-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1584306093494224758690754209880', 'a10': 1, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.21402729138467, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '4410.1', 'coefficient_field': '1.1.1.1', 'conductor': 4410, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1], [1, 2, 11], [1, -2, 13], [1, -4, 17], [1, 0, 19], [1, 8, 23], [1, 0, 29], [1, 2, 31], [1, -8, 37], [1, -2, 41], [1, 2, 43], [1, 10, 47], [1, -2, 53], [1, 4, 59], [1, 10, 61], [1, -2, 67], [1, -12, 71], [1, -10, 73], [1, -16, 79], [1, 16, 83], [1, 14, 89], [1, -6, 97], [1, -14, 101], [1, 20, 103], [1, 12, 107], [1, 2, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 1], 1]], [1], [[[1, 2, 11], 1]], [[[1, -2, 13], 1]], [[[1, -4, 17], 1]], [[[1, 0, 19], 1]], [[[1, 8, 23], 1]], [[[1, 0, 29], 1]], [[[1, 2, 31], 1]], [[[1, -8, 37], 1]], [[[1, -2, 41], 1]], [[[1, 2, 43], 1]], [[[1, 10, 47], 1]], [[[1, -2, 53], 1]], [[[1, 4, 59], 1]], [[[1, 10, 61], 1]], [[[1, -2, 67], 1]], [[[1, -12, 71], 1]], [[[1, -10, 73], 1]], [[[1, -16, 79], 1]], [[[1, 16, 83], 1]], [[[1, 14, 89], 1]], [[[1, -6, 97], 1]], [[[1, -14, 101], 1]], [[[1, 20, 103], 1]], [[[1, 12, 107], 1]], [[[1, 2, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-4410-1.1-c1-0-44', '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/4410/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.601025916918524e-61, 0.12038083889553891, 0.23998395854430313, 0.35800556248536713, 0.4735915984293714, 0.5858172454225218, 0.693671587880622, 0.7960486666437147, 0.8917457180299626, 0.9794690209673284, 1.0578474002310976, 1.1254531017896174, 1.1808294751912074, 1.2225246698315497, 1.249130372548466, 1.2593244757029074, 1.2519164594178545, 1.225894191827046, 1.1804707921179847, 1.115130160473372, 1.029669756721677, 0.9242392074734646, 0.7993733428652559, 0.656018312484394, 0.49554950935849185, 0.3197801443439949, 0.1309594632574604, -0.06824021308941677, -0.2747482202983343, -0.48513238607864007, -0.6956480088137086, -0.9022986954581353, -1.1009084316754854, -1.2872039000785753, -1.4569057011275237, -1.6058267760245617, -1.7299759930198617, -1.8256645496564854, -1.8896125755810265, -1.9190531053925026, -1.9118304397673636, -1.8664898359407442, -1.7823554742608207, -1.65959374282692, -1.4992590717914918, -1.3033198347780657, -1.0746622161859294, -0.8170704159592053, -0.5351821204987123, -0.23441879932215373, 0.07910892183742389, 0.39871982624923513, 0.7173028658457712, 1.0274776104506005, 1.3217711417715494, 1.5928074530946408, 1.8335047919953906, 2.037275854995638, 2.1982253332772443, 2.3113390385436445, 2.3726587261370335, 2.3794367929971183, 2.330265270828959, 2.2251739645266766, 2.0656932012874987, 1.8548774495984333, 1.5972870256875098, 1.2989262080699135, 0.9671373023542729, 0.6104515067390313, 0.23839878691535205, -0.13871966333330696, -0.5100914663266107, -0.8646794463600154, -1.191527065557751, -1.4800746585039568, -1.7204774650838495, -1.9039159582251832, -2.0228887374725697, -2.0714783333589404, -2.045580655357986, -1.9430895219804503, -1.7640287289262706, -1.5106254227696523, -1.1873201250797436, -0.8007105561634891, -0.3594283898688154, 0.12604982651500446, 0.6436541950857644, 1.1800298971413068, 1.7208949384398509, 2.251437724239025, 2.756743317941529, 3.2222358776804856, 3.634123766837781, 3.9798332476878016, 4.248416530409828, 4.430920286868741, 4.520701558444306, 4.513679281696083, 4.408511399450105, 4.20668967550847, 3.9125468297304664, 3.53317338280676, 3.078244559729875, 2.559760650427044, 1.9917072606443342, 1.3896447975781707, 0.7702392146627923, 0.15074838418299175, -0.4515196209862568, -1.019758658073265, -1.5382085655565318, -1.9926724619793208, -2.370989099113028, -2.6634432199238245, -2.863098659316544, -2.9660413115563635, -2.971522003251892, -2.881992663191626, -2.70303285891833, -2.4431676473964496, -2.113581624422246, -1.7277379086938955, -1.3009144144654337, -0.849673008517146, -0.3912798798751846, 0.056902443029769205, 0.4780296098801575, 0.8563740940480112, 1.177885807861748, 1.430693625431676, 1.6055286731591953, 1.696052941208837, 1.6990801461541918, 1.61467971909857, 1.4461591624847316, 1.1999246494636095, 0.8852244542458915, 0.513784414500228, 0.0993489511538659, -0.34285497254482394, -0.7967103470021668, -1.245836013516009, -1.6742213514735327, -2.066844558174592, -2.4102497521642032, -2.693059575202719, -2.9064023878616077, -3.044236467177587, -3.1035577005320407, -3.0844819714781577, -2.990198564695923, -2.8267962703975957, -2.6029692211395075, -2.3296146191155835, -2.019339187439196, -1.6858951970235403, -1.3435700976936633, -1.0065559668105941, -0.6883260695150338, -0.4010457359596456, -0.15504348654844635, 0.041634088193987166, 0.18356367407999075, 0.2681672022107832, 0.295804000038607, 0.26972837953412593, 0.19591390032606923, 