-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1302785514699209192450901758794', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.8793852415718169, 3.2551907253974948], 'a6': [0, 0], 'a7': [4.758770483143634, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.923534996511162, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-0.6945927106677214, -4.303201246315035]]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.505', 'coefficient_field': 'CDF', 'conductor': 1368, 'conductor_radical': 114, 'conjugate': '1633978560399129874704458998233', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.8793852415718169, -3.2551907253974948], [-2.5, -4.330127018922194]], [[1.0, 0], [-4.758770483143634, 0], [7.0, 0]], [[1.0, 0], [-4.36958506180819, 0], [11.0, 0]], [[1.0, 0], [0.5, 0.8660254037844386], [-6.5, 11.258330249197702]], [[1.0, 0], [-3.064177772475912, 5.307311585351507], [-8.5, -14.722431864335457]], [[1.0, 0], [-0.6945927106677214, -4.303201246315035]], [[1.0, 0], [1.8793852415718169, 3.2551907253974948], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.694592710667721, -4.667171480581237], [-14.5, 25.11473670974872]], [[1.0, 0], [-7.36958506180819, 0], [31.0, 0]], [[1.0, 0], [7.128355544951824, 0], [37.0, 0]], [[1.0, 0], [1.7587704831436335, -3.046279835657235], [-20.5, -35.50704155516198]], [[1.0, 0], [-0.37938524157181674, 0.6571145140441789], [-21.5, -37.239092362730865]], [[1.0, 0], [3.0, 5.196152422706632], [-23.5, 40.703193977868615]], [[1.0, 0], [-2.573977952239538, -4.458260590840977], [-26.5, 45.89934640057525]], [[1.0, 0], [-4.638155724715451, 8.033521368623607], [-29.5, -51.09549882328188]], [[1.0, 0], [-4.258770483143634, -7.376406854579428], [-30.5, 52.827549630850754]], [[1.0, 0], [0.6847925309040954, 1.1860954561695738], [-33.5, 58.023702053557386]], [[1.0, 0], [5.822948255619545, -10.085642228577619], [-35.5, -61.48780366869514]], [[1.0, 0], [2.2587704831436337, -3.9123052394416735], [-36.5, -63.21985447626402]], [[1.0, 0], [7.073977952239538, -12.252489224900925], [-39.5, -68.41600689897065]], [[1.0, 0], [4.90672638762271, 0], [83.0, 0]], [[1.0, 0], [-4.184792530904096, -7.248273282660644], [-44.5, 77.07626093681505]], [[1.0, 0], [-5.822948255619545, 10.085642228577619], [-48.5, -84.00446416709055]], [[1.0, 0], [2.064177772475912, 3.57526077778263], [-50.5, 87.4685657822283]], [[1.0, 0], [6.758770483143634, 0], [103.0, 0]], [[1.0, 0], [-4.128355544951824, 0], [107.0, 0]], [[1.0, 0], [-0.06417777247591214, 0.11115916264487528], [-54.5, -94.39676901250381]], [[1.0, 0], [-2.408785780862695, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-1368-19.11-c1-0-10', 'leading_term': '1.945080170992832948606527147935993432953406999596074047', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1368/2/s/j/505/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.945080170992833, 1.8903948910379385, 1.8292143677964556, 1.7613711360343132, 1.686556992707163, 1.6043842291383197, 1.5144535528527587, 1.4164245650025615, 1.310084958421714, 1.1954151675224916, 1.0726458787065059, 0.9423064676806758, 0.8052629851717188, 0.6627447332727342, 0.5163587694963585, 0.3680918769441862, 0.22029968798540037, 0.07568278453868861, -0.06275024856811315, -0.1917326489701412, -0.30780177205916426, -0.40737315598399937, -0.48682531899802584, -0.5425938792033053, -0.5712731928294729, -0.5697233087630521, -0.5351796526689186, -0.4653625032344672, -0.35858302556038657, -0.2138424017829729, -0.03092046471283023, 0.18954978723595486, 0.4460253227812794, 0.7360171639689668, 1.0560783720452838, 1.4018183818842407, 1.767945502621966, 2.148338646486013, 2.536148482928703, 2.923927262067945, 3.3037855366140914, 3.6675729664536876, 4.00707935068808, 4.314251037284547, 4.581416951728482, 4.80151770489572, 4.968330627489546, 5.076683171725851, 5.1226469538417385, 5.103704810419617, 5.018883626367517, 4.868846371996623, 4.655937759455953, 4.384179181509427, 4.059210102665275, 3.6881747960485827, 3.2795552093450784, 2.8429527390110207, 2.388823723871551, 1.928175460231329, 1.4722314092097606, 1.0320759302432845, 0.618290251534148, 0.2405924031206011, -0.09250557522186695, -0.37400973460316245, -0.5987126249464477, -0.7634059632100397, -0.8670270056808417, -0.910730070637872, -0.8978771237866965, -0.8339441974215086, -0.7263435725487879, -0.5841649993071095, -0.4178426373615387, -0.23875772572611292, -0.05879009592158954, 0.11016562123059408, 0.25670101487216773, 0.37039246085146094, 0.44227669672405, 0.4652828231744033, 0.43460097503590994, 0.34796961224250683, 0.20586594680918563, 0.011587383307491025, -0.2287840948938302, -0.5065380523125019, -0.8106107086027434, -1.1279723204161323, -1.4441149949987973, -1.7436242225420397, -2.010813042087853, -2.230394102865147, -2.3881621501572745, -2.471657821940096, -2.470783218508914, -2.37834058182743, -2.1904676182922773, -1.9069464818589938, -1.5313681061547595, -1.071139275961263, -0.537326345677627, 