550392009, -4.530146052545815, -7.010764027602725, -5.639510900610613, -1.804095227347071, 0.6137000714398324, 0.09219264858935475, -1.0380288149656631, -0.31573608778105733, 1.2804725547154738, 0.9510034639007072, -1.5227746892430827, -3.0489345064815394, -1.4377121397116004, 1.3380010478263413, 1.6112571186970055, -1.0335349346302614, -3.2056005231905362, -2.338506138511992, -0.026990645370775654, 0.5356496754773655, -0.7892143057949342, -1.0811809509496104, 1.052292835033561, 3.0950083904617083, 2.0994910834679725, -0.9143090049116982, -2.1173272889765555, -0.1257850026469387, 2.119069495811306, 1.5655422136601376, -0.6888553832650353, -1.1953166034640454, 0.7070149421736629, 1.9769868550047447, 0.49302991433045085, -1.6837989327980716, -1.3195234357490524, 1.128915970082799, 2.0840114223174684, 0.14430760884300084, -1.7111361843973087, -0.39761192199731865, 2.715051731694098, 3.677788248116348, 1.5503362007055623, -0.4819360317277864, 0.027504798555880484, 1.3136918078989928, 0.4847621663053122, -1.6667974880026537, -1.641134680747249, 1.2957167568328942, 3.476768403314495, 1.8265023251331596, -1.7189363189393578, -2.910708265978109, -1.0508175523659564, 0.558631360280992, -0.06772278736783488, -0.7848157226539794, 0.7853235435655853, 2.920916916094625, 2.0653702973258374, -1.5401389609818077, -3.6014039200144192, -1.6827784351491715, 1.3866231442626167, 1.6941152657432652, -0.2663860292076383, -0.917323560710076, 0.6267363422252008, 1.3854315814823737, -0.3745400618145821, -1.9912038382330493, -0.43695203718656034, 2.636702892158313, 2.9103083311585234, -0.2746570334168181, -2.8621220801908467, -1.979961320750703, 0.13787740731252318, 0.005438219983786361, -1.7095789408405895, -1.6616800022804008, 0.37562552668362936, 0.8225928282267432, -1.990453536097034, -4.747868057165828, -3.8378576924410726, -0.7126505119000239, 0.42167427319998096, -0.9759373566353341, -1.2408414158765935, 1.4142738144121807, 3.8589348743559184, 2.8546939346437465, 0.06981272703280236, -0.6368938072836439, 0.7448955526791949, 0.7129926574760478, -1.6161632933582388, -2.598226057966001, 0.26183044392921795, 3.9609376417903777, 4.085940325871864, 1.1758935843751628, -0.4653191938214899, 0.5431911564635193, 1.056946094632009, -0.8949665793583054, -2.6416978924772194, -1.3590387847532828, 0.9117424927096609, 0.21096576175501397, -2.884610283620832, -3.7754798048474174, -0.8445483896743905, 2.0104711101427974, 1.3116662116881257, -0.9852260274090434, -1.1115266725263857, 0.47845093308920206, 0.48220901762159474, -1.0750790620209005, -0.4756904085557164, 3.2967779209619033, 5.972070619154039, 4.004391699157419, -0.03205202739451551, -1.2468064381603559, 0.5195260928283598, 1.3622116736509142, 0.06189785408068838, -0.33118805491906395, 1.6150898037575725, 2.6131996049134822, -0.07171776260087148, -3.5935249108543035, -3.409186838684482, -0.19532391011879194, 1.3222670357493205, -0.2248237161935658, -1.1259264732220728, 0.9031357051253852, 2.867968869398816, 1.5724914493655362, -0.9987060446058226, -1.0438912826660456, 0.6162381881167291, -0.05341485275162311, -3.249810625518718, -4.4859874103199875, -1.662533183727242, 1.4815310842528686, 1.2857364317744029, -0.21360584191265708, 0.9081640930367987, 3.731999965566758, 4.055699493106665, 1.4692998957386012, -0.03884493950560018, 1.0869670698620508, 1.381085300710202, -1.4575262155883768, -4.073959274322251, -2.562610871661001, 1.0504070577351852, 1.774579865989904, -0.6476058897499695, -1.8363967768200447, -0.18362735312594305, 0.8971307965741199, -0.7007264736156553, -2.036422799373229, -0.48703405883753925, 1.147923127943462, -0.9765954250125286, -4.908533039594159, -5.3213908862693, -1.6835030804183837, 1.0679401860680464, 0.2805922560721457, -1.0457379080217533, -0.27750665068852054, 