-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1561073419067845899798098675285', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.6804261373209242, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.67882563723714, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '8100.1', 'coefficient_field': 'CDF', 'conductor': 8100, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.6804261373209242, 0], [7.0, 0]], [[1.0, 0], [-1.6804261373209242, 0], [11.0, 0]], [[1.0, 0], [5.145025443368211, 0], [13.0, 0]], [[1.0, 0], [1.3195738626790758, 0], [17.0, 0]], [[1.0, 0], [0.32464179184022807, 0], [19.0, 0]], [[1.0, 0], [-3.7892410978875146, 0], [23.0, 0]], [[1.0, 0], [-8.645835232217117, 0], [29.0, 0]], [[1.0, 0], [4.145025443368211, 0], [31.0, 0]], [[1.0, 0], [1.3557843454806962, 0], [37.0, 0]], [[1.0, 0], [-7.150093372529363, 0], [41.0, 0]], [[1.0, 0], [-7.290050886736421, 0], [43.0, 0]], [[1.0, 0], [12.965409094896193, 0], [47.0, 0]], [[1.0, 0], [8.830519509850287, 0], [53.0, 0]], [[1.0, 0], [8.81531572236683, 0], [59.0, 0]], [[1.0, 0], [-9.970477024057345, 0], [61.0, 0]], [[1.0, 0], [-4.176167997008679, 0], [67.0, 0]], [[1.0, 0], [-0.8911850394334097, 0], [71.0, 0]], [[1.0, 0], [-7.820383651527982, 0], [73.0, 0]], [[1.0, 0], [-9.655971090539422, 0], [79.0, 0]], [[1.0, 0], [-4.856594134329603, 0], [83.0, 0]], [[1.0, 0], [17.476354742067404, 0], [89.0, 0]], [[1.0, 0], [8.934266541255726, 0], [97.0, 0]], [[1.0, 0], [-10.856594134329603, 0], [101.0, 0]], [[1.0, 0], [11.682045715018738, 0], [103.0, 0]], [[1.0, 0], [-5.115502467425556, 0], [107.0, 0]], [[1.0, 0], [-7.171100067847527, 0], [109.0, 0]], [[1.0, 0], [17.645835232217117, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 53, 'label': '2-90e2-1.1-c1-0-53', '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/8100/2/a/ba/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.264942165909329e-61, 0.1923470966947394, 0.38322838413666455, 0.5711399967813396, 0.7545053063777442, 0.9316466690399741, 1.1007662674360992, 1.2599380665476927, 1.407112184425907, 1.5401322362689598, 1.656765498739217, 1.7547451031345778, 1.8318229241873252, 1.8858313933591364, 1.9147521275918817, 1.9167890163233376, 1.8904432391698678, 1.8345875834459342, 1.7485373872794672, 1.632115446855672, 1.485708294948001, 1.3103113843977918, 1.1075608977885676, 0.8797501564345008, 0.6298289201258797, 0.36138425411029385, 0.07860208927013418, -0.21379088982415645, -0.5106048347093705, -0.8062830074543944, -1.0950153227556354, -1.3708671094702445, -1.6279204240743321, -1.860424662463891, -2.062952685877877, -2.230558223963231, -2.3589299649477224, -2.4445375098543556, -2.4847642725792185, -2.4780224650547606, -2.4238455270791137, -2.32295374925943, -2.1772893949179175, -1.990018346770477, -1.7654961744549904, -1.5091975209540855, -1.2276088148366722, -0.9280855004773308, -0.6186762043499718, -0.3079174823029515, -0.00460397755634973, 0.28246008249077936, 0.5447211553269479, 0.7741407299368162, 0.9634554836418487, 1.1064246517370642, 1.1980559593400886, 1.2348017085882645, 1.2147171652140218, 1.1375742462516385, 1.0049246634429103, 0.820108101341803, 0.5882026700474849, 0.31591672370262974, 0.011423121089514833, -0.315860941027405, -0.6555433392363471, -0.9965685231953489, -1.3275621293953472, -1.637198148483349, -1.9145768033118247, -2.149600380860983, -2.3333337696499417, -2.4583364262425595, -2.5189529554555437, -2.5115504469034744, -2.4346921547476286, -2.289239007622615, -2.0783727419289044, -1.8075370956621009, -1.4842963964688154, -1.1181139270149452, -0.7200555421421276, -0.3024270274183763, 0.12164349368581942, 0.5386642961262444, 0.9352640543631217, 1.298683689396108, 1.6172577184557035, 1.8808665190133855, 2.081341392713223, 2.2128055199466248, 2.271935815103503, 2.258133279113191, 2.17359262334582, 2.0232656031642646, 1.814716521567648, 1.5578725941177247, 1.2646761411577587, 0.9486497187072647, 0.6243891397649726, 0.3070027027726997, 0.011517676133275492, -0.2477229505734823, -0.4576493573678183, -0.6070152137038115, -0.686886092253479, -0.6910445183353935, -0.6162930293173753, -0.46264032105419545, -0.2333600048269909, 0.0650834749743733, 0.423241799633617, 0.8290170688828666, 1.2681123724770238, 1.7245823794616917, 2.1814630201798386, 2.621455434350317, 3.0276364135044074, 