Table lfunc_lfunctions
L-functions
{'Lhash': '617497238158472449807298857034', 'a10': [0, 0], 'a2': [0, -1024.0], 'a3': [0, -21924.0], 'a4': [-1048576.0, 0], 'a5': [0, 0], 'a6': [-22450176.0, 0], 'a7': [0, 722753248.0], 'a8': [0, 1073741824.0], 'a9': [9979691427.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 139.73867214353106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1024.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '50.49', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1331788327537020995563338363613', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1024.0]], [[1.0, 0], [0, 21924.0], [-10460353203.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -722753248.0], [-558545864083284030, 0]], [[1.0, 0], [-49976398572.0, 0], [7400249944258161000000, 0]], [[1.0, 0], [0, 24351400354.0], [-247064529073450400000000, 0]], [[1.0, 0], [0, -5768874283278.0], [-69091933913008730000000000, 0]], [[1.0, 0], [-30250225982620.0, 0], [714209495693373300000000000, 0]], [[1.0, 0], [0, 145464074718144.0], [-39471584120695487000000000000, 0]], [[1.0, 0], [-1167107530943250.0, 0], [5132842708382183000000000000000, 0]], [[1.0, 0], [7431907384909648.0, 0], [20825506393391553000000000000000, 0]], [[1.0, 0], [0, -54621676523378696], [-855531895666462800000000000000000, 0]], [[1.0, 0], [20889593910177080, 0], [7386879101213258000000000000000000, 0]], [[1.0, 0], [0, -76193896658949000], [-20083415214428110000000000000000000, 0]], [[1.0, 0], [0, 508989722403999940], [-130033429462229770000000000000000000, 0]], [[1.0, 0], [0, -1341490659556639200], [-1621038246414955000000000000000000000, 0]], [[1.0, 0], [2306403035584928000, 0], [15413179794770735000000000000000000000, 0]], [[1.0, 0], [-5268341017122878000, 0], [31040344686800427000000000000000000000, 0]], [[1.0, 0], [0, -10904975405120901000], [-222623423334106740000000000000000000000, 0]], [[1.0, 0], [13367810994741254000, 0], [752359350923790900000000000000000000000, 0]], [[1.0, 0], [0, 17952853611107730000], [-1348279907365869100000000000000000000000, 0]], [[1.0, 0], [118985112237438260000, 0], [7082211906170644000000000000000000000000, 0]], [[1.0, 0], [0, -134353218394716670000], [-19982045332214680000000000000000000000000, 0]], [[1.0, 0], [347081364860908400000, 0], [86534669543385680000000000000000000000000, 0]], [[1.0, 0], [0, -376521927584699650000], [-527480512638944850000000000000000000000000, 0]], [[1.0, 0], [774303083485457800000, 0], [1232391940347446500000000000000000000000000, 0]], [[1.0, 0], [0, 425393386046988900000], [-1860294571709496000000000000000000000000000, 0]], [[1.0, 0], [0, -1804788694483765600000], [-4140562374860212000000000000000000000000000, 0]], [[1.0, 0], [-3921748138195436000000, 0], [6108807736878339000000000000000000000000000, 0]], [[1.0, 0], [0, -677306921360947300000], [-13021089174137413000000000000000000000000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23184005, 'index': 12, 'label': '2-50-5.4-c21-0-12', 'leading_term': '2.1422039072458666459168711621653994601703156828506857136', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/50/22/b/b/49/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 20}, 'plot_values': [2.1422039072458667, 1.9321000722533221, 1.6753975903900813, 1.378888551198517, 1.05074229642652, 0.7002862847862679, 0.33774972658886054, -0.026022803880972896, -0.3798796389155094, -0.7126833316318283, -1.0136357276515406, -1.2725973279254423, -1.4803915700183186, -1.6290850212326378, -1.7122351065333532, -1.7250978708286349, -1.6647893751030722, -1.530395619003701, -1.32302733283903, -1.0458175489154828, -0.7038615014206633, -0.3041000689773934, 0.14485038325972546, 0.6329173320678246, 1.1488347079408738, 1.6804416043492114, 2.215008797629596, 2.739583920838015, 3.2413455234751054, 3.707955916022522, 4.127902655923906, 4.4908187839483436, 4.787772462244562, 5.011517484830483, 5.156697206577201, 5.21999573907068, 5.200231755254975, 5.098391887664589, 4.91760245066176, 4.663040015153199, 4.341783162358251, 3.9626094882677227, 3.53574357029113, 3.072563092497573, 2.5852716100092836, 2.0865474760574734, 1.5891792231429787, 1.1056981565897532, 0.6480190671140004, 0.2270997907403997, -0.1473701589300062, -0.46724247804591473, -0.7261361808870025, -0.9196100026074011, -1.0452757651681175, -1.1028491484244312, -1.094136206912483, -1.0229559400716783, -0.8950011996341274, -0.7176421416928573, -0.49967824216547657, -0.25104653517199715, 0.01750484920564176, 0.29476762554419605, 0.5694377148518173, 0.8304814765428976, 1.0674921274442637, 1.2710249030771663, 1.4329001230346277, 1.546464282762861, 1.6068005826545335, 1.6108818852926865, 1.557660916144436, 1.4480945364592746, 1.2851010569186896, 1.073451758803128, 