0.3094541923116313, -1.7357950697027642, -3.6699240034110954, -1.531013140652627, 2.850786611630145, 3.98803192588327, 1.0708643484408173, -1.0831051981426698, 0.09798914246864224, 1.3656658109936632, -0.10724407569328966, -1.7934878895460664, -0.6096305545317724, 1.235803083379623, -0.12990935006502918, -3.2518187248316437, -3.329299027278644, -0.21045043898007923, 1.1745565342831177, -1.114508560853658, -2.9833133738032145, -1.2912407267562642, 1.1185907181303083, 0.7102322623928152, -0.6079993771323793, 0.8134105393707827, 3.4917428881855033, 3.069254125845653, 0.00022988561014956427, -0.8041928215350806, 1.8904827959730253, 3.597359112489726, 1.726540330649747, -0.16501799967258313, 1.2958965701198315, 3.4200092604326695, 2.1590707612960065, -0.8812019326428582, -1.2736112501216992, 0.6849645628436032, 0.9994335647026403, -0.3966373603008852, 0.7953523128273895, 5.296241867844099, 7.843929083359129, 5.114246313246078, 0.8849935896142137, -0.16007297838446183, 0.6424875340091764, -0.3520872392176197, -2.081246765459272, -1.0810522784473413, 1.3626192660122114, 0.6340504822104227, -3.0930523199317146, -4.393628031736469, -1.2735352728757277, 1.5930972413764741, 0.5996552734798583, -1.2798009097428173, -0.2569749034493681, 1.7558874283172812, 1.153546291522267, -0.5371047074795272, 0.43464393033240556, 2.643454186440059, 1.338888879931515, -3.063074234220504, -4.7908997179097375, -1.7609586662746406, 1.3404250040341903, 0.9555576353614301, -0.21275934838403043, 0.840149242072021, 1.7042059801499385, -0.5740579611028261, -3.1799365209656596, -1.7737791853802092, 1.8027259803689306, 2.2262136332612634, -0.4702876649278631, -1.219517828157383, 1.2247291650549033, 2.4155531326174198, 0.3491887509891443, -1.0200688775412803, 0.9779508633969449, 2.884835466454837, 1.3865347858958472, -0.6691315173916682, 0.5436954161528689, 2.7580127892216364, 1.56850801180462, -1.4775964893192794, -1.258439617402427, 1.9944512320719197, 2.956066413585444, 0.2469243319156581, -1.5877107183680286, -0.2705662148296056, 0.692431944331239, -0.8672655469960604, -1.4540407538484732, 1.467074576258231, 4.053311780777011, 2.3005836601196257, -0.7743213785971844, 0.010578691184584498, 3.285708751609176, 3.6806475161036127, 0.9315420078219173, -0.4015466121853055, 0.6264903461341991, 0.3344573559833785, -1.7547059480259766, -1.298610615762936, 2.704048567007347, 4.934078144356201, 2.2229924656759006, -1.027311368639414, -0.15061221000635233, 2.371711365844291, 1.9598904870895713, -0.14020664792526172, -0.06248010481012327, 1.0541008472379754, -0.48679603844811925, -3.069664088107075, -1.7002738809811984, 2.9173538733991418, 4.599437104836113, 1.5516263845797171, -1.1038717124328756, -0.2625111922463281, 0.7254737807141944, -0.6604878457993055, -1.159485322329742, 1.7286810922334426, 4.18515058636828, 2.3370718184621877, -0.8033661452884797, -0.5941749628878088, 1.0729108939514735, -0.4919710010411654, -3.89891813751197, -3.84992625991843, -0.5063889766914571, 0.8499643550801317, -0.9329144649363326, -1.535732579740414, 0.2678298624440097, 0.32001923889246836, -2.6871734540761345, -4.029371102693489, -1.2320322246971969, 1.211677506486704, -0.3548696879685974, -2.351042706475086, -0.5571101280147404, 2.2630789789379415, 1.4440024937624056, -1.2668084185270412, -1.2308313993837834, 0.6328782998331941, 0.18041016160874818, -1.5729494059113982, -0.17151966853176154, 3.3522010582395216, 3.303036602782208, -0.7444358434252212, -2.731718301303366, -0.15974257775496062, 2.2532401336104497, 1.2143269185726657, -0.24513569756586034, 0.2198214753110222, -0.467518991202406, -4.008777214332278, -5.715070670948686, -1.9456195183845788, 2.8721977535490377, 2.8899220066233724, -0.05981846484273019, -0.6669454767356127, 0.505610503530489, -0.6979583229757037, -3.339903931537502, -2.997421346712885, -0.39585627856538314, -0.2976976699433689, -2.365259974496628, -1.3658538912486868, 