-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_363.149', 'a10': [0.6548607339452851, 0.7557495743542583], 'a2': [-0.8707460771197771, -0.49173292464560375], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5163974616389619, 0.8563490302515889], 'a5': [-0.9418443636395247, -0.33604939321543015], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8973984286913584, -0.4412211012432213], 'a8': [-0.028556050793696254, -0.9995921928281892], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.685764912895941, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '363.149', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 363, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_363.134', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^64', 0, 'a^18', 'a^61', 0, 'a^63', 'a^82', 0, 'a^15', 0, 0, 'a^29', 'a^17', 0, 'a^36', 'a^56', 0, 'a^87', 'a^79', 0, 0, 'a^25', 0, 'a^12', 'a^93', 0, 'a^81', 'a^98', 0, 'a^4', 'a^100', 0, 'a^10', 'a^14', 0, 'a^48', 'a^41', 0, 'a^33', 'a^42', 0, 'a^5', 0, 0, 'a^89', 'a^57', 0, 'a^16', 'a^76', 0, 'a^47', 'a^19', 0, 0, 'a^35', 0, 'a^52', 'a^13', 0, 'a^101', 'a^68', 0, 'a^54', 'a^90', 0, 'a^20', 'a^74', 0, 'a^78', 'a^21', 0, 'a^3', 'a^2', 0, 'a^105', 0, 0, 'a^39', 'a^97', 0, 'a^106', 'a^96', 0, 'a^7', 'a^69', 0, 0, 'a^45', 0, 'a^92', 'a^43', 0, 'a^11', 'a^38', 0, 'a^104', 'a^80', 0, 'a^30'], 'euler_factors': [[1, 'a^64'], [0], [1, 'a^61'], [1, 'a^63'], [0], [1, 'a^29'], [1, 'a^56'], [1, 'a^87'], [1, 'a^25'], [1, 'a^98'], [1, 'a^4'], [1, 'a^48'], [1, 'a^42'], [1, 'a^5'], [1, 'a^57'], [1, 'a^19'], [1, 'a^13'], [1, 'a^101'], [1, 'a^20'], [1, 'a^21'], [1, 'a^3'], [1, 'a^39'], [1, 'a^96'], [1, 'a^45'], [1, 'a^104'], [1, 'a^24']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-363-363.149-r0-0-0', 'leading_term': '0.441578665298340246105002034340+0.114233985502758405284939245859*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/363/149', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4561152497894668, 0.6084830929032413, 0.579559099054262, 0.12827115109811302, -0.7265953903925727, -1.630611898960963, -2.0585252056205174, -1.6368807817198192, -0.450543486137575, 0.8936484646838103, 1.5687445874126535, 1.07684870427999, -0.30018000827426183, -1.51739079264076, -1.3567937759242426, 0.7199607787010773, 4.040730746981751, 6.972698019087224, 7.898796080432407, 6.301720425619454, 3.1668715182952742, 0.3448937463876363, -0.7176354872554274, 0.05146814712634438, 1.4267956350276336, 1.9504959554367012, 1.1203621682425653, -0.2823892886832554, -0.9880922869063646, -0.4407978752138603, 0.6830698657733576, 1.1258283912746603, 0.27352236085380566, -1.2117293805388067, -1.998370786596271, -1.3934455711447775, -0.0788165970367822, 0.5165825560927145, -0.3238098432310628, -1.7543130942113743, -2.0929370377667493, -0.5655796908707174, 1.6191224040502041, 2.0862122285850058, -0.5455170184559824, -5.129615772693813, -8.657088473364894, -8.699055550102916, -5.462888889039384, -1.5509119456441816, 0.3721931372801717, -0.1822932246616563, -1.4541090573846844, -1.4620708381194785, -0.023428564624179565, 1.2440675764387046, 0.8127358265705977, -1.047527279483833, -2.5556277016957765, -2.329430022721318, -0.80220766377058, 0.38959480956469905, 0.3059961078771092, -0.29702819520462925, -0.02419994899924746, 1.2842411938000327, 2.132121152379956, 1.0665816432317956, -1.3657151007098645, -2.796455292390596, -1.4643161317238769, 1.651245665415794, 3.506808594942978, 2.0529406490386912, -1.492886850901796, -3.7166471668031758, -2.468876051996388, 0.8949356473666005, 2.909958794632808, 1.5767247102180777, -1.6833251508600737, -3.699778635206102, -2.908162347227801, -0.7163712402268645, 0.4173481537575443, -0.2087424785685008, -1.0628890621167408, -0.5501749537412816, 