-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1349004798190808938291959784475', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': -2, 'a5': -1, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': '1.1.1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 2, 3], [1, 1], [1, 4, 7], [1, -3, 11], [1, -2, 13], [1, -6, 17], [1], [1, 0, 23], [1, 3, 29], [1, 7, 31], [1, -8, 37], [1, 6, 41], [1, 4, 43], [1, -6, 47], [1, 6, 53], [1, 15, 59], [1, -5, 61], [1, -2, 67], [1, 3, 71], [1, -8, 73], [1, -5, 79], [1, -12, 83], [1, 15, 89], [1, -8, 97], [1, -15, 101], [1, 16, 103], [1, 0, 107], [1, -11, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [[[1, 2, 3], 1]], [[[1, 1], 1]], [[[1, 4, 7], 1]], [[[1, -3, 11], 1]], [[[1, -2, 13], 1]], [[[1, -6, 17], 1]], [1], [[[1, 0, 23], 1]], [[[1, 3, 29], 1]], [[[1, 7, 31], 1]], [[[1, -8, 37], 1]], [[[1, 6, 41], 1]], [[[1, 4, 43], 1]], [[[1, -6, 47], 1]], [[[1, 6, 53], 1]], [[[1, 15, 59], 1]], [[[1, -5, 61], 1]], [[[1, -2, 67], 1]], [[[1, 3, 71], 1]], [[[1, -8, 73], 1]], [[[1, -5, 79], 1]], [[[1, -12, 83], 1]], [[[1, 15, 89], 1]], [[[1, -8, 97], 1]], [[[1, -15, 101], 1]], [[[1, 16, 103], 1]], [[[1, 0, 107], 1]], [[[1, -11, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 43, 'label': '2-1805-1.1-c1-0-43', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1805/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-4.50621662942777e-61, 0.08540604056953635, 0.1698375387096435, 0.252258423134031, 0.33151419924445896, 0.40628387588806014, 0.47504409771416184, 0.5360478641757369, 0.5873191785627508, 0.6266640330900933, 0.6516973761288382, 0.6598851425951472, 0.6486000309800704, 0.6151894303175646, 0.5570536843605965, 0.4717326854477685, 0.3569985903191173, 0.21095223445384456, 0.03212059420340967, -0.180447579162111, -0.42709103262678777, -0.7074534298002964, -1.020412244181081, -1.3640224604581883, -1.7354783140134853, -2.131096075129975, -2.5463205305779533, -2.9757573270700886, -3.413232720194616, -3.851881526644828, -4.284263220969161, -4.7025051710629775, -5.098470995640319, -5.4639509839273455, -5.7908704795445365, -6.071511137461628, -6.298739057921725, -6.466233028140425, -6.5687055043506914, -6.602108583613144, -6.563817082272509, -6.452780984867698, -6.269639973984512, -6.016793507988036, -5.698420978082327, -5.320447834226631, -4.890455193194989, -4.417532290113563, -3.9120731527706436, -3.385520999625485, -2.850066011394637, -2.3183042182903755, -1.8028671915632322, -1.3160339387483737, -0.8693377891831984, -0.4731820387078199, -0.13647862936210672, 0.13367588463937344, 0.33227342701338014, 0.45660406687762634, 0.5063915412791626, 0.4838462110266418, 0.39362981330409613, 0.24272955950939146, 0.04024260285111523, -0.20292446173155548, -0.4744327482661933, -0.76095304942123, -1.0486575798101196, -1.3237436932550175, -1.57296962799335, -1.7841809265595279, -1.9468056152452635, -2.052296586489342, -2.094500943970331, -2.069938340793941, -1.9779735180719016, -1.8208722416241114, -1.603734502288366, -1.3343040143201261, -1.0226585064601457, -0.6807908150600096, -0.32209610523935966, 0.03921459396914422, 0.3887502027942361, 0.7125972033126923, 0.997969432243159, 1.233819662115318, 1.41138320679632, 1.5246258560791173, 1.5705719261126752, 1.549493009636588, 1.4649439540728524, 1.3236394526942468, 1.1351721127917334, 0.9115806271015414, 0.6667843508722514, 0.41590779196154726, 0.1745248740230556, -0.0421420247656806, -0.22002963795110567, -0.34700752458861006, -0.41357759022175966, -0.41346123182592254, -0.3440401053031917, -0.20662260051149484, -0.006515875572958987, 0.24710757271461797, 0.5415497502596528, 0.8611238184711653, 1.187867461525858, 1.5024029732847937, 1.784905311214664, 2.016132253730819, 2.1784657769230917, 2.256911190268673, 2.240000679032697, 2.120550802346622, 1.8962291554171913, 1.5698936382355833, 1.1496782520271767, 0.6488116042565859, 0.08516776323415905, -0.519436905345724, -1.1401734919959041, -1.7503166059999118, -2.3224952816552293, -2.830018413752514, -3.248208459492816, -3.5556745266876044, -3.7354569467360563, -3.775980083685339, -3.6717583368022053, -3.4238117321679638, -3.0397616567489045, -2.5335934842805394, -1.9250902558931262, -1.2389592917879384, -0.5036906558131663, 0.24979819209985238, 0.989664346751265, 1.6847112633363117, 2.305948098713616, 2.8280530979961824, 3.2306609608905066, 3.499402083709743, 3.6266337517831717, 3.611819182337747, 3.4615289921866523, 3.1890602016830556, 2.8136891629638137, 2.3595956166835768, 1.8545142286660068, 1.328186289528645, 0.8106967611106135, 0.3307897036772029, -0.08574225221110691, -0.41750159343078835, -0.6486783026558112, -0.7699198796825579, -0.7788257972623618, -0.6800344821667884, -0.4848944815577949, -0.21073595764285663, 0.12021739598160872, 