0.08275155374604423, -0.05936512183228816, -0.2185497264821009, -0.38200471253326923, -0.536648819302107, -0.6697615335122021, -0.7696147681978082, -0.826062189962861, -0.8310582236040219, -0.7790816750612058, -0.667443027785196, -0.49645961551728834, -0.2694888364675121, 0.007183912046198402, 0.3245991263921683, 0.6715087440316004, 1.0348768196845093, 1.4004731237922101, 1.753532728198244, 2.079451108010027, 2.364482134792573, 2.5964056927548023, 2.765132575762113, 2.8632168049334314, 2.886249456033131, 2.833113342776028, 2.7060842405681345, 2.510771472529631, 2.255898288917827, 1.9529301955907776, 1.6155668569843435, 1.2591200485654341, 0.8998060192891315, 0.5539852418746666, 0.23738562829692308, -0.03565331131345213, -0.2528782884533715, -0.40472717483005033, -0.48481016379760083, -0.49024180966815983, -0.42180549769056075, -0.28393983038224235, -0.08454501440434181, 0.16538381420608708, 0.45228071207060827, 0.7606668169075449, 1.0739112775134427, 1.375058849782385, 1.647683835851596, 1.8767280313253734, 2.0492804094069235, 2.1552584509029193, 2.187955260778617, 2.1444227263463227, 2.0256687021370476, 1.8366551977071934, 1.5860943712575137, 1.286049316406913, 0.9513566652378742, 0.5988974072024322, 0.24675055166328402, -0.08672910034691256, -0.3838631337969739, -0.6285832723562423, -0.807298314608013, -0.9096483154552018, -0.9291049277247552, -0.8633838783025151, -0.7146445072180516, -0.4894617316611755, -0.19856720929455868, 0.14363169605907106, 0.5197348952630235, 0.9102033846610524, 1.2943432631220868, 1.6513717026098091, 1.9615113040974328, 2.20705659560081, 2.373356593188636, 2.4496604063273693, 2.429778735290277, 2.3125225433399863, 2.101890814695944, 1.806991633667532, 1.441694244305956, 1.0240236062834074, 0.5753225462871937, 0.11921920750476579], 'positive_zeros': ['1.24979713906101910546215642697558', '2.33204798281233056497306690115848', '3.31087163591472057096060241034790', '4.06629526197223222816484229229899', '5.12093189466540454647169223996312', '5.94705054602857403405343515865756', '6.57323036473501188579582470227617', '7.62956306664857265185293718480544', '7.950071907738146671044592304392172'], 'prelabel': '2-4410-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.93414082166784, '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': 2038027397734477177, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24979713906101910546215642698', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33204798281233056497306690116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31087163591472057096060241035', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 35.21402729138467, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 4410, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 0, -1, 0, 1, -2, 0, 2, 0, 0, 1, 4, 0, 0, -1, 0, 2, -8, 0, 1, -2, 0, 0, 0, 0, -2, -1, 0, -4, 0, 0, 8, 0, 0, 1, 2, 0, -2, -2, 0, 8, -10, 0, 0, -1, 0, 2, 2, 0, 2, 0, 0, 0, -4, 0, -10, 2, 0, 1, -2, 0, 2, 4, 0, 0, 12, 0, 10, -8, 0, 0, 0, 0, 16, -1, 0, -2, -16, 0, -4, 2, 0, 2, -14, 0, 0, -8, 0, 10, 0, 0, 6, 0, 0, 1], 'euler11': [1, 2, 11], 'euler13': [1, -2, 13], 'euler17': [1, -4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 8, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -8, 37], 'euler41': [1, -2, 41], 'euler43': [1, 2, 43], 'euler47': [1, 10, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -2, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, -10, 73], 'euler79': [1, -16, 79], 'euler83': [1, 16, 83], 'euler89': [1, 14, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 2, 11], [1, -2, 13], [1, -4, 17], [1, 0, 19], [1, 8, 23], [1, 0, 29], [1, 2, 31], [1, -8, 37], [1, -2, 41], [1, 2, 43], [1, 10, 47], [1, -2, 53], [1, 4, 59], [1, 10, 61], [1, -2, 67], [1, -12, 71], [1, -10, 73], [1, -16, 79], [1, 16, 83], [1, 14, 89], [1, -6, 97]], 'index': 44, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4410/e', 'ModularForm/GL2/Q/holomorphic/4410/2/a/e/1/1', 'ModularForm/GL2/Q/holomorphic/4410/2/a/e'], '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': '2-4410-1.1-c1-0-44', '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': '2-4410-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.93414082166784, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2038027397734477177, 'z1': {'__RealLiteral__': 0, 'data': '1.24979713906101910546215642698', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 19989573
{'Lhash': '1584306093494224758690754209880', 'Lhash_array': ['1584306093494224758690754209880'], 'label': '2-4410-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4410/2/a/e'}
-
id: 24565803
{'Lhash': '1584306093494224758690754209880', 'Lhash_array': ['1584306093494224758690754209880'], 'label': '2-4410-1.1-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4410/2/a/e/1/1'}
-
id: 102739
{'Lhash': '2038027397734477177', 'Lhash_array': ['2038027397734477177'], 'label': '2-4410-1.1-c1-0-44', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4410/e'}