0.9615871989069518, 1.7114610765552287, 0.879635118896161, -0.32534368970235394, -0.2396568282527005, 1.011407999148517, 1.533044927295427, 0.08056463773675124, -2.1231896379440367, -2.640966549947988, -0.8382312550609543, 1.063696373578245, 0.4873124701162715, -2.226555905082295, -3.815635530188945, -1.733136159645964, 2.6522352201992945, 5.171589930153776, 3.2751687995691228, -1.1799197321039263, -3.9460346925180647, -2.8917793541193637, 0.08456966522851013, 1.6466174317950708, 0.7849341105538434, -0.6312190461680766, -0.7190483240920262, 0.03824956882192727, -0.17604536940747947, -1.7136349035436975, -2.7659028147803446, -1.7350451443212704, 0.508792740582167, 1.5713910987286346, 0.528453495620231, -0.9716410723607474, -0.9980843641324612, 0.03270075486137798, 0.029763389594101974, -1.5418521405983174, -2.2966459535812325, 0.27114138986200953, 5.059743278251786, 7.696382794035865, 5.1838122070755865, -0.46441358369069946, -4.136529382932078, -3.076110458258039, 0.44826143999931595, 2.233311065637791, 1.0408848479227983, -0.5705126166821856, -0.043626616404290476, 1.882002909412196, 2.45201486296483, 0.7095886465499789, -1.3152574787915137, -1.4297606693327436, -0.12570131226369424, 0.35564475155488057, -0.7427912214718096, -1.7279997985180373, -1.0371818807120277, 0.385123249858625, 0.3909349195339511, -1.1699718326696527, -2.021554086633032, -0.72214485092658, 0.8621558366737937, -0.2832086812662072, -3.9662006158183303, -6.1779659120484265, -3.677808944539547, 1.7491564271376188, 4.9842300532901, 3.4459114352782976, -0.0817784242308475, -1.1413930080071524, 0.9490479892763485, 2.7238933838574306, 1.3969642149627166, -1.594017866042969, -2.7493592083117857, -1.1328917930144153, 0.7381993611533401, 0.5474143770332375, -0.8917423605561052, -1.2571923895437482, -0.17075677160787406, 0.566876837340886, 0.05531843367153189, -0.12303552210713645, 1.6407811086361015, 4.0829107478136715, 4.285966954214382, 1.68152389973912, -0.8611892076107709, -0.7725615960462497, 0.6872321109190875, 0.2679566921111914, -2.3097213692124963, -3.2899790614982503, 0.23847239245249402, 5.810372208208807, 7.818440205244711, 4.140190279280167, -1.2542098984783663, -3.0859768992438794, -0.7880827963043715, 1.7174149560761993, 1.5328869851617095, 0.0007896230329422308, -0.12821098147471274, 1.1195250043166873, 1.3675819128933735, -0.20051313374163607, -1.506087016891307, -0.7370060868517689, 0.8595005673293301, 0.8054124842675646, -0.8902733411705721, -1.748701190426533, -0.6147518771244769, 0.5062443242256345, -0.49632524206237527, -2.397970925912554, -2.243935666750154, 0.0025705448774395586, 0.7785588335664051, -2.0846155268841757, -5.498342518426295, -4.416194438689459, 1.4586142077427933, 6.584023657850513, 6.0195924261377804, 1.2009631526960833, -2.3144494836780307, -1.7954203001714286, 0.22220817063600917, 0.47839990190106746, -0.5010740196599025, -0.042038437068942544, 2.0500993755397268, 3.0133287254975807, 1.3158875700688513, -0.9728312775525427, -1.173055190056513, 0.23442896154573611, 0.6653184983077343, -0.5098013375634108, -1.2103600069362241, -0.22186222578591794, 0.7244523167244782, -0.08634191744437603, -0.9323172606507848, 1.3312097763659039, 6.114488778788261, 8.631613645823382, 5.817055506320012, 0.7429831897862587, -1.0447233640004003, 1.296073078653535, 3.033430299292406, 0.5470236937441662, -3.703969265840835, -4.7153861701888236, -1.7994734704599917, 0.8031374082102712, -0.01197586403815563, -2.3088316702785647, -2.4984893889642743, -0.5038477157871579, 0.75164784679565, 0.06699169321212468, -0.5505966294666417, 0.47887898089615627, 1.6683075323209517, 1.0252927892246189, -0.4565394081705513, -0.19739527458539433, 1.7314126048707725, 2.408630938386324, 0.6127699584571034, -0.9372096168171604, 