3.384165737020238, 3.6769602036264026, 3.894304859729813, 4.027373932092354, 4.070637237205036, 4.0221322572989004, 3.8835874821899474, 3.660388806047344, 3.36138748550409, 2.998555124951321, 2.586498050756887, 2.1418499559150836, 1.6825675347630418, 1.2271586997972028, 0.7938766304545245, 0.39991514612550594, 0.060641580696200986, -0.21109761086575782, -0.405565863168268, -0.5165916158919256, -0.5418665693031847, -0.4830708524058544, -0.3458165221501274, -0.13940903391332654, 0.12356524783647964, 0.4278091836941265, 0.7560186518678932, 1.0896892919714303, 1.4099900643784031, 1.6986636427821764, 1.9389116150290542, 2.1162223709865873, 2.219101458968805, 2.2396680522861248, 2.1740868476705866, 2.022811988975209, 1.7906281609061363, 1.4864834465616241, 1.1231184534959668, 0.7165061162928256, 0.2851259978083316, -0.1508946335554621, -0.5707336118460298, -0.9538759380811043, -1.281117253532837, -1.5355199310434693, -1.7032744242713227, -1.774422301315384, -1.7434033965070765, -1.6093974933421393, -1.3764405492511416, -1.0533062465150729, -0.6531550910512194, -0.19296482456360523, 0.3072330101772567, 0.8252754719383604, 1.3379062346458268, 1.8218793979160286, 2.2550752110032017, 2.6175723992569204, 2.892623121962532, 3.0674806841678075, 3.1340368183864613, 3.089234353909648, 2.9352319859664493, 2.679310121907512, 2.3335198128580914, 1.914089920392678, 1.440620242701744, 0.9350996726733196, 0.42079797060015933, -0.07891312068848556, -0.541749325423729, -0.9476524491881798, -1.2798186316462912, -1.525561724656447, -1.67696522765896, -1.7312867224827855, -1.6910913159526708, -1.564104592686784, -1.362790285968883, -1.103672523501679, -0.8064363172843311, -0.4928521925188154, -0.18558080953157477, 0.09307944612158874, 0.32243507672857696, 0.48456313644520244, 0.5653360772255762, 0.5552486811721509, 0.4499999404071435, 0.2507953996573806, -0.03564981259980563, -0.39741103594271127, -0.8179445386510114, -1.2769397131652784, -1.7513896586619444, -2.2168242795132724, -2.648640375891836, -3.023456997452602, -3.3204219697264956, -3.522397177702453, -3.61695587484693, -3.5971347292376565, -3.461896059798907, -3.2162711021388346, -2.871172364308413, -2.4428812610146333, -1.9522352570610129, -1.4235557015284004, -0.8833724318379514, -0.35901320840317513, 0.12286560793119014, 0.5377265242272486, 0.864496168584939, 1.0867327190768528, 1.1935489519568612, 1.1802372583875866, 1.0485590657801676, 0.8066795046130959, 0.4687478759655233, 0.054144400337726106, -0.41356726319786, -0.907925239996668, -1.4010219242923356, -1.865043095282116, -2.2738073614594136, -2.604218816165914, -2.8375499446756374, -2.9604807781889346, -2.9658335906439537, -2.8529593705266407, -2.627751941576862, -2.3022868529198446, -1.8941038011028357, -1.4251721337236902, -0.9205976984471662, -0.4071448271645048], 'positive_zeros': ['1.23146979048232082764371199717475', '2.34447782051954629856768543658886', '3.00168405481693189380235743242112', '3.92403998176683022503862785656440', '4.78318570469792800809332639777366', '5.19370950570824984585935498537932', '6.33758484107047460082019552176999', '6.68218101811703885060454974484168', '7.48369500254062751897195672675549'], 'prelabel': '2-90e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.042314693994332, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23146979048232082764371199717', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34447782051954629856768543659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00168405481693189380235743242', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.67882563723714, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 8100, 'conductor_radical': 30, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8100/2/a/ba/1/2'], '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': '2-90e2-1.1-c1-0-53', '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': '2-90e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.042314693994332, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23146979048232082764371199717', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1561073419067845899798098675285', 'Lhash_array': ['1561073419067845899798098675285'], 'factors': ['2-90e2-1.1-c1-0-53'], 'label': '2-90e2-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8100/2/a/ba/1/2'}