-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1219531880552901980071133710007', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.205891660851936, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '2280.1', 'coefficient_field': '1.1.1.1', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, -6, 17], [1, 1], [1, 4, 23], [1, 10, 29], [1, -4, 31], [1, -10, 37], [1, -6, 41], [1, 0, 43], [1, 12, 47], [1, -10, 53], [1, 0, 59], [1, 10, 61], [1, -4, 67], [1, 0, 71], [1, -10, 73], [1, -4, 79], [1, -12, 83], [1, -14, 89], [1, 2, 97], [1, -6, 101], [1, 16, 103], [1, -20, 107], [1, -2, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -6, 17], 1]], [[[1, 1], 1]], [[[1, 4, 23], 1]], [[[1, 10, 29], 1]], [[[1, -4, 31], 1]], [[[1, -10, 37], 1]], [[[1, -6, 41], 1]], [[[1, 0, 43], 1]], [[[1, 12, 47], 1]], [[[1, -10, 53], 1]], [[[1, 0, 59], 1]], [[[1, 10, 61], 1]], [[[1, -4, 67], 1]], [[[1, 0, 71], 1]], [[[1, -10, 73], 1]], [[[1, -4, 79], 1]], [[[1, -12, 83], 1]], [[[1, -14, 89], 1]], [[[1, 2, 97], 1]], [[[1, -6, 101], 1]], [[[1, 16, 103], 1]], [[[1, -20, 107], 1]], [[[1, -2, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-2280-1.1-c1-0-11', 'leading_term': '1.827873442134534143919430729951500000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2280/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.8278734421345342, 1.8217110113081978, 1.8031182051528025, 1.7717906024434762, 1.727260236490908, 1.6689513605466892, 1.5962523515433686, 1.508598626892619, 1.4055611674400728, 1.2869354352401714, 1.1528259844469195, 1.0037227195164462, 0.8405654257638158, 0.6647938060067089, 0.4783807783038427, 0.28384723628842706, 0.08425687869832339, -0.11680988224917574, -0.31530348796117336, -0.5067743362983865, -0.6864629153414584, -0.8494098265187001, -0.9905838570879458, -1.105025521183858, -1.1880027321440343, -1.2351745287537217, -1.2427580902663586, -1.2076936774008251, -1.1278016670283704, -1.0019255434063168, -0.8300546016719488, -0.6134202377779117, -0.3545600641085654, -0.0573447141048986, 0.273036915173002, 0.6301370951107651, 1.0063551138542586, 1.3930897117704237, 1.780936549092303, 2.159927325695417, 2.5198053144444454, 2.8503302514229603, 3.1416038279037077, 3.3844055319063386, 3.5705273724549755, 3.693095163348867, 3.7468636129954973, 3.728472517793012, 3.6366519277450062, 3.472365264115868, 3.238881017587341, 2.94176581518097, 2.5887942638646013, 2.1897739821728783, 1.7562875187842737, 1.3013563083441395, 0.8390352923110742, 0.38395018644744366, -0.049207549250572864, -0.4462103433779438, -0.793828997690936, -1.0803509312325936, -1.296060575005059, -1.4336606952098174, -1.4886147575013033, -1.4593927292928337, -1.3476059106927125, -1.1580204005860706, -0.8984435116467107, -0.5794826741338198, -0.21418190455780955, 0.1824534755230725, 0.5940277594307367, 1.0034003243650038, 1.393380288181049, 1.7474416697372015, 2.0504282054429543, 2.289216138963369, 2.453303906064151, 2.5352997318051744, 2.5312817218927153, 2.441009969417772, 2.267976344246891, 2.0192847470948125, 1.705362393980168, 1.3395107991268018, 0.9373131596837619, 0.5159224103321738, 0.0932609082966855, -0.3128318493100252, -0.685463218458665, -1.0095208558241306, -1.272433413642219, -1.4648184624520648, -1.5809819369686473, -1.6192397164468981, -1.5820400322888728, -1.475874901331156, -1.3109792800838493, -1.1008276161381676, -0.8614483804357036, -0.6105874174000941, -0.3667599754872295, -0.14823854356894936, 0.027971346440052863, 0.14711274957461468, 0.19756216538139992, 0.17156675004176922, 0.06578922114935964, -0.11837533406980881, -0.37473537588089534, -0.6925032521699427, -1.0567575956720001, -1.4491509459048504, -1.848831678195968, -2.2335364154811033, -2.5807981362539447, -2.8692068638905996, -3.0796546994608653, -3.1964954562154855, -3.2085514958607497, -3.109906572279736, -2.9004333561231035, -2.5860174249848584, -2.178455237377943, -1.6950211676096245, -1.1577171292492214, -0.5922366350679015, -0.02669227636936287, 0.5098294726280048, 0.9888104475423719, 1.383856475061832, 1.6721797351607708, 1.835922577679667, 1.8632441018427608, 1.7491020830542119, 1.4956783470373933, 1.112414678320823, 0.6156478070100877, 0.027854762157767464, -0.6234573878864204, -1.3071620110845572, -1.9901494919882292, -2.639100944347232, -3.2223000739594343, -3.7113797892827294, -4.082901750304243, -4.319674725711535, -4.411731100512879, -4.356899485315315, -4.160934135614802, -3.8371875225535614, -3.405839419739987, -2.8927226694830415, -2.3278107195472586, -1.7434535011412988, -1.1724648434205398, -0.6461752461255971, -0.19256766051315455, 0.16538943575728576, 0.4111078954689814, 0.5353580766902276, 0.5367956010504304, 0.4220002418710753, 