0.48223395515580325, 0.8476766030660936, 1.1887272511983424, 1.479130108560672, 1.6958479120513623, 1.820529281269104, 1.840695601132453, 1.750571861363518, 1.5515068191865085, 1.2519525012226684, 0.8669999644627115, 0.4174957622109195, -0.0712099990664725, -0.5708094502225868, -1.0517826652984599, -1.4852355897369995, -1.8447153223460722, -2.1078878714273617, -2.2579707936858187, -2.2848273824596474, -2.1856495156484343, -1.9651817046689406, -1.6354677574108158, -1.215131978242734, -0.7282370295060822, -0.2027885030567712, 0.3310199645799148, 0.8427091845350084, 1.3034417073404545, 1.687848052546373, 1.9756312127069133, 2.152842025060256, 2.2127385884108253, 2.156169579909722, 1.991452429669244, 1.7337508419918912, 1.4039899065128694, 1.0273787544745379, 0.6316382071604321, 0.24505219555096105, -0.1055246623857597, -0.3965661327401009, -0.6095473834946902, -0.732272917872605, -0.7597624883087868, -0.6946272336342149, -0.5469026799665618, -0.3333426028344324, -0.07621554790481165, 0.19831855404470666, 0.46214328058622783, 0.6872996868772444, 0.8481316313436399, 0.9233094585323248, 0.8975843591626332, 0.7631415153008559, 0.5204455323182847, 0.178505105934695, -0.2454767797950841, -0.7270581949232762, -1.236067207977535, -1.7385721110859615, -2.199185741708387, -2.5835499486341282, -2.8608296457150773, -3.006040862156659, -3.002044359926284, -2.841055532013565, -2.525551357888519, -2.0684943199226455, -1.4928388413197355, -0.8303349387522735, -0.119693023316135, 0.5957803203958099, 1.2709264890131644, 1.8616801390119748, 2.328018883280193, 2.6367161333080786, 2.7637051727946367, 2.695885454532846, 2.432237224713964, 1.9841556653756836, 1.3749678250574695, 0.638651145871264, -0.18217245307778418, -1.0388420986086966, -1.8796953057855381, -2.653337483695414, -3.3119255773510163, -3.8142444389718584, -4.128366582389749, -4.233712825897662], 'positive_zeros': ['1.06417714624828988770031977778529', '3.30897413440669327666321670556883', '3.76032779270688982178507540089124', '4.85687055939197751337392409508573', '5.78864269288415358256356915362766', '6.21260132573943813797134499627049', '7.15688226851931363649415056933244', '8.125110666225905114287996427727861', '9.127628990679212829761037204252382'], 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 528242284348825028, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06417714624828988770031977779', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30897413440669327666321670557', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76032779270688982178507540089', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, -2, -1, 0, -4, 0, 1, 0, 3, 4, 2, 0, 2, 4, 6, 0, 0, 2, 8, 0, 0, 0, 1, 0, 4, 8, -3, 0, -7, 0, -6, 0, 4, -2, 8, 0, -4, 0, -6, 0, -4, -6, -1, 0, 6, -8, 9, 0, -12, -4, -6, 0, -3, 0, 0, 0, -15, -4, 5, 0, -4, -8, -2, 0, 2, -12, 0, 0, -3, 0, 8, 0, -2, 0, -12, 0, 5, -4, -11, 0, 12, -16, -6, 0, 6, 0, -15, 0, -8, 0, 14, 0, 0, 0, 8, 0, 3, -2], 'euler11': [1, -3, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 2], 'euler23': [1, 0, 23], 'euler29': [1, 3, 29], 'euler3': [1, 2, 3], 'euler31': [1, 7, 31], 'euler37': [1, -8, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 15, 59], 'euler61': [1, -5, 61], 'euler67': [1, -2, 67], 'euler7': [1, 4, 7], 'euler71': [1, 3, 71], 'euler73': [1, -8, 73], 'euler79': [1, -5, 79], 'euler83': [1, -12, 83], 'euler89': [1, 15, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 2], [1, 2, 3], [1, 1, 0], [1, 4, 7], [1, -3, 11], [1, -2, 13], [1, -6, 17], [1, 0, 0], [1, 0, 23], [1, 3, 29], [1, 7, 31], [1, -8, 37], [1, 6, 41], [1, 4, 43], [1, -6, 47], [1, 6, 53], [1, 15, 59], [1, -5, 61], [1, -2, 67], [1, 3, 71], [1, -8, 73], [1, -5, 79], [1, -12, 83], [1, 15, 89], [1, -8, 97]], 'index': 43, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1805/a', 'ModularForm/GL2/Q/holomorphic/1805/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1805/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1805-1.1-c1-0-43', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-1805-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 528242284348825028, 'z1': {'__RealLiteral__': 0, 'data': '1.06417714624828988770031977779', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20735255
{'Lhash': '1349004798190808938291959784475', 'Lhash_array': ['1349004798190808938291959784475'], 'label': '2-1805-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/a'}
-
id: 24554637
{'Lhash': '1349004798190808938291959784475', 'Lhash_array': ['1349004798190808938291959784475'], 'label': '2-1805-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/a/1/1'}
-
id: 92107
{'Lhash': '528242284348825028', 'Lhash_array': ['528242284348825028'], 'label': '2-1805-1.1-c1-0-43', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1805/a'}