3.016446653288158, 4.803929757517351, 1.791210381209358, -0.9405266880227054, -0.13453461834522484, 0.6893356816465555, -1.1026020935722685, -2.0433534985500694, 0.3547000352341423, 2.0596099189207795, -0.38339171811946754, -3.152426920388991, -1.740374497422424, 0.9821432471598789, 0.11208471287458631, -2.3793195972007664, -1.5669786193483657, 1.1784706292389542, 0.8589706142905809, -1.7590501290736746, -1.679730341050872, 0.9412030368193512, 1.3548632232243545, -0.49311281529963047, 0.18140823514224932, 3.4989154550152404, 3.9238161526992963, 0.26221835986885145, -1.7765167218103477, 0.5056059675672515, 2.3954598714203406, 0.5901710941386568, -1.3354015114431794, -0.4074167858852038, 0.21555252216336243, -1.8075071785471784, -2.4771833432116472, 1.1861085782331617, 4.48018971291185, 2.3770137971366814, -1.814941030829605, -2.206288840874993, -0.037915511190041065, -0.11857567791805242, -1.6463716163383901, -0.7154282885477232, 1.220211021529652, -0.04907985362242419, -2.658980376670943, -1.2243787604577556, 3.076842013135163, 3.8361956279531033, 0.40693255385741006, -1.3034663486866047, 0.6014050728284521, 1.5541072867756358, -0.15617768533318058, -0.5119139692692758, 1.6389998828868837, 1.8435079555059128, -1.0544287328667121, -1.6959796277848151, 2.2128640988670623, 5.096221367142982, 2.882765796829463, -0.3574048892883446, -0.3196942294205607, 0.24166585978265545, -1.951079980840735, -3.679352472576195, -1.489351920078962, 1.0560921785737236, -0.38914107274005183, -2.799637483468649, -1.3992264705132265, 1.4053298659351756, 0.7418927170039222, -1.3264114928943604, 0.30257051015045966, 3.88153350549182, 3.719107469406504, 0.444114475349107, -0.5800285676519156, 0.8075992082988328, 0.3090457564052764, -1.4954125779762688, 0.006826209672083327, 3.739963805325533, 3.6058049687153337, -0.6619498564428897, -2.6450458964514576, -0.3413320747741435, 1.1220568095878194, -0.4422416039534358, -0.7891113629837794, 1.6884994814852354, 2.5062627623085523, -0.05129116036055928, -1.4050597527646371, 0.211260718665622, -0.21872648226851069, -4.861377807665349, -7.82239787904136, -4.849918628563827, -0.46556546845858693, 0.2422907686669311, -0.4899806750085492, 0.5874970994526912, 0.8822463685466226, -1.8225936437858998, -3.148759695851853, 0.4716476299320503, 4.290578565738142, 2.8032873885392857, -0.8055909210641571, -0.6602129645128152, 1.6629783295551235, 1.3053202744482058, -0.41856735331807127, 0.47822116788260566, 1.926586004788705, -0.3240131034564011, -3.660709320286445, -2.6716401270823873, 0.7603838963865959, 0.7669821980938534, -1.7121961909562287, -1.0516982961525347, 2.2134862597713707, 2.522831435674399, -0.10676557775361911, -0.4976016714268618, 1.4886237635603048, 1.0612125552556546, -1.5320120067937952, -1.1301831146101609, 2.0336438989878536, 2.1505329521181293, -1.2784555402503974, -2.3351271058280996, 0.2923780275127113, 1.1466760188690606, -1.355736645745908, -2.0565681154605198, 0.7829328853683921, 2.185174722881217, 0.14945264619896861, -0.8993318225115838, 0.5222951394495201, -0.268058797098818, -4.324966225137005, -5.59432886431444, -1.5350086617789718, 1.9401185512326857, 0.794823321331358, -0.77129947924751, 0.7948348690731478, 2.005772914378507, 0.1813182981729733, -0.9556788581600788, 0.7195079674811092, 0.584798684877982, -3.72907336148152, -6.4193114737136385, -3.1834819053997476, 1.0207283783846866, 0.6878250557714085], 