Formats: - HTML - YAML - JSON - 2026-10-15T06:13:06.350430
  • lfunc_lfunctions • Show schema
    {'Lhash': '2015732682576302867009781060650', 'a10': [-1.7660444431189781, -3.058878703906754], 'a2': [-0.766044443118978, -0.6427876096865394], 'a3': [-1.4396926207859084, 1.2080455471101075], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [3.3190778623577253, 1.2080455471101075], 'a6': [1.8793852415718169, -7.704816656998374e-61], 'a7': [0.8263518223330697, 0.3007674663608706], 'a8': [0.5, -0.8660254037844386], 'a9': [0.09239626545204768, -0.5240052604587699], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.766044443118978, 0.6427876096865394]]], [37, [[1.0, 0], [3.443563014047729, 5.0141673055735305]]]], 'bad_primes': [2, 37], 'central_character': '74.71', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3161230407108684249050742996160', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.766044443118978, 0.6427876096865394]], [[1.0, 0], [1.4396926207859084, -1.2080455471101075], [0.520944533000791, -2.9544232590366244]], [[1.0, 0], [-3.3190778623577253, -1.2080455471101075], [3.83022221559489, 3.2139380484326967]], [[1.0, 0], [-0.8263518223330697, -0.3007674663608706], [5.362311101832846, 4.499513267805775]], [[1.0, 0], [1.6736481776669303, -2.8988436777141864], [-5.5, -9.526279441628825]], [[1.0, 0], [1.1133407984528387, 6.314069429304249], [-12.216004070216808, 4.446261863233693]], [[1.0, 0], [0.520944533000791, -2.9544232590366244], [-15.974774553360442, -5.814342436536369]], [[1.0, 0], [-3.553033419238747, 2.981349031643783], [3.2993153756716764, -18.711347307231954]], [[1.0, 0], [2.9187480877851173, 5.055419982538329], [-11.5, 19.91858428704209]], [[1.0, 0], [-1.6342853314536299, 2.8306652281422298], [-14.5, -25.11473670974872]], [[1.0, 0], [1.1206147584281831, 0], [31.0, 0]], [[1.0, 0], [3.443563014047729, 5.0141673055735305]], [[1.0, 0], [-1.490199820236374, -8.451343148104126], [-38.527397452222246, 14.022825876352417]], [[1.0, 0], [-5.61586701824112, 0], [43.0, 0]], [[1.0, 0], [-2.564177772475912, -4.441286181567069], [-23.5, 40.703193977868615]], [[1.0, 0], [0.25237387009353146, -0.09185657662061078], [40.60035548530583, -34.067743313386586]], [[1.0, 0], [7.159100257716242, -2.60569939793621], [45.196622144019706, -37.92446897150582]], [[1.0, 0], [-0.36958506180819073, -2.0960210418350798], [-57.32124986794041, 20.863228742865793]], [[1.0, 0], [8.017540966287267, 2.918146263738451], [51.32497768897153, 43.066769848998135]], [[1.0, 0], [-10.071918558999553, 8.451343148104126], [12.329020614352055, -69.92135046386677]], [[1.0, 0], [8.573977952239538, 0], [73.0, 0]], [[1.0, 0], [-10.883255634833636, -3.9611811029893658], [60.51751100639927, 50.780221165236604]], [[1.0, 0], [-0.724155377117396, 4.106889224824294], [-77.9944875252304, -28.387671896030504]], [[1.0, 0], [7.86958506180819, -2.8642947185241336], [68.17795543758905, -57.208097262102]], [[1.0, 0], [-8.532088886237956, -14.778011445657894], [-48.5, 84.00446416709055]], [[1.0, 0], [0.5432332394751211, 0.9409075711311408], [-50.5, 87.4685657822283]], [[1.0, 0], [5.607411011951033, -9.712320771620403], [-51.5, -89.20061658979718]], [[1.0, 0], [-1.666374217691586, -9.450477805473975], [-100.5471104240922, 36.596155335846554]], [[1.0, 0], [1.7018666706430658, 1.4280356956495022], [18.927651365695407, 107.34404507833068]], [[1.0, 0], [3.5471036327369414, 2.9763733499771576], [19.62224407636313, 111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-74-37.34-c1-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/74/2/f/a/71/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.6996824312872112, 0.6816991965665813, 0.6698622157789784, 0.6616710708990778, 0.6539603755267624, 0.6430879213342914, 0.6250890252229265, 0.5957878999671279, 0.5508815928517254, 0.4860201359504106, 0.39690319217104203, 0.2794059787273614, 0.12973986562729084, -0.05535291995876146, -0.27837572822335244, -0.5408341462335368, -0.8429853072261202, -1.1835952204352826, -1.5597219686302917, -1.9665444267303993, -2.397257023663676, -2.843050715563752, -3.2931984994113184, -3.735260272126681, -4.155416528567814, -4.538933321110214, -4.870752259304177, -5.136189472110302, -5.321716930531274, -5.415789049815022, -5.4096679158967955, -5.298192763956181, -5.080434459769356, -4.760174623041867, -4.346152460183619, -3.8520308626356696, -3.296047045468643, -2.7003316851074524, -2.0899034090877575, -1.4913713276907268, -0.9314053247575967, -0.43505988404531126, -0.02405988642907569, 0.28482644708561505, 0.4811938502530936, 0.5620537699664957, 0.5324172705969815, 0.40531427989115354, 0.201193304691399, -0.05330772626452039, -0.3271757242087959, -0.5873224332913083, -0.8012175942392936, -0.9396573144179623, -0.9794373949810483, -0.9056869568293995, -0.7136247789073381, -0.4095312306827609, -0.010782336847940664, 0.4551332468564998, 0.9526037900128381, 1.4407819881401247, 1.8771645711453344, 2.221571764392891, 2.4401688598220517, 2.5091366650485427, 2.4175990179181968, 2.169457613712923, 1.7838668448209836, 1.2941995232527963, 0.7454991417086614, 0.1905727045284579, -0.31496579861214974, -0.7182548390515432, -0.9748015291939055, -1.0535597569613064, -0.9408882601525447, -0.6428849580719782, -0.18573484500609982, 