0.4005841420653006, 2.7693196142465197, 2.1451911827906898, -1.4445696842207538, -3.182232695450552, -0.04790738688351082, 4.464959277858616, 4.675506778840967, 0.39501636579267324, -2.8095751646442935, -1.1592174699122968, 2.5549970246145466, 3.2995758612665296, 0.6114874054521533, -1.5997495034599876, -1.0482701927292841, 0.3093435416600742, 0.17191657501541974, -0.5032513316317351, 0.28586800221003206, 1.7021138092878636, 1.1573919258793397, -1.3138042968220525, -2.63985039450375, -1.2583606024364427, 0.4779256894185517, -0.028525048111470996, -1.6122982892469764, -1.455139247492851, 0.024005954835687893, -0.3297719077092731, -2.74519981601565, -2.801195741515727, 2.473857600762548, 9.099471034781942, 10.061157535179856, 4.166594789535493, -2.321686537168492, -3.6360931002047066, -1.0553869691922992, 0.43522934302338345, -0.4370988021199491, -0.5345077977375805, 1.7650467372295506, 3.773806251414581, 2.843793406725562, 0.5470963666568776, 0.11527653143069452, 1.477336370030239, 1.7738703190864586, 0.1843641029797123, -0.887139730409119, -0.001723207447962502, 0.8719720507099771, -0.2127155089376006, -1.6617034738701961, -0.9103797073611146, 0.9000599206975991, 0.22970101206897112, -2.9033167349674884, -3.916292030683484, -0.27421388044185346, 3.888416906061063, 2.8493780479608875, -2.5911086737953237, -5.850947812809986, -3.434622199176476, 0.7078406160547954, 1.2706519984356268, -1.176011889922445, -2.1183847849678363, -0.37275729758296405, 0.582478840402878, -1.4191009687576635, -3.7577176575820688, -3.2236906812900776, -0.8284110497610191, 0.21311702335320223, -0.4789976042669084, -0.5908194058236866, 0.4055228475055031, 0.3808416714477778, -1.258046608152189, -1.8164985835125438, 0.37971217294911375, 2.5635286714108263, 1.2888983237037759, -2.0250071485931023, -2.8839698650539, -0.6499586396903648, 0.31058980186711904, -2.3691215833456036, -4.684766580173102, -1.9577794027044082, 3.557894233790303, 4.998618487780141, 0.32249920106087, -4.8463698750163, -4.995109286745881, -1.6345937517019073, 0.12651018325476313, -0.8702815720984729, -1.4764453697626463, -0.20559858819969704, 0.6994302613245001, -0.21620425448153302, -0.8238059354439975, 0.8527228696505281, 2.9218134420142685, 2.460753277989186, 0.25850575573049284, -0.549668336810911, 0.2769032286416426, -0.1357625478579869, -2.478166718205826, -3.538331097082409, -1.4649612467065432, 0.6588250212216946, -0.3998547546250865, -2.0957761488650926, 0.7051728210773177, 7.284066809284107, 10.578443358506854, 6.537836837050319, -0.07954453998811423, -2.1473958957524837, 0.5378953923433045, 2.342003335753345, 0.5786188476791526, -1.5101145985475177, -0.9117349054459476, 0.5786224277252743, 0.17009733903057903, -0.9976749672568248, -0.14602799054158105, 1.9567822655203637, 1.983064471065354, -0.4266469630097776, -1.9613161638594845, -0.9231760708012564, 0.4069148206639522, 0.08345903106615789, -0.23693775839070502, 1.1366722792724708, 1.978444969312123, -0.4493026409890969, -3.6919874178337686, -2.4696970696164655, 3.105588139727968, 6.37400344546417, 3.1109937989568865, -2.336153287979565, -3.231159605520098, 0.17388614642331326, 1.9783664182313703, -0.005913347932827238, -1.5087872411944583, 0.7617390812981839, 3.8320352741338937, 3.39118974950184, 0.4570470640736967, -0.7316124953773285, 0.5596816696260035, 1.2109491280232558, -0.04280331372454809, -0.8843963842147081, -0.057039349295698046, 0.29948587056551096, -1.2141453386282297, -2.2375592742956947, -0.5699458850752337, 1.5761627867860915, 0.8322222834781778, -1.5946352842594904, -1.7411052176203992, 0.18173362340976498, -0.4317246831229002, -4.78174837330412, -7.473217441521242, -4.158180016757729, 1.4059077875211603, 2.4053943972468943, -1.1074458385898747, -2.6201215408899055, 