'positive_zeros': ['0.689139477137518677085423388229', '1.94959786327593270887244059059', '3.149827925159435046636241636010', '4.13802185675961459910000776867', '5.34750771862690839408475958403', '6.19005152567025106031685066484', '6.99601422497312673939979606369', '8.155934236647265508219326073754', '9.14387644486945866341314487525', '10.04270827662264178308320976070', '10.52828038338774611249908585774', '11.800256077960570403859167058440', '12.853410992398992867574510981247', '13.34531641853496602831651176719', '14.37869142045981117220810182340', '14.93809662647928464967132672035', '16.50259275213783523346519992131', '16.846147038578454099531882159102', '17.43060916996303509955225980570', '18.760746605268924276508679690363', '19.28967006634846442508905783791', '20.35680286138019690608018436233', '20.96460478879828615150306918259', '21.98506872450967342389139886441', '22.48708331619730400494947421241', '23.51113990283655050372739894857', '24.38781277517840193727885791747', '25.11635860054787703930644129010', '25.81881782873898529313359857184', '26.6505699849578057794998474634', '27.41721665876330149654230256247', '28.334858700995833067983076582273', '29.25376724084168497672952878195', '29.84327008683636723660360436726', '30.15972913951675004622988187537', '31.74809314507289261250464474530', '32.20781137844793962147144387043', '32.87047782642788004575358190577', '33.57347016901901911840660915105', '34.52508225744772003008974335823', '35.208503906202997344488587096434', '36.25465426269233641005592477266', '36.70877753317719004698177375172', '37.375162094185384827278225862164', '38.34122413769377135490939681459', '39.07640189336085970356999756146', '39.89940025096038377920403780528', '40.52711797138474397637578759795', '41.31117363229636168863321772067', '42.04894874252337317597427259992', '42.82974676637843381273344588399', '43.47940421950006459860240654233', '44.575388834002217310349878346262', '44.99417572158536740495678237745', '45.695183388224200454092089297632', '46.44273382086760365483297667312', '47.34393327945735457701942456253', '48.27987431619080334738330740396', '48.73311901809582169679492042693', '49.26734357643178485451588083921', '50.18682218908213260978982511987', '51.092595424382251419872930267123', '51.83231563485415000389873265445', '52.39316722587940031568726277422', '53.0758320412825029777643184359', '53.79364779138025613942018170775', '54.66448671308618003583516634576', '55.59528927540695170070563019376', '55.93867250530536839768021278148', '56.81756952066730620631876094189', '57.31194551820294616921471883703', '58.53550383010381461661385135604', '58.87579159899461773307308530730', '59.54991211224257893385739674534', '60.63503619375257801649063120349', '61.09473115098693069204471151035', '61.67653809121570224094045869721', '62.48016421070229912957479796841', '63.58939862515764626301163145598', '63.944378653489735323259435269623', '64.57515494038421762117850153894', '65.47593253204343094308512978688', '65.96259391041992355684065658292', '66.945915012342443807538841987486', '67.66626318454271844171737834567', '68.337814601856222106349805895219', '68.85043640215304602162234577352', '69.42735086895285053819403043169', '70.6218904157322785630238075186', '71.17098547796799901611342689320', '71.88846744515368625210447447786', '72.26568521411333952953292896115', '73.11937634938935304928037874656', '74.082593710845425413270371246488', '74.65285464313471022220612665027', '75.207933321091698662958135112627', '76.11173758619525616885282154123', '76.74678418138938565424500471866', '77.180590353335397606435688504388', '78.26256090863725250756853931196', '78.98954030621607003561680153976', '79.2364560967030050953080372568', '80.57057835985853475133125985598', '80.66866427965934501769326568955', '81.432323873620994780279843485542', '82.39956439550667183698841412643', '83.04983807824272432031425909678', '83.77787161288673645467341087522', '84.27428046457735201544760851935', '85.06279616133983054444613266524', '85.53873052044351564408742325339', '86.70645832102627472732025584392', '87.235449887955219860698555048874', '87.87930651553743182046447184231', '88.209842