-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1475183095817770081633921893806', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0.8161295639744651, 0], 'a6': [0, 0], 'a7': [6.233306078947916, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.55060032897724, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [9.924506306025943, 16.201980575894147]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.721', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '773582845356911137182759771843', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8161295639744651, 0], [25.0, 0]], [[1.0, 0], [-6.233306078947916, 0], [49.0, 0]], [[1.0, 0], [-7.419916639188812, 0], [121.0, 0]], [[1.0, 0], [0, -0.6411912330140079], [-169.0, 0]], [[1.0, 0], [-26.464278325003775, 0], [289.0, 0]], [[1.0, 0], [9.924506306025943, 16.201980575894147]], [[1.0, 0], [14.146189777690601, 0], [529.0, 0]], [[1.0, 0], [0, 45.54518313594793], [-841.0, 0]], [[1.0, 0], [0, 24.853644796514583], [-961.0, 0]], [[1.0, 0], [0, 15.72284215739785], [-1369.0, 0]], [[1.0, 0], [0, 23.775151610436286], [-1681.0, 0]], [[1.0, 0], [-47.289231408813414, 0], [1849.0, 0]], [[1.0, 0], [-89.42377154492632, 0], [2209.0, 0]], [[1.0, 0], [0, 16.792459739104487], [-2809.0, 0]], [[1.0, 0], [0, -4.086252103101831], [-3481.0, 0]], [[1.0, 0], [94.19953537797664, 0], [3721.0, 0]], [[1.0, 0], [0, -39.826930547537124], [-4489.0, 0]], [[1.0, 0], [0, -124.42998788977009], [-5041.0, 0]], [[1.0, 0], [68.50166912711755, 0], [5329.0, 0]], [[1.0, 0], [0, 34.21259806424824], [-6241.0, 0]], [[1.0, 0], [-11.088276820853071, 0], [6889.0, 0]], [[1.0, 0], [0, -115.79072543053992], [-7921.0, 0]], [[1.0, 0], [0, 150.70503261253444], [-9409.0, 0]], [[1.0, 0], [-81.4617651515977, 0], [10201.0, 0]], [[1.0, 0], [0, 3.6477847532674668], [-10609.0, 0]], [[1.0, 0], [0, 138.03403129743188], [-11449.0, 0]], [[1.0, 0], [0, 111.30240905433838], [-11881.0, 0]], [[1.0, 0], [0, 50.17302386558744], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 77, 'label': '2-2736-19.18-c2-0-77', 'leading_term': '2.4583697651998058894334259049221052880511619249270563126', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2736/3/o/r/721/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.458369765199806, 2.568634994476365, 2.657376499428936, 2.7237045020129225, 2.7668988445576805, 2.786419213916114, 2.7819189760876935, 2.753262208646139, 2.700543248771405, 2.624107835927198, 2.5245747304400323, 2.402856539985618, 2.2601783901486248, 2.0980930351695757, 1.918491020951333, 1.723604582852405, 1.516004082899228, 1.2985859609706343, 1.0745513876692876, 0.8473750578230087, 0.6207638471326985, 0.39860536412064107, 0.18490675833880363, -0.01627551379027027, -0.20091392036851682, -0.36509469936673994, -0.505107611649031, -0.6175385976513299, -0.6993630714956993, -0.7480373700530409, -0.7615857141868418, -0.7386799445308562, -0.6787092730463742, -0.5818373512031982, -0.44904410103321746, -0.28214998941303737, -0.08382074910371376, 0.14244904013583706, 0.39237460609400904, 0.6609424064995972, 0.9424942270122538, 1.230833191936578, 1.5193502254883162, 1.8011687934265768, 2.069305060075464, 2.3168399375355446, 2.537098906292307, 2.7238349734753213, 2.8714097298279717, 2.9749671903637047, 3.0305949753989725, 3.035467423318748, 2.98796543484637, 2.8877682364686295, 2.7359128180294325, 2.534817540227234, 2.2882673093013213, 2.0013587595796376, 1.680405044517914, 1.3328010822656415, 0.9668513963493524, 0.5915639952065591, 0.21641500235666442, -0.14891006348887495, -0.494791397796772, -0.8119585577590024, -1.0917741177701599, -1.32650837184113, -1.5095959693471623, -1.6358655179720352, -1.7017336478183125, -1.705355805530868, -1.6467271278310225, -1.5277281093669928, -1.3521113979341186, -1.1254278774413462, -0.8548921818040661, -0.5491898586706027, -0.21823050091974294, 0.12714678829620363, 0.47550731139655156, 0.8151840722300501, 1.1346590133329475, 1.4229496625664442, 1.669987965528566, 1.8669778358665636, 2.006718189705424, 2.0838789574289613, 2.0952187826099773, 2.039734801753986, 1.9187370084483686, 1.7358421817967133, 1.4968851248528294, 1.209747922318554, 0.8841109840014527, 0.5311326786770791, 0.16306726457981396, -0.2071665300227655, -0.5664516432253052, -0.901957092394413, -1.2016229780650212, -1.4546277829952894, -1.6518197454244976, -1.7860948709749769, -1.8527056416144696, -1.849486652171901, -1.7769861959502538, -1.638496144293912, -1.439976208517108, -1.1898727024787223, -0.8988360890347656, -0.5793457304692056, -0.24525420300941106, 0.08873288897698818, 0.4076226119927264, 0.6967245452091776, 0.94224180180187, 