0.8350884565049922, 4.536493262478665, 3.6368052684795904, 0.12715307438623005, -1.1174651602096135, 0.1614354517992163, 0.4385867898233897, -1.1035765786169223, -1.701782194441415, -0.3821994543035648, 0.39090087929097644, -0.5203900151054892, -0.6514698875460259, 1.487466783612504, 3.1097093593691145, 1.4498772895708538, -1.3917489436340726, -1.6295259850021293, 0.10686514156943336, 0.2452556086099162, -1.114090415530397, -0.2612412366555257, 2.7237833570601047, 2.117781286997729, -4.876405987369232, -12.080029322688635, -11.533954456188372, -4.238795938818933, 1.4928309946248646, 1.4152915072163104, -0.4765803256687502, 0.19943013922483457, 1.8379555663369262, 1.1635151811056343, -0.5718436673725116, -0.09271369521652288, 1.838961130430134, 1.6651898925651112, -0.7540802968815228, -1.8644104167494668, -0.4247149618226534, 0.6918008311433931, -0.2543712921550468, -1.079798356860119, -0.159749221489241, 0.23908800871928956, -1.7827093741735487, -3.493917482232305, -1.7237797194959632, 1.0338955620202213, -0.12391672800057785, -4.06923082535272, -4.273019854127862, 1.118698011037298, 5.529901208692724, 3.261710326021585, -2.1698922610784313, -3.511967785361067, -0.27135665564609657, 1.8608637347419759, 0.5240642722468035, -0.5454047960071529, 1.1629474971681233, 2.661169400209886, 1.0051739812031737, -1.513736546403823, -1.3211585884433865, 0.6101536589793777, 0.9723694780840488, -0.11060788561710827, 0.03331712755617287, 1.2974729443506237, 1.0926622153290961, -0.3326191367569983, 0.2000151484071589, 2.7441046161282516, 3.0485260949626465, -0.43630255689768827, -3.0493860021695816, -0.9313376395232906, 2.426207192895814, 1.4993102494247599, -2.204590855039032, -2.465919002143791, 1.2395422654624129, 2.3426482582362382, -2.4384110731190543, -7.505793751282707, -6.577461647612352, -1.6283677147253144, 1.0025229951609442, 0.039593723868278995, -0.6488867151571147, 0.43561868827142536, 0.7090673216457375, -0.7308781254763619, -1.1719183451887205, 0.4944656257406835, 1.4275515368041984, -0.037925182377327886, -1.1230073238727973, 0.5610438858942602, 2.573698849274023, 1.7738900827097388, -0.1604259722744313, 0.14873797033038627, 1.466205969954736, 0.20370040818239998, -2.151466871677022, -0.20115705580878068, 5.991664843299491, 9.106739965965533, 5.017617158663624, -0.5223067030180242, -0.1570579851504102, 4.398080233082013, 5.735831451021088, 2.1611150615523957, -0.8880746891552258, -0.19977196930813704, 1.0912375869345285, 0.10467674627523996, -1.0309551479897998, 0.05671939240383809, 1.2943585871269536, 0.11071044913565001, -1.5679151093701982, -0.6336697233441085, 1.5278020292907406, 1.3451181188372527, -0.7354519848373732, -1.2744296053183521, -0.043556220048781076, 0.07900277771736301, -0.7493997081174102, 0.8856111716733248, 4.540657909682531, 4.644686222865309, -0.5982035770594254, -4.522896282451813, -1.0283999308468457, 5.875296309352385, 7.516731593142317, 2.9341580175335045, -0.9410142294150229, -0.5332030979856635, 0.21508436696811836, -1.815525392934902, -3.3585401387721623, -1.0255973788492658, 2.3181601347052565, 2.1544823817321266, -0.4730903599393779, -1.3610520371721004, -0.16057720383252555, 0.2276803082046454, -0.3689739160057437, 0.518585157179116, 2.516957244111422, 2.482201937006808, 0.4322401415920486, 0.013968632454366798, 1.8341029720247242, 1.7960703191393979, -1.6075952352615073, -3.7876409750019993, -1.5467850131032592, 0.9097860346055715, -1.2915482610668507, -4.875491429184614, -3.0348227165541055, 3.2519853594754045, 5.995350486613495, 2.3257973011554856, -1.5397447790536536, -0.45250290854003583, 2.3522709652963085, 1.8659673700143942, -0.4479775231490112, -0.23027482589836046, 1.9563553935201403, 2.2268740103601554, 0.4195295119218361, -0.2736570922362358, 