951138494272092458315665', '89.16949075638059203026880280197', '90.10559102224921094772721821809', '90.6099016077095318346153288963', '91.23561278819022274752562010295', '91.95584373511141259053767758293', '92.48637145896045846779294297456', '93.45912390114083056850939812859', '93.94462393488822426047278799555', '94.82756617740341240038704565005', '95.44353419282042297451536487942', '95.83403121352982982588196810372', '96.875026406137551033990594327990', '97.30858430427186577434924984301', '98.36795146184850886009670427477', '98.55403799690852306529939362673', '99.58498777681248700740249354475', '100.20414914688288226026110991719', '100.83435369204436080042568329911', '101.15971436775275650133000081160', '102.62762461945374555238582931452', '102.877235887180156454824580422604', '103.379135766457249309965733464230', '104.18803279895725199554862927943', '104.74888771063390394150467413197', '105.72836730680472079735015289430', '106.32834923119932134677101240848', '106.90940514253525615655721989926', '107.682940898916873781357200009952', '108.06287755249527270660293416020', '108.85194602149941808760290974892', '109.83010429947991300621372354221', '110.51499792207523147349636259827', '110.76249312819092665227323915866', '111.507924949377385608213939851258', '112.334900651462057205883909961018', '113.07087296276369164678641978961', '113.61414809455227500528329085720', '114.418205199367709040334497873349', '114.88881799413081626516661153200', '115.7943086586400153200231904427', '116.179489368880178789974564632507', '117.02433143293490863377984968023', '117.62933024871552541182326396191', '118.46231951347620742861142563823', '119.10747828537722452140571865827', '119.54960886095250550151781939711', '120.18708621293742118870527154870', '121.145669486225847102179695555072', '121.5613618170734967420265684518', '122.6285249567651307710247702637', '122.96373167996614372049666094367', '123.493089107346506883944393333758', '124.18061864111968962422094008296', '125.17868162304096628023271951573', '125.642461028955201655780001917613', '126.53347155947287679286090891794', '126.889751463223266107207080197380', '127.44478527328882732035902637552', '128.2451311099862661951040277272', '129.19889339507881799087588720240', '129.73489070416022533809554664279', '130.1990870075185377296368270777', '130.7839964743233942054853776303', '131.77192127757451716837809553413', '132.28003920230551663450866598196', '132.76386321888381303258354815766', '133.80384330650056499932835208639', '134.23749728533092883080478855498', '134.954526720060002933913956980233', '135.35870588694756719753210630548', '136.36108881482829592788547196219', '136.83501449109304294126031790096', '137.5516499763944066730432919448', '138.27900596786399546144978571705', '138.941193491013819851382889045587', '139.40421460134011024740144812802', '140.015865501260961606273136663215', '140.88311370095256051418894619562', '141.57666865886851209155891631459', '142.40204098819109771910030229737', '142.72079224222678962473257218967', '143.05111742351689280249791390555', '144.17081867825958425629256469995', '144.992204063408744965724245149438', '145.47056331157024297866600603702', '145.843450867864555556785729045645', '146.95524372311437291668847811411', '147.120992239215037072583258179426', '147.91940649895708153057377404919', '148.90789627661252525330651882992', '149.3999216274518434687194352625', '149.84525872392935689479841594123', '150.58917323332176618292620876351', '151.21738771193240106595019067603', '152.04626685283343405989714805618', '152.51313355030608997556120661993', '153.28961449031273621423913694979', '153.85270368945832680387408269921', '154.57341440380039833129457327008', '155.22035418236546464453161453413', '155.60298239279615424716730922603', '156.58364662735859570861009043375', '157.1376299