0.3860980447585233, 1.013776177147684, 1.6297937436099563, 2.164959616016352, 2.5559546081646283, 2.752645649370386, 2.724311991021191, 2.464007852398972, 1.990451463498962, 1.3470800485209204, 0.5982203931394023, -0.17733765621144462, -0.8947511231301369, -1.4726295242813783, -1.8425640734092927, -1.957542973503399, -1.79818548507206, -1.3759339031619513, -0.7326687288072969, 0.06337488263471791, 0.9250584659370624, 1.7563906561090652, 2.4640422382341765, 2.968949439538011, 3.216549800034207, 3.1842986155264597, 2.885397930296702, 2.3681076791089417, 1.7105509732172095, 1.0115067389100956, 0.3782277241044413, -0.08724454357172619, -0.3015380719628587, -0.21141330864671803, 0.19834136082053488, 0.9017364838864079, 1.8336949759295376, 2.8973250764544582, 3.975525205874583, 4.945480246781325, 5.694173108326637, 6.132845563471164, 6.208434987607686, 5.910386565282324, 5.271850931090562, 4.365045803705108, 3.291381120791027, 2.1677024684752513, 1.1105840438734462, 0.22090888244721224, -0.42904360838459554, -0.8041320227618852, -0.9092764934656007, -0.7863768157182848, -0.5057459398102687, -0.15343254815756527, 0.18353824967138446, 0.43162862393932977, 0.5426019014424155, 0.5007353505638501, 0.3242106562077722, 0.06041034662529324, -0.22413036472147235, -0.4574395379936414, -0.5771392465850953, -0.5441354645735638, -0.3524484147296898, -0.03323681440012096, 0.34800068531161543, 0.7009171950741061, 0.9251943643680565, 0.9284847705566202, 0.6444365921479523, 0.047631653464863394, -0.8373833023692754, -1.934941108540358, -3.12570911272994, -4.262062410087296, -5.1892972268877635, -5.769499466716728, -5.90425853216564, -5.552404276538948, -4.739577837653012, -3.557648979846208, -2.1535862529039296, -0.7091191707276631, 0.5858844063165418, 1.5622430539313505, 2.097886114846541, 2.1375087582613572, 1.702065997471689, 0.8862952900332595, -0.15560541513474185, -1.2340434817224148, -2.1540671482638536, -2.746520345171613, -2.8951893241814597, -2.555405639237259, -1.760950449148776, -0.6180528055462899, 0.7125376660478284, 2.0423737677266485, 3.186451478422782, 3.9933266696584595, 4.369035162104348, 4.290730071913545, 3.807772824096254, 3.030253744218868, 2.107173762324107, 1.1983789373235165, 0.44545798859994545, -0.053025309517217796, -0.25742893247282206, -0.19121093269202075, 0.06722597549432086, 0.40327884441185136, 0.6916938794001322, 0.8238131254764808, 0.7310677708142369, 0.3999854917577161, -0.12436519479205232, -0.7472864842671759, -1.3440372476433107, -1.7862323573201877, -1.969747466705812, -1.838410135125567, -1.3984872740932617, -0.7207284734200782, 0.07083159211076032, 0.8214443971257875, 1.3753707886061912, 1.6069717778345094, 1.4469467268076674, 0.8983071372332703, 0.03859568451665832, -0.992465304440133, -2.017806438666319, -2.855682758850683, -3.3538692118959257, -3.418634201868862, -3.032673859837051, -2.2583200826394765, -1.225259105664326, -0.1051319028372886, 0.9219080730901483, 1.7018990602874395, 2.1359261369975453, 2.1971608936934293, 1.9325325651727872, 1.4486828485065084, 0.8851974846174345, 0.3808810467268288, 0.040444219038698256, -0.09096742322415922, -0.03951357538560813, 0.10236501777418636, 0.19716731493799997, 0.09558444882017154, -0.3252007739648558, -1.126562086711298, -2.284867710659386, -3.685246154478468, -5.135148988024683, -6.396036590317272, -7.227554403276247, -7.435642524236226, -6.914788670312074, -5.675414328636908, -3.8500804272998095, -1.676307196484552, 0.5414958690979935, 2.484167698283324, 3.8741423107887574, 4.525065443554099, 4.374887115685413, 3.4958120513813458, 2.07906969148577, 0.3975141543887698], 'positive_zeros': ['1.59013270866072073062704600361149', '5.25838212421876824016455278449921', '6.10008485594824768482219715413167', '7.25307361417278530826443201261018', '8.920002900746058253705129010598021', '9.792830713763479052593183120254705', '11.22108590087094980326940917592017', '12.24059055514355753039499905888493', '13.72130744303775566914454541995197', '14.07589548316873670257593598046331'], 'prelabel': '2-74-37.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.07850844723298615, 'root_number': '0.8807829838304243 - 0.4735201531030908*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.078508447233', 'prec': 37}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59013270866072073062704600361', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '5.25838212421876824016455278450', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.10008485594824768482219715413', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.34', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/f/a/71/1'], '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': '2-74-37.34-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-74-37.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.07850844723298615, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59013270866072073062704600361', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2015732682576302867009781060650', 'Lhash_array': ['2015732682576302867009781060650'], 'factors': ['2-74-37.34-c1-0-1'], 'label': '2-74-37.34-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/f/a/71/1'}