-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4815014610391664902539692689381', 'a10': [41196.99136118752, 0.0], 'a2': [-16.892443989449806, 0.0], 'a3': [109.81688388394785, 0.0], 'a4': [-226.6453360633012, 0.0], 'a5': [-2438.7821789977315, 0.0], 'a6': [-1855.075560105502, 0.0], 'a7': [-2401.0, 0.0], 'a8': [12477.524967517642, 0.0], 'a9': [-7623.252014019515, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.605250853147113, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2401.0, 0]]]], 'bad_primes': [7], 'central_character': '7.1', 'coefficient_field': 'CDF', 'conductor': 7, 'conductor_radical': 7, 'conjugate': '4815014610391664902539692689381', 'degree': 2, 'euler_factors': [[[1.0, 0], [16.892443989449806, 0], [512.0, 0]], [[1.0, 0], [-109.81688388394785, 0], [19683.0, 0]], [[1.0, 0], [2438.7821789977315, 0], [1953125.0, 0]], [[1.0, 0], [2401.0, 0]], [[1.0, 0], [28548.26870891005, 0], [2357947691.0, 0]], [[1.0, 0], [-138148.7470410134, 0], [10604499373.0, 0]], [[1.0, 0], [101009.82295544614, 0], [118587876497.0, 0]], [[1.0, 0], [488928.0418080918, 0], [322687697779.0, 0]], [[1.0, 0], [140071.40667016414, 0], [1801152661463.0, 0]], [[1.0, 0], [6317156.381809087, 0], [14507145975869.0, 0]], [[1.0, 0], [1009027.233216882, 0], [26439622160671.0, 0]], [[1.0, 0], [-11920643.87289782, 0], [129961739795077.0, 0]], [[1.0, 0], [21510589.850110203, 0], [327381934393961.0, 0]], [[1.0, 0], [-16595693.400372462, 0], [502592611936843.0, 0]], [[1.0, 0], [26744086.934092272, 0], [1119130473102767.0, 0]], [[1.0, 0], [-37499084.99875834, 0], [3299763591802133.0, 0]], [[1.0, 0], [-18190742.22180134, 0], [8662995818654939.0, 0]], [[1.0, 0], [25011086.03381472, 0], [11694146092834140, 0]], [[1.0, 0], [218571980.23777604, 0], [27206534396294948, 0]], [[1.0, 0], [-312688004.3405463, 0], [45848500718449030, 0]], [[1.0, 0], [289037858.8729283, 0], [58871586708267910, 0]], [[1.0, 0], [-468684702.423883, 0], [119851595982618320, 0]], [[1.0, 0], [77540718.72261378, 0], [186940255267540400, 0]], [[1.0, 0], [-337679922.1349482, 0], [350356403707485200, 0]], [[1.0, 0], [736733072.5011488, 0], [760231058654565200, 0]], [[1.0, 0], [-197427972.44083503, 0], [1093685272684361000, 0]], [[1.0, 0], [1274494154.5818434, 0], [1304773183829244700, 0]], [[1.0, 0], [-1819365620.8348858, 0], [1838459212420154600, 0]], [[1.0, 0], [231425426.49805617, 0], [2171893279442309400, 0]], [[1.0, 0], [1519832403.8343189, 0], [3004041937984268300, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-7-1.1-c9-0-3', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7/10/a/a/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.0, 0.20902189672092727, 0.4155189271450313, 0.6169311807425841, 0.8106314967246027, 0.9938989091495212, 1.163900499584447, 1.3176843144115187, 1.4521858450619662, 1.5642503304546092, 1.6506727983310094, 1.7082572918662544, 1.7338961073600596, 1.7246690799192383, 1.677961986484859, 1.5916019901789162, 1.4640067422704235, 1.2943423215255079, 1.0826836792847987, 0.8301697484503835, 0.539143964202414, 0.21326975301929776, -0.14239028929112163, -0.5213431434721182, -0.9156933325117861, -1.316240297086438, -1.7126533616447934, -2.093729485698119, -2.447735013600747, -2.7628277148239757, -3.027549687029736, -3.2313754143915387, -3.3652927725758826, -3.422388485433098, -3.39840398591019, -3.292223393000367, -3.1062529886882153, -2.846651741093344, -2.5233755700026155, -2.150004544871992, -1.7433321945120186, -1.3227094795892214, -0.9091523097639619, -0.5242400120033291, -0.1888517665916084, 0.07819270126831541, 0.2615046269979558, 0.3504129335829849, 0.34006143051461407, 0.23221127492603927, 0.035651640960555064, -0.2338609304638348, -0.5541871059305837, -0.8979303822877689, -1.2340786346803454, -1.530090188127106, -1.754306288642042, -1.8785289170652604, -1.8805683150382249, -1.7465428816248005, -1.4727092193974676, -1.0666149961233449, -0.5474033693827116, 0.05484548350217561, 0.7007753271029212, 1.344368877898091, 1.9363741616151569, 2.4283076587067476, 2.776719821845163, 2.9473503879054137, 2.918773183400979, 2.6851395250059156, 2.2576794395332556, 1.664710424639103, 0.9500295381320726, 0.16971689912133628, -0.6124562274535641, -1.3306602518688904, -1.9231870325287141, -2.3385829510234832, -2.5410971068515797, -2.5148279282309143, -2.2660433980357912, -1.8233090673613581, -1.2352724119337744, -0.5662023281721937, 0.11035730923746276, 0.719221036706041, 1.1916937595121277, 1.473301742063589, 1.5302108006582509, 1.353516761059048, 0.9607968805384828, 