0.055663418610270625, 0.6905545787776899, 1.3478148136360972, 2.0063824089855995, 2.64448154428528, 3.2404919924359437, 3.77383622805146, 4.225844904878801, 4.5805613771188645, 4.825447487414625, 4.951956226077232, 4.955941992232504, 4.83788587933052, 4.602921401705557, 4.260655037110099, 3.824785482008092, 3.31253515692329, 2.7439167891033467, 2.140866368386054, 1.5262809708460248, 0.923005470955593, 0.3528156825522529, -0.1645532635879623, -0.6122856227647488, -0.9772266783933813, -1.2504490399241244, -1.4276132671935984, -1.509102202515621, -1.4999194179617696, -1.4093540006305416, -1.2504259168078695, -1.0391377985666754, -0.7935695649955284, -0.5328612388161358, -0.27613612651094815, -0.0414207703789979, 0.1553805499263959, 0.30140065218561585, 0.38756220883749737, 0.4091245913766261, 0.3659911043812253, 0.26275513997080496, 0.10847750470880957, -0.08379831405457261, -0.2977716325423248, -0.5148157180102196, -0.7150672764734558, -0.8786169834431714, -0.9867366640675225, -1.02307498917486, -0.9747534781976768, -0.833298303111099, -0.595350776846963, -0.2631101838468282, 0.1555237308677732, 0.6471254325612151, 1.193234997929281, 1.7711481130818334, 2.354969357349851, 2.916877793051479, 3.4285406483528567, 3.862600900206658, 4.194158493533837, 4.402163224465449, 4.470640186785497, 4.389676092971205, 4.156106433900038, 3.7738587813145745, 3.253925783148812, 2.613961582599788, 1.8775163971089042, 1.0729446345386582, 0.2320410009749432, -0.6115245731671788, -1.4238897079223247, -2.172708454709955, -2.8287916919468628, -3.3675868549435437, -3.7704126177050163, -4.025376989281739, -4.127924531900724, -4.08097912757235, -3.894671760226015, -3.585666821563562, -3.176124079592414, -2.6923552498546064, -2.1632527388410643, -1.6185824060495357, -1.0872411716163817, -0.5955833369925919, -0.16591629083008558, 0.18474308040969867, 0.4455750101819997, 0.6124701658623118, 0.6881170080266943, 0.6816565790889247, 0.6079249265150003, 0.486329322578068, 0.3394279030030082, 0.1913017999512888, 0.06582299836850651, -0.015070988336604509, -0.03298355945582183, 0.025559357381213132, 0.16804550179019956, 0.395304174081499, 0.7012755697360051, 1.0732435528069388, 1.4925242225264475, 1.9355729467591813, 2.3754447219625243, 2.7835185967107257, 3.1313780911307267, 3.392727376587053, 3.545218367385744, 3.5720672690703434, 3.4633504671251263, 3.21688834984342, 2.8386506727408514, 2.342646889111068, 1.7502976469585776, 1.089317309061163, 0.39216971114332144, -0.30581170712559386, -0.9685247421692162, -1.5612891047768125, -2.052987589561342, -2.418019135711531, -2.637935010420244, -2.7026477874367827, -2.6111287911282948, -2.371541657109047, -2.0007956220090746, -1.5235397918175524, -0.9706564886861764, -0.3773453832010823, 0.2190818046910432, 0.7815556692620708, 1.2756005863515214, 1.6715296424691326, 1.9463378897576051, 2.0851670797284223, 2.0822420298409194, 1.9412128139267955, 1.674875859183135, 1.3042882318995161, 0.8573301542950096, 0.3668083522879975, -0.13177540316960795, -0.6026424702828984, -1.0121801695405193, -1.3312441045001786, -1.5371628976017697, -1.6153071786845095], 'positive_zeros': ['1.02771656043443994500905779604279', '1.76666267177002707174778107922397', '3.73283721723274827514032231770380', '4.47288433553394648561383533638014', '4.98355793472549819679874330247695', '6.02985381817192567098938745587219', '7.30479455571430664432478451628310', '8.097257066277226682124131724611046', '8.530259303339463906471112908466119', '9.178724253221013078920270372312017'], 'prelabel': '2-1368-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.305077154396121, 'root_angle': -0.2853599477013698, 'root_number': '0.62435973899496718904135717386466489732404646720993534575 - 0.7811369382650755481255059878118179135687237320182992141*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1426799738506849', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02771656043443994500905779604', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76666267177002707174778107922', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73283721723274827514032231770', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.923534996511162, 'bad_primes': [2, 3, 19], 'central_character': '19.11', 'conductor': 1368, 'conductor_radical': 114, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1368/2/s/j/505/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-1368-19.11-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1368-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.305077154396121, 'root_angle': -0.1426799738506849, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02771656043443994500905779604', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1302785514699209192450901758794', 'Lhash_array': ['1302785514699209192450901758794'], 'label': '2-1368-19.11-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1368/2/s/j/505/1'}