0.4933818449015876], 'positive_zeros': ['0.9929081923985439259783134898', '2.599511979114639157013972797004', '3.68823667619404315372482630409', '4.604878908610535021997883309843', '6.61886607136212269356069306999', '7.17539695001792841633011234224', '8.370386415267240628404926843572', '9.18484430646020485333557207196', '10.05963011350934938859298336286', '11.27131652818685089911002705635', '11.79696090606520019860207593034', '12.88977864077107594657693583798', '13.70581916073717244060526633131', '15.51264367304075404019832446005', '15.89188272253947201230357359846', '16.87932698037390144495730366655', '17.650855344170909938310252615317', '18.92388440629146299756318816172', '19.51891928214248828086258251359', '20.008011365046168841321918205241', '21.08071563278330864314273228549', '22.02714988299144210305712825469', '22.99752087033643633974863606450', '23.9806533987389993530608886955', '24.84281918204419578867090087563', '26.0710303597080871584508972353', '26.50088539353035248827518394249', '27.30745914044647053759887142298', '28.33194494537670149345239623539', '28.82247192530113461583936140825', '29.698720021383505739416734106702', '30.73725973731686785633176191267', '31.31723825498136409876882386897', '32.31546556705123668841549152753', '33.35523263657926295996415025017', '34.365390776725248868168213785124', '35.153598378162027774826452128354', '35.916573509165176686538528892709', '36.18712529971359634954152092740', '37.42637111518780248739576691982', '38.22112102926074406515727470412', '39.05069668423407334829683939086', '39.3843320312089758455450675989', '40.29211083431387525855283413685', '41.53650385858034157676802152292', '42.45831066756570615393910366126', '43.29427114038391047327073433242', '43.758212347500259039393533845161', '44.78116611080919936018222478433', '45.65809850986052303294569229464', '46.076734973572990388973681205716', '47.088714076307371264207829514110', '47.59609360874527194621834084337', '48.55074333371724357614855194577', '49.02960774947187372146251085813', '50.21251861719856257135923050393', '51.24116773511768926686475628995', '51.76166942771269101638324422218', '52.64438098277935708324310596475', '53.5978811887344574847783270150', '54.18412134660987425149739194802', '55.04389658133963404007241217638', '55.64872166583229004745762129152', '55.98136375432767178466183921738', '57.36467530512226224384513183310', '57.968291616779397068630386967811', '58.47865380072334467054556098628', '59.361123601370176953241861120926', '60.54189605294476805702233239489', '61.32860456862466144286584929212', '62.18771570751427546149141464850', '62.54122583311217604249472330745', '63.404846383543196988613685552787', '64.19471036349124812767888388175', '64.848577758647513109983872511579', '65.749272154312613915407587793274', '66.16172104270142830038728977623', '67.187135665242692960688775754309', '67.62681311151645632138776116425', '68.68182656231462441022408848979', '69.765426867554830912582247077481', '70.580851324382378574680405861079', '71.084529474922984618025329849811', '71.57066137128261994732184601023', '72.66050550717862754115922820685', '73.38497588665561064175455379596', '73.94861884501038384452741928445', '74.73691895750907356326501252148', '75.29319839953633580947786881799', '75.81670941630993769100094316599', '77.24934603436121893660571724474', '77.67600503650281985605187236875', '78.4767649730215656734237019725', '79.549733547554193896863838693675', '79.9983176001837390160257439371', '81.01744127831069965668704210949', '81.581421519498321649456005838168', '82.08573903585627424991990394898', '83.01099753238918071380369013497', '83.47684631516874023029000084654', '84.46032933311329710425151384744', '84.94838505690630728835869971883', '85.819570920351376432025