-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '382244212906972271406846439794', 'a10': [-0.41541501300188644, 0.9096319953545183], 'a2': [-0.9594929736144974, -0.28173255684142967], 'a3': [-0.6548607339452851, 0.7557495743542583], 'a4': [0.8412535328311812, 0.5406408174555976], 'a5': [0.14231483827328514, -0.9898214418809327], 'a6': [0.8412535328311812, -0.5406408174555976], 'a7': [-1.243016655170507, -2.721826811532478], 'a8': [-0.6548607339452851, -0.7557495743542583], 'a9': [-0.14231483827328514, -0.9898214418809327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9594929736144974, 0.28173255684142967]]], [3, [[1.0, 0], [0.6548607339452851, -0.7557495743542583]]], [5, [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]]], [23, [[1.0, 0], [4.04911393429593, -2.56995648739245]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.271', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '1791916608268577694958089884262', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [0.6548607339452851, -0.7557495743542583]], [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [1.243016655170507, 2.721826811532478], [-4.584025137616996, 5.290247020479808]], [[1.0, 0], [2.9025543183334612, -0.8522668450553659], [9.253788861142993, -5.947048992011573]], [[1.0, 0], [2.3239774534034727, -5.08880079422819], [-8.513189541288705, -9.824744466605358]], [[1.0, 0], [-2.154860733945285, 1.384844904938944], [7.062055221032069, -15.463743921026813]], [[1.0, 0], [-4.205738012620157, -2.7028637009044645], [7.892885247035842, 17.28300791173585]], [[1.0, 0], [4.04911393429593, -2.56995648739245]], [[1.0, 0], [0.5757075255604853, -0.3699847609398635], [12.047035377054707, -26.379327865281034]], [[1.0, 0], [-4.813047351732986, -5.554552745138344], [-4.411759986471839, 30.684464698308915]], [[1.0, 0], [-0.5045873280811393, -3.509481953505307], [-35.5012400237364, 10.424104603132898]], [[1.0, 0], [0.41438346132591874, -2.8821002796180495], [-39.339211918194394, -11.551034830498617]], [[1.0, 0], [6.059654793655398, -6.993214425071089], [-6.119538045751261, -42.56232200088011]], [[1.0, 0], [7.6245520165272955, 0], [47.0, 0]], [[1.0, 0], [2.275409664716986, 4.982452171404957], [-34.70761889910011, 40.054727440775686]], [[1.0, 0], [5.2071865580026735, -11.402148094531405], [-38.63678330277182, -44.58922488690124]], [[1.0, 0], [-8.844194869065438, -10.2067449784839], [-8.681205134670394, 60.379107954736895]], [[1.0, 0], [2.1535295410948287, 0.6323333265908448], [56.363986699689136, 36.22293476952504]], [[1.0, 0], [6.543159066765844, 1.921244849512331], [59.72900083101386, 38.385498039347425]], [[1.0, 0], [-2.457632129228292, -1.5794242656901403], [30.325295949137708, 66.40313566087984]], [[1.0, 0], [-2.2851895259276884, 5.003867080324826], [-51.73399798167752, -59.704216373986405]], [[1.0, 0], [0.4082810434184033, 2.839657030794074], [-79.63791681000329, 23.383802217838664]], [[1.0, 0], [-1.9256514186855016, 2.222320204264737], [-12.666020606322377, -88.094108327403]], [[1.0, 0], [-1.0631828186650392, 7.394598928140081], [-93.07081844060625, -27.32805801361868]], [[1.0, 0], [-0.9792170843392044, -6.810604418309757], [-96.90879033506424, 28.4549882409844]], [[1.0, 0], [14.41450226790824, -4.23247974837803], [86.64911388161165, -55.68600419792655]], [[1.0, 0], [6.165894484376157, 7.115821564085245], [-15.22768769524151, 105.9108942812598]], [[1.0, 0], [9.363250786945782, -6.017395900210722], [45.28023641720562, -99.1498874936425]], [[1.0, 0], [-10.354565121354808, -3.0403746424853457], [95.06164920992347, 61.09241237248253]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-690-23.18-c1-0-0', '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/690/2/m/a/271/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.43216057473104047, 0.26626979519464894, 0.08199145389696295, -0.12336073576314047, -0.35106823226990025, -0.5995932946891553, -0.8636063576946987, -1.1335315023984942, -1.3956257149676108, -1.6325962697230145, -1.8247585402229596, -1.9517165384409954, -1.9945028509110396, -1.9380485345190077, -1.7737781356686406, -1.5020539314314874, -1.1341411160347934, -0.6933457202810538, -0.21500108048499805, 0.25494597240653744, 0.6628701440284684, 0.9518710051670336, 1.0673869985901883, 0.9635503201088473, 0.6096229157630897, -0.004281109596386559, -0.8630300811902821, -1.9246478986780413, -3.121422905788695, -4.364247574026727, -5.550088588006338, -6.572041539118423, -7.33098851046139, -7.747518647087316, -7.772558864882012, -7.39514951261959, -6.646019880716619, -5.596069901861833, -4.349508094299486, -3.032155145774144, -1.776190709381993, -0.7032747947807316, 0.0916060214701155, 0.5531300844387286, 0.6733289579255695, 0.4925046994716437, 0.09288414517269668, -0.41433844242160844, -0.9067886122851578, -1.2708277756230493, -1.4203704699998223, -1.311371266871156, -0.9493159671351361, -0.38813540952783543, 0.2795928376883829, 0.9397167094735102, 1.478002340666092, 1.8022160521437978, 1.8606454842766245, 1.6533626093502651, 1.2337279667902106, 0.6993983541490837, 0.17412387696423753, -0.21647909416146954, -0.3706060657852662, -0.23226733407633626, 0.19505674817056723, 0.8463392930050943, 1.605538696981558, 2.3272107247209313, 2.8652708852659527, 3.103249399792222, 2.9797424437483135, 