0.20502054157882707, -0.09355126429995617, -0.4479194883772407, -0.8287588793893413, -1.2051183985631275, -1.5464351625991686, -1.8245303005529563, -2.0154580739044494, -2.1010875312488806, -2.070311859298663, -1.9198035680607721, -1.6542623421420337, -1.2861350262188758, -0.8348217142306975, -0.32541603200877534, 0.21294082975098838, 0.7489861061539818, 1.251415247076702, 1.6909774152197339, 2.042445826261375, 2.2863287312318223, 2.4102026810541872, 2.4095738256787627, 2.2882039032464396, 2.0578732910067714, 1.737591670134233, 1.3523049321741623, 0.9311823081563378, 0.5055978457360231, 0.10694311407392447, -0.23557833630478067, -0.49702081309367513, -0.6584839219990344, -0.7084885202964379, -0.6438390481516251, -0.46990468504870486, -0.2002917175527833, 0.14407790443660226, 0.5364245521610286, 0.946009168965722, 1.3403426258999387, 1.6875527026269073, 1.9587413666949225, 2.130162843301582, 2.1850628454031726, 2.1150408103146234, 1.9208287644301112, 1.6124204468771597, 1.208529864294, 0.7354063641415951, 0.22508020445406582, -0.2868449356802857, -0.7637011730091982, -1.170391399716554, -1.475961675550213, -1.655923692282968, -1.6941545769109585, -1.5842287205929555, -1.3300748229486097, -0.9458983491742825, -0.45536185785796596, 0.10993053552776644, 0.7125468386396697, 1.3117959887294208, 1.8665730688290492, 2.3382789183180304, 2.693603176461195, 2.906966139669338, 2.9624362722324262, 2.854975496195849, 2.5909111618014307, 2.1875886320109896, 1.672217794106951, 1.0799862300133007, 0.4515668395576162, -0.1698057392246781, -0.7414811344866948, -1.2245333420107531, -1.586663642517587, -1.8046491999824175, -1.8661506873901215, -1.7707371016046516, -1.5300419675625605, -1.1670283865231779, -0.7144062348304016, -0.21230837555100332, 0.2946107969551653, 0.7604461466179058, 1.1414435715730675, 1.3992818774838478, 1.503989983519134, 1.4362792800154671, 1.1891123892868163], 'positive_zeros': ['0.962041023238845099053363878952389', '1.94416852136943820176158401884014', '3.39156409204262818849202841222339', '4.13362534201749987180283134496233', '5.16940849835265890817106579659025', '6.08317621586618125737703438550152', '6.35198931281804077801342630786323', '7.50281712761657102889086692836274', '8.147138876990079866417523759053142', '9.287180121684984784965900213764674'], 'prelabel': '2-2280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1387971774104927074, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.962041023238845099053363878952', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.94416852136943820176158401884', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39156409204262818849202841222', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.205891660851936, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 2280, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 0, 0, 1, 0, 4, 0, 2, 0, -1, 0, 6, 0, -1, 0, 0, 0, -4, 0, 1, 0, -1, 0, -10, 0, 4, 0, -4, 0, 0, 0, 10, 0, -2, 0, 6, 0, 0, 0, 1, 0, -12, 0, -7, 0, -6, 0, 10, 0, 4, 0, 1, 0, 0, 0, -10, 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 0, 10, 0, -1, 0, 0, 0, 4, 0, 1, 0, 12, 0, 6, 0, 10, 0, 14, 0, 0, 0, -4, 0, -1, 0, -2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, -6, 41], 'euler43': [1, 0, 43], 'euler47': [1, 12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, -6, 17], [1, 1, 0], [1, 4, 23], [1, 10, 29], [1, -4, 31], [1, -10, 37], [1, -6, 41], [1, 0, 43], [1, 12, 47], [1, -10, 53], [1, 0, 59], [1, 10, 61], [1, -4, 67], [1, 0, 71], [1, -10, 73], [1, -4, 79], [1, -12, 83], [1, -14, 89], [1, 2, 97]], 'index': 11, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2280/b', 'ModularForm/GL2/Q/holomorphic/2280/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/2280/2/a/b'], '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': '2-2280-1.1-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2280-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.266836258968926, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1387971774104927074, 'z1': {'__RealLiteral__': 0, 'data': '0.962041023238845099053363878952', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20620583
{'Lhash': '1219531880552901980071133710007', 'Lhash_array': ['1219531880552901980071133710007'], 'label': '2-2280-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2280/2/a/b'}
-
id: 24556520
{'Lhash': '1219531880552901980071133710007', 'Lhash_array': ['1219531880552901980071133710007'], 'label': '2-2280-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2280/2/a/b/1/1'}
-
id: 98876
{'Lhash': '1387971774104927074', 'Lhash_array': ['1387971774104927074'], 'label': '2-2280-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2280/b'}