861256508', '86.5655663430744233261954993507', '87.52595951041767979641600265048', '88.21893594515805061016044405327', '89.12456548612435024637849661117', '89.90474182637335294840762101794', '90.374839240439153280173574411159', '90.87498990873374501186582968762', '91.71871160906868083195797917468', '92.69316903798636919616190505869', '93.11923190115463438891122918012', '94.05545067063800849522869119445', '94.30778079394245377174481134922', '95.196914274168541392042468488089', '96.43013572367039218017028447802', '97.33389138151147142459890136696', '97.69680212786998162859546352008', '98.22496104289772716869186915242', '99.52696049362539017766417682151', '99.632371095761171630527131883494', '100.657235480414669860944103857443', '101.25038746500079548845534969209', '101.837324458678150708017592818393', '102.64129073812399349172515768719', '103.153234607453543393057634593764', '104.079442433258708316435385976270', '104.860578837748104204364805904698', '105.87030918570291630520817134566', '106.423010187062864426360938702022', '107.247469796801189475871155147767', '107.638247208192641795130031433129', '108.9100906124516957022258231622', '109.1998632122834483083941396328', '109.87781513281429823084429736684', '110.402247905309540769693454734294', '111.20943126021879565617022336965', '111.99566412563490177001101824661', '112.907322973633433397327122139056', '113.19118613681062976715140609230', '114.17191421190268820944884716715', '115.01621076449335149175517118968', '116.169544569070812325884835379957', '116.34815801277538731169500415795', '117.22886742436692144709853755293', '117.761075424364050264416773713026', '118.321210671883231629693448735687', '119.419875353227474364143110448692', '119.90052533166498198877420008482', '120.28548096152938853493142052138', '121.42208197168305606905476808380', '121.81780665158595372222458876402', '122.45786824158282045023578453738', '123.74520662907283805613315933834', '124.32398656432725936798634421771', '125.06662101662709252708357444017', '125.78971089262769538783808357148', '126.28889374988129368736493788019', '126.89733653793542705711842366613', '127.76232489197480104775211296827', '128.6152894974159359109508649290', '129.094944326381823527047136118023', '129.46328557658090366656213811044', '130.27406261778399225382092455689', '131.0877455110424708570209071153', '132.039790161448233340461506576482', '132.79751343645087408275041671536', '133.43681558571906459877833750272', '133.99301828057771014963760208602', '135.058771491345783764854281596268', '135.5158347530599670954162111065', '136.241340907574846635480043503237', '136.891661254379793454480761652238', '137.28074510445896972438535480995', '138.19251372462305595964547584454', '138.854485167502706223380486759755', '139.65163586750843724233353463834', '139.94690492611935005285176447182', '141.15804343809283817012285943107', '141.78603752051008693538990822617', '142.44425690794807827279393598492', '143.45118963004320251570329316237', '144.026394084964844376660076435540', '144.48351827265357153969620172392', '145.39721936707717976566631172029', '145.79472986692984278766951453516', '146.374140298466252680216472626801', '147.332571114716192275090551993975', '148.10244555879862247278260430630', '148.4973359028292427163412699365', '149.092929811455558418750620162310', '149.809056262215063126994315359237', '151.13276937595784383956238062945', '151.76719248803129865295372644882', '152.15247943581159542640268536404', '152.9996897614680175091214348277', '153.45348829943371199270394054769', '154.28234456532512137844530645104', '155.07410590371024577793033314428', '155.56902297801767066707777002454', '156.29173333160135713164358131004', '156.62679143816871297896419668186', '157.667541184507731314971030591707', '158.11357048781254335454035547178', '159.00798219986860320802946336828', '159.86701046984937896000092447633', '160.64851777378676279923884984737', '161.335928820849917605128405639422', '161.7105836694905988575801645811', '162.607863994804311419868734297643', '163.33236475717444207303539019146', '164.02462003977640860342895211041', '164.36522789182702748171802509601', '165.225670007342278176097265829763', '165.591971208955735621302278478515', '166.52964733690022145943718596454', '167.26092872950722006232218508678', '167.937167378575072066529483524262', '168.65218308039164171866632803650', '169.24863266467285480935402823960', '170.44244316920513133619296763763', '170.94572637705151287434204793098', '171.45679966269706547649452016649', '172.045816113659567592291471791', '172.73421391820896097072152430183', '173.43146676524707662074860864766', '173.992100554149434413860986369867', '174.96081221971357472006999623260', '175.27928317456678381383142254119', '175.96106906601111784029447171971', '176.57509526447138844786306542206', '177.76844958355132330729736161304', '178.13825396044091208465534726399', '179.23954906984626330409807775828', '179.721837059731655912746473004941', '180.331675534527920065931160732657', '180.92764246956510031349786284797', '181.57886855276394295492862453565', '182.27216150156072685836508297667', '183.01302668252507944501840818306', '183.76280312473121247342480485930', '184.09031581924111927645438368328', '184.59078109929986589203301686060', '185.59469720884597447166063496665', '186.29619115555638102249407089876', '187.38362328168226696159365266252', '187.92833040576870556042821783143', '188.18958815383788080851996091626', '189.14559758461885365108027283287', '189.94052610505839774146990279297', '190.66968792738270227984631820306', '191.0497093627135768518521038051', '191.46298233149811247407458575420', '192.59056168109781693303279371806', '192.80859069533005590025675861894', '193.62094420981234183359391727648', '194.52120605993872276288102513142', '194.89005466019384584696633840498', '195.78042259836496276241728263643', '196.71260459843643067226828290716', '197.23251034030812786725155135608', '198.04972388972558374685830238461', '198.474424683344660825996901595943', '199.463712658885717122527975764268', '199.81319808186448308038843418320'], 'prelabel': '1-363-363.149-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.685764912895941, 'root_angle': 0.08057851239669421, 'root_number': '0.874549768089672122093834258054+0.484935772174316615288912712889*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0805785123967', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(110)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.520118987366083475467797360770-0.0694675340040834132811276315224*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.992908192399', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.59951197911', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.68823667619', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.685764912895941, 'bad_primes': [3, 11], 'central_character': '363.149', 'conductor': 363, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/363/149'], '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': '1-363-363.149-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': '1-363-363.149-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.685764912895941, 'root_angle': 0.08057851239669421, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.992908192399', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_363.149', 'Lhash_array': ['dirichlet_L_363.149'], 'factors': ['1-363-363.149-r0-0-0'], 'label': '1-363-363.149-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/363/149'}
Lfunction data - 1-363-363.149-r0-0-0