1.1318395584340473, 1.2551676590220122, 1.3043150658294274, 1.2741760911506677, 1.1627113994659772, 0.9710906260348546, 0.7037079789391821, 0.36806720979262264, -0.025462341521036644, -0.46401151593058615, -0.9326865393539442, -1.4151363858770343, -1.8941907169547891, -2.3525433007995513, -2.7734532735607313, -3.141435171810301, -3.4429084407950548, -3.6667781519489826, -3.804920939892171, -3.852553632069343, -3.808466577395314, -3.675109116671059, -3.4585207644440317, -3.1681082390927515, -2.816275207180165, -2.4179182053490127, -1.9898083706161187, -1.5498840602106012, -1.116483910818143, -0.7075531461788601, -0.3398578112368541, -0.028241967969041448, 0.2150383245944193, 0.3808731929769903, 0.463722482770104, 0.4618833901627433, 0.37758759475834186, 0.21692077329684661, -0.010434652751793214, -0.29162456795782865, -0.6111991603358208, -0.9518157325734147, -1.295037870377152, -1.622195463783126, -1.9152665743659727, -2.157740385511306, -2.335420589847319, -2.4371305977652313, -2.4552858440968786, -2.3863040867854384, -2.230831706093102, -1.993772322187252, -1.6841131842016637, -1.3145543271032187, -0.9009549954180631, -0.46162083698713857, -0.016463429739821147, 0.41392959120967987, 0.8092705456954948, 1.150547598628304, 1.4209534493062226, 1.606721195400716, 1.6978254526538958, 1.688512636226301, 1.577632014334691, 1.368748391102767, 1.0700276407597837, 0.6938973112156269, 0.2564956104475815, -0.22306726456773907, -0.723601838467302, -1.2228443217695049, -1.6985258040417646, -2.1294536934832777, -2.496551988993315, -2.783808188828428, -2.979078499430612, -3.074709366857189, -3.0679419393120733, -2.961076491088046, -2.7613856021330765, -2.480777420504946, -2.1352230124913443, -1.7439739816656943, -1.3286075801640542, -0.911945854604664, -0.5169024535169856, -0.16531516601672902, 0.12317621562595198, 0.3321486463649678, 0.4492576866931647, 0.46689636850331623, 0.3826148845403305, 0.19927687279808173, -0.07505852801295301, -0.4275254989298147, -0.8410936666337876, -1.2954324541811542, -1.7679544985584472, -2.2349849958404073, -2.672996514799442, -3.0598445955826064, -3.3759385992851363, -3.605284899805167, -3.736345530101983, -3.762664546180744, -3.6832262159273466, -3.5025230853234635, -3.2303273062142406, -2.8811745240852153, -2.473585271165691, -2.029063338290864, -1.5709232020298411, -1.1230085452009146, -0.7083706434167903, -0.347978477527541, -0.0595316432962932, 0.14355755502822976, 0.25295482845450373, 0.26592113677832424, 0.1855245302960848, 0.020531069895788907, -0.21502323715575547, -0.5025599323985526, -0.8199486853762163, -1.1427095812413433, -1.4453633384556697, -1.7028566312300277, -1.8919845553137473, -1.9927313973358516, -1.9894543617415548, -1.8718426473618173, -1.6355958797283872, -1.2827808036784185, -0.8218425374901199, -0.2672656451501523, 0.3611002453874297, 1.03901665166261, 1.7390833957934535, 2.4321512275032076], 'positive_zeros': ['1.16371427233354070099920784023449', '1.84762973310885932705657432908677', '3.17826793479316641594602948489891', '3.99316506267300882174765891622871', '4.89729653314118281423969433708830', '5.72465901091226343767100601177282', '6.34455537431112524120874784986106', '7.52082665070108710051209561686937', '7.86902020501984274342502475941245', '8.787052303782369332331481542136254'], 'prelabel': '2-2736-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 0.3250582826838458, 'root_number': '0.5223424371592602035134462170273832625055568030647737790 + 0.85273581978390253694706946607327605746227338851001921511*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1625291413419229', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16371427233354070099920784023', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.84762973310885932705657432909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17826793479316641594602948490', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 74.55060032897724, 'bad_primes': [2, 3, 19], 'central_character': '19.18', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/3/o/r/721/12'], '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': '2-2736-19.18-c2-0-77', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-2736-19.18-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.634268951623945, 'root_angle': 0.1625291413419229, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16371427233354070099920784023', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1475183095817770081633921893806', 'Lhash_array': ['1475183095817770081633921893806'], 'label': '2-2736-19.18-c2-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/3/o/r/721/12'}