895916598414260165089', '157.87970484780154017373164068998', '158.52366030941749037571953822018', '158.80707824112968466608105116883', '159.60835283544818368278390403550', '160.47438649794739168832790883276', '161.25778060814770790609707649380', '161.53685548410384442367775950860', '162.28252954686663298462776522196', '162.80717321194582156725621534739', '163.52772857331391442753929745285', '164.41202883166987868888306237283', '164.92166425240450082925910839594', '165.59882319896415762889955207841', '166.02853549498947617518389312245', '166.7691811486553172179866789803', '167.34997751013216473673368392261', '168.383920942164569808625255674951', '168.83300640528057073737496992215', '169.12790073800614302988545364540', '170.14118796408717684522318556623', '170.58295589771515830705514966057', '171.38421175304139651815391345897', '171.96721440274881312918641138631', '172.47287262111085084257429365815', '173.49080111675867558114791605880', '173.88835312785081535233927717095', '174.42311942312694641647713980919', '174.99939579031199521699402107081', '175.890407275347014870198980984047', '176.600759820246093985625549049799', '177.11599985693983759611906608593', '177.61986900466526746521973831371', '178.43194052451900700242754499357', '179.02463516093344281836334298323', '179.35021545604616037526911946899', '180.68681668928023671990797583507', '181.013785967334013122824548939343', '181.4392123261226726322222089205', '182.004949217919926576364568649582', '182.78314110031429906359725703', '183.66147595777685616503644334290', '184.147261900526655786821807272035', '184.89388537566622536834913401365', '185.23447806326155809497440894590', '185.91082681954795607998284047928', '186.79232418588247603515675796641', '187.28285594071246912744112895040', '187.91455242664063096496177235150', '188.73555832525190336870311088681', '189.147784726391756564274149808377', '189.81222491332307738518426414479', '190.42721396141848396658585060268', '191.13869358286288712235917460233', '191.84259397245738931020813898312', '192.35015360079214235851322921156', '193.04943321694891013152645000684', '193.76974177638901854691256428087', '194.267248841639875422690792023931', '194.65793641314413846219350935566', '195.72505348114766261555715824226', '196.35509555781731724307090852825', '196.76502626389382548631463067483', '197.52433409804418109643607418112', '198.01292877973683727866915856591', '198.49702376587151435439596165737', '199.58340069694291543541141695534'], 'prelabel': '1-648-648.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0092993486406883, 'root_angle': -0.23765432098765432, 'root_number': '0.0774924206719309462623706995201-0.996992941167792064800001681034*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.237654320988', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.09144664380697952271461973079-0.331800315199473501079919350249*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.689139477138', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.94959786328', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.14982792516', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.0092993486406883, 'bad_primes': [2, 3], 'central_character': '648.59', 'conductor': 648, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/648/59'], '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': '1-648-648.59-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-648-648.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0092993486406883, 'root_angle': -0.23765432098765432, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.689139477138', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_648.59', 'Lhash_array': ['dirichlet_L_648.59'], 'factors': ['1-648-648.59-r0-0-0'], 'label': '1-648-648.59-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/648/59'}