0.3946050495364364, -0.28205126107756456, -0.992838289181151, -1.6570631569222165, -2.1994395227520798, -2.5594486988888194, -2.6990776486552592, -2.607859358448413, -2.30443796750026, -1.8343023742474942, -1.263829833371593, -0.6712925690910951, -0.13593564082257076, 0.2734347944228532, 0.508763123740722, 0.5504308407205869, 0.4110798221652541, 0.1348180888997027, -0.20832068940861717, -0.5321066761437513, -0.7468250040123862, -0.7732459488849233, -0.5558375311543287, -0.07319126374328373, 0.6560774223986884, 1.5731205333765412, 2.584720882250003, 3.5747122665774116, 4.4195663441872455, 5.006037950393176, 5.248320983933775, 5.102092870747247, 4.573152645046434, 3.7190605867874194, 2.643179367686027, 1.481658953697701, 0.3850278423550186, -0.5030284754692825, -1.0665636216683407, -1.234716764336143, -0.992710431037426, -0.3845957560600927, 0.49291584139050454, 1.5047914006037368, 2.4981014562990724, 3.325395768474344, 3.8673219834804984, 4.050805071715042, 3.859751115830858, 3.336421518826491, 2.573162250309882, 1.6958153849828772, 0.8416041459794387, 0.13530292605864772, -0.3321185432878633, -0.5185458022465618, -0.4366927518746927, -0.1498202504035106, 0.2421149474281608, 0.6233997981238892, 0.8867170131616242, 0.9559167537460089, 0.8029400801041507, 0.4554051810500671, -0.006948466321808839, -0.4666640735628594, -0.7913966236832883, -0.8609939598442731, -0.5936423671496139, 0.034157772190251345, 0.9780449803052136, 2.129080878315304, 3.3298535514990064, 4.400863650373299, 5.172515593249019, 5.516720442414457, 5.371927186991262, 4.756426555668467, 3.766868657816962, 2.561733543575664, 1.3324640675105686, 0.2675246880466214, -0.48374469963034117, -0.8403198340204333, -0.8057072149750646, -0.4675613943154053, 0.01969439632577675, 0.46621983973677145, 0.6861257847173738, 0.5370851652746795, -0.047876601981593055, -1.0431184596564071, -2.3315736716924844, -3.72464092363855, -4.9971851058495655, -5.930852084261226, -6.357024606996516, -6.190631859628745, -5.4477490271636455, -4.24317193703486, -2.768275132645913, -1.2536007237289994, 0.07610837411662016, 1.0450490784184523, 1.5586188123448879, 1.6180378685550516, 1.3143755646757713, 0.8035190979331684, 0.2678318610060502, -0.1267798688539932, -0.268629953786904, -0.12424411762111867, 0.25687599879711914, 0.7577252678538468, 1.225762496640706, 1.513677125153152, 1.519047036298791, 1.2130751456936515, 0.6510377604328805, -0.038640197941181564, -0.6846149631666213, -1.1152735534579192, -1.2036074941342656, -0.9031635797293691, -0.26565173671442105, 0.5651173165967199, 1.3827292092748824, 1.965116186272725, 2.128432685630322, 1.7751332182873023, 0.9243154411768066, -0.2839065245614505, -1.6123879626200628, -2.7750219681357686, -3.4987011921917803, -3.585277941240064, -2.9591030350723653, -1.6886204583266544, 0.02376758599355421, 1.8820612341398, 3.558612244436425, 4.7637726761064405, 5.307299406857983, 5.13728994392057, 4.347585195044553, 3.151992278975798, 1.8315877981613058, 0.6678312669994074, -0.12236350473256122, -0.4339717071349758, -0.2923686807349022, 0.16104450100002865, 0.7119218644176112, 1.1333752888931026, 1.2479757502477817, 0.9752936622387587, 0.35271295859183505, -0.47575902075637894, -1.299562878031543, -1.8997801046908003, -2.1098301216310413, -1.8622937367063053, -1.2090828974080452, -0.30924026691613243], 'positive_zeros': ['3.79837678420596625160071144778464', '7.85307835004733678158176389772777', '8.815004289195965606401040694218631', '11.05889941982065285218625329280236', '13.22126393463707655086164512155823', '15.08781012950683421113327219960076', '16.45240372921716870509386384916811', '18.50866241667015281535077673490366', '19.40675896893413344248306842164000'], 'prelabel': '2-7-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8987498132052871, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.79837678420596625160071144778', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.85307835004733678158176389773', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.815004289195965606401040694219', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.605250853147113, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 7, 'conductor_radical': 7, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7/10/a/a/1/1'], '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': '2-7-1.1-c9-0-3', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-7-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8987498132052871, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '3.79837678420596625160071144778', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4815014610391664902539692689381', 'Lhash_array': ['4815014610391664902539692689381'], 'label': '2-7-1.1-c9-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7/10/a/a/1/1'}