2.503426693007133, 1.7539171925028034, 0.8675832340824486, 0.010639173527182352, -0.6552792368558484, -1.007915252307154, -0.9919611009412682, -0.6329799473850899, -0.033954221753968554, 0.6455780236724284, 1.2239230444391545, 1.5380255859768426, 1.481683806215137, 1.0323265704849294, 0.25965372705164536, -0.686727666523062, -1.6088180469047164, -2.3044762566058594, -2.6146680331889547, -2.4627462031792073, -1.8760854453433946, -0.9840482554926266, 0.008446975579999341, 0.8667135479666676, 1.381501230689374, 1.4208854547688725, 0.966212086844898, 0.12261542824447616, -0.8997686584333835, -1.8309277127536123, -2.402974382317404, -2.415016382903453, -1.785497206741428, -0.5788821675470334, 1.0008721172595678, 2.6499713974130352, 4.0294968260885575, 4.840769946785089, 4.893875695420267, 4.152915029832065, 2.74667563613407, 0.9414596913163726, -0.9181058333181891, -2.4865588086495602, -3.494985969755383, -3.8096783710152673, -3.4578591565158137, -2.6143399896093156, -1.5526791673228078, -0.5733402155508474, 0.07282541705129558, 0.24628249426538643, -0.04991787087622068, -0.6769633731736086, -1.402855927972312, -1.9689681439156055, -2.1624913743354464, -1.8751996938604956, -1.1327516816757013, -0.08684925439226204, 1.0272097729160607, 1.955511163409726, 2.494759192764394, 2.5463879689591886, 2.1405249151706744, 1.4234118678970913, 0.6123728543952832, -0.06823940302199445, -0.4512028983537757, -0.4718013558603893, -0.1811283677031609, 0.2763535521173205, 0.7138462841209724, 0.9658724432863968, 0.944487802625213, 0.6699695758271662, 0.2655371068040938, -0.08321869240741085, -0.19222645517574166, 0.05380423879007744, 0.6527519281301676, 1.472301990252343, 2.2797817232879107, 2.8082199563132284, 2.8403199771435634, 2.2851174000738332, 1.2225971185080053, -0.10027136936178284, -1.324834601388522, -2.0746660732248765, -2.062819246720368, -1.181525743538842, 0.45319765240326565, 2.517770822250905, 4.556737196066846, 6.099034939295576, 6.783272122774037, 6.456548314432429, 5.217819467686089, 3.3920437390127653, 1.4411234319435946, -0.16379098632930206, -1.0723252313619431, -1.1496823765699307, -0.5085539235354177, 0.5312414188470084, 1.5434279838152303, 2.126271468345239, 2.0247401814422297, 1.2072250171133694, -0.12611511469300707, -1.605592404998148, -2.8055370631576677, -3.374231942748144, -3.1403875312030536, -2.163688349293657, -0.7143870363990292, 0.8109796474990026, 2.010848125569317, 2.5986422402081, 2.4841232205142023, 1.7913074523631856, 0.8086523038019875, -0.11107931023367179, -0.6679142771529034, -0.710336386349965, -0.27866206554658934, 0.4171331804343208, 1.0765068419317847, 1.4167976320204128, 1.2737944201773053, 0.6600337141201892, -0.23911172280388385, -1.1302358259214107, -1.7153692620451517, -1.7984349268797848, -1.357654467264509, -0.5582148857281742, 0.300187743054548, 0.8838875603649031, 0.939968586424801, 0.3858425000944947, -0.657575546418226, -1.9013850501095988, -2.981715562656278, -3.579091157440177, -3.5235504851305426, -2.8494300677592688, -1.7808110804389081, -0.6525419939204494, 0.2057787071741553, 0.582347944673859, 0.452700537467846, -0.018314366794704977, -0.5428019281211347, -0.820552476764589, -0.65413567271298, -0.026102923721371057, 0.8908623307391842, 1.7960154372987396, 2.373514505146985, 2.4154829246914735, 1.9092280877011496, 1.0541936895645534, 0.19881022121544864, -0.2833914290790695, -0.13565865021955564, 0.6736893489909724, 1.918601857706033, 3.1750822937853074, 3.9576961696657498, 3.8886172450057517, 2.841007991182344, 1.0045728730864147, -1.1540812130038733, -3.0281163156482926, -4.061868312247243, -3.933994910296743, -2.6698478166827604, -0.6427016924464811, 1.5397745815078998, 3.2284513706405646, 3.942009323628831, 3.5228554231066527], 'positive_zeros': ['0.30153751580928731043466560584834', '2.30609512678866969139261479965592', '3.12427718685936586183511657408150', '5.23257208319256870549316521747572', '5.77402754402811598760689492000783', '6.69874876648152040597951073697368', '7.79856020931427711605331304335912', '8.202098653825315988543863202979356', '9.501694440134936039499236231446139', '10.13132495505144624181904259953257'], 'prelabel': '2-690-23.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.5964519680621158, 'root_number': '-0.2983970934178405 - 0.9544418131241865*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.298225984031', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30153751580928731043466560585', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.30609512678866969139261479966', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.12427718685936586183511657408', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.18', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/m/a/271/1'], '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': '2-690-23.18-c1-0-0', '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': '2-690-23.18-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.2982259840310579, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.30153751580928731043466560585', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '382244212906972271406846439794', 'Lhash_array': ['382244212906972271406846439794'], 'label': '2-690-23.18-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/m/a/271/1'}