0.8195999750228091, 0.5314531843239576, 0.21809551777832165, -0.1105301994925643, -0.4439703072481373, -0.7716263996685834, -1.083127247162507, -1.368693832102263, -1.619484886043278, -1.8279108514276603, -1.987905145018494, -2.0951429482396318, -2.1471994522190854, -2.1436414907868064, -2.0860487396688736, -1.977963071814668, -1.8247671570702075, -1.6334958944315787, -1.4125866801262192, -1.1715767590588062, -0.9207578990320647, -0.6708002918858564, -0.43235885831040183, -0.2156759608651978, -0.03019487438365693, 0.11580179768180231, 0.21551524312109133, 0.26390274679438186, 0.2578884655740746, 0.19650400622989977, 0.08095254350704821, -0.08540710694701273, -0.29715718527431995, -0.5469962331756469, -0.825987743905129, -1.1238742747083412, -1.4294465151015248, -1.7309545705996539, -2.016546908097502, -2.274721092360681, -2.4947696830266137, -2.667204499296044, -2.78414291533743, -2.839640921299507, -2.8299593478987313, -2.753751859459884, -2.612166002275626, -2.408851663993452, -2.1498746504917636, -1.8435366011425558, -1.5001060140070837, -1.1314686071740931, -0.7507084690273493, -0.37163432168969346, -0.008267621206204043, 0.3256889571226352, 0.6173829327896803, 0.8553231694038498, 1.02985089993527, 1.1335518339549675, 1.1615923575313107, 1.1119653299349157, 0.9856340857702022, 0.7865668632255176, 0.5216578732540352, 0.20053545712488796, -0.164737905565244, -0.5600647433942397, -0.9697979127363313, -1.3772955289065845, -1.7655259211829106, -2.1177006824608284, -2.417912334168023, -2.6517524473360803, -2.806886298365505, -2.873561305326444, -2.845028563817326, -2.7178597205357313, -2.4921450931508544, -2.171563240248724, -1.7633169507604485, -1.277935681758914, -0.7289496343160554, -0.13244571813206238, 0.4934795850345109, 1.1293511861292453, 1.7550073214742041, 2.3503268379708335, 2.895964419246406, 3.374065594912203, 3.7689337296854095, 4.067622652140213, 4.2604311172662594, 4.341278821588133, 4.307948081151297, 4.162180380114226, 3.9096226077177634, 3.5596237057513718, 3.124888412449207, 2.62100056993015, 2.0658338213735528, 1.4788722342625689, 0.8804672427689634, 0.2910601326519801, -0.2695990377852627, -0.7832047649371142, -1.2335912226546597, -1.6073408602516046, -1.8942814876195582, -2.0878512696636276, -2.18531637148971, -2.1878320129070294, -2.10034416142156, -1.9313357488688847, -1.6924278574009015, -1.3978525041292376, -1.0638191901256955, -0.707802021778133, -0.34777774830495606, -0.001447320621435737, 0.31452555148638545, 0.5852259411869746, 0.79811845695333, 0.9435697016312881, 1.015239558411665, 1.010324099065889, 0.9296393982504693, 0.7775425613606805, 0.5616935257975981, 0.29266835480162223, -0.01655851370539968, -0.3512395829963459, -0.6955586872314865, -1.0333822013427534, -1.3490224905727195, -1.6279782535283862, -1.8576172644381541, -2.0277694723661326, -2.1312023762760144, -2.163955902652525, -2.1255204393556193, -2.0188489420973976, -1.8502018011729773, -1.6288310791791984, -1.3665184353844373, -1.0769881728295314, -0.7752230347795984, -0.47671533010793554, -0.19668942783209287, 0.050666559304476784, 0.2529220958292295, 0.40004257832588785, 0.4849123532765649, 0.5037152486086726, 0.45615208861828416, 0.34548238340041726, 0.17838585370734805, -0.03535172695708766, -0.28331514137439906, -0.5510773056221546, -0.8229289894359829, -1.0826857998749382, -1.3145331000072333, -1.503866942764647, -1.6380885292493805, -1.7073112192834399, -1.7049426976440336, -1.6281103983929934, -1.4779054807696514, -1.259429213793353, -0.9816351689308201, -0.6569706899075552, -0.30083121893144354, 0.06914929064251515, 0.43393994219020077, 0.7740472083891301, 1.0704972431300104, 1.305818044352459, 1.464972238383903, 1.53619260256394, 1.5116762032029258], 'positive_zeros': ['0.48711943026516728961471297607306', '1.52492512125284861820082996785603', '3.48679391756447898342699087377670', '4.35489133392152480753343372743800', '5.53126476269469219251245594783983', '7.04425102208540116385835235576974', '7.48989315666565868412558606717811', '9.142283332375504660123348635321001', '9.953544504111557726251248356988808', '11.19477130178134744118842036792996'], 'prelabel': '2-50-5.4-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.821111290548409, 'root_angle': -0.07379180882521663, 'root_number': '0.89442719099991587856366946749251049417624734384461028971 - 0.44721359549995793928183473374625524708812367192230514485*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 54}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48711943026516728961471297607', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.52492512125284861820082996786', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.48679391756447898342699087378', 'prec': 100}}