-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1562986394613399396267125880591', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': -3, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.762974500266903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1], [1, 3, 7], [1, -1], [1, -2, 13], [1, 3, 17], [1, 1, 19], [1, 1, 23], [1, -6, 29], [1, -4, 31], [1, -1, 37], [1, 5, 41], [1, -4, 43], [1, 3, 47], [1, 10, 53], [1, -11, 59], [1, -14, 61], [1, -2, 67], [1, 5, 71], [1, -2, 73], [1, -5, 79], [1, 8, 83], [1, 10, 89], [1, 17, 97], [1, 11, 101], [1, -2, 103], [1, 18, 107], [1, 12, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [1], [1], [[[1, 3, 7], 1]], [[[1, -1], 1]], [[[1, -2, 13], 1]], [[[1, 3, 17], 1]], [[[1, 1, 19], 1]], [[[1, 1, 23], 1]], [[[1, -6, 29], 1]], [[[1, -4, 31], 1]], [[[1, -1, 37], 1]], [[[1, 5, 41], 1]], [[[1, -4, 43], 1]], [[[1, 3, 47], 1]], [[[1, 10, 53], 1]], [[[1, -11, 59], 1]], [[[1, -14, 61], 1]], [[[1, -2, 67], 1]], [[[1, 5, 71], 1]], [[[1, -2, 73], 1]], [[[1, -5, 79], 1]], [[[1, 8, 83], 1]], [[[1, 10, 89], 1]], [[[1, 17, 97], 1]], [[[1, 11, 101], 1]], [[[1, -2, 103], 1]], [[[1, 18, 107], 1]], [[[1, 12, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-2475-1.1-c1-0-38', '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/2475/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-5.979928743569691e-61, 0.09640535771240431, 0.1922068262573855, 0.286768634836356, 0.3793933764554545, 0.46929634456812985, 0.5555856245242093, 0.637249209277927, 0.7131499729100085, 0.7820289062156893, 0.84251663218606, 0.8931528959596755, 0.9324134686774769, 0.9587437109844257, 0.9705978965063166, 0.9664832835312762, 0.9450078311103008, 0.9049303743472925, 0.8452119976515708, 0.7650672731758235, 0.6640139669071188, 0.5419197616378971, 0.39904451045173994, 0.23607652312508265, 0.05416140757399053, -0.1450779548722642, -0.3595316230960508, -0.586604177545899, -0.8232286568823733, -1.0658935986119897, -1.310683647595747, -1.5533338691490794, -1.7892975394546407, -2.013826792629821, -2.2220650902765295, -2.409150056587036, -2.570324802402113, -2.7010554584616626, -2.797152265675121, -2.854891243156589, -2.871133187509517, -2.8434365633032805, -2.770160737630499, -2.6505560021789933, -2.4848369233119545, -2.274235770442543, -2.0210330985775737, -1.7285630018068407, -1.4011911064013851, -1.0442640266867993, -0.6640297514985901, -0.2675292472879238, 0.1375395645114409, 0.542983397208788, 0.940297793209836, 1.320870082886448, 1.6761964467624917, 1.9981076861675493, 2.2789976916515395, 2.5120481291023222, 2.6914425666231914, 2.8125631628839654, 2.872163146978765, 2.8685086519898726, 2.801484023873806, 2.6726555109100363, 2.4852892358476066, 2.244320544023177, 1.956273179072084, 1.6291282287526785, 1.2721443652567097, 0.8956325296430274, 0.5106898265038636, 0.12889894733247456, -0.23799912735569304, -0.5784501423486246, -0.8814392691931514, -1.136840719798855, -1.3357530721754753, -1.4708090368580857, -1.5364486971497988, -1.5291459472416358, -1.4475789267136048, -1.2927366911408846, -1.0679561356514766, -0.7788852565841048, -0.4333711381303956, -0.041273516612529475, 0.385792674309888, 0.8347798252181148, 1.2915868307546794, 1.7414842481064507, 2.1695727592489926, 2.56126062742539, 2.9027446403641135, 3.1814783350043103, 3.3866111491099797, 3.5093825741285443, 3.543456400802908, 3.4851817425903, 3.333769657834471, 3.0913768137798936, 2.7630906668208133, 2.3568139777286645, 1.8830500256657812, 1.3545935056226768, 0.7861356572309905, 0.1937955419289966, -0.40540757486555873, -0.9941231975249095, -1.5552603811933283, -2.0725794320873416, -2.5312630460659302, -2.9184456064935476, -3.2236803795481324, -3.439326165725923, -3.560837546506403, -3.586946129272245, -3.5197240358720117, -3.364525167927554, -3.129804359738828, -2.826819224860972, -2.469224131788536, -2.0725701207109624, -1.6537285139802973, -1.2302593064126977, -0.8197479957163929, -0.4391362023645932, -0.10407213876728022, 0.17169333613507592, 0.3768407132626851, 0.5029239097450122, 0.5447017944688881, 0.5003447057329181, 0.37150635815274496, 0.16325688469839778, -0.11612160944764985, -0.4554699221290494, -0.8412045046411382, -1.2578704638961142, -1.6887727745275583, -2.116660095798315, -2.5244330520115374, -2.8958474580703615, -3.2161828385729523, -3.472847731637561, -3.6558956643986313, -3.7584292566811444, -3.776874519552445, -3.711112883425775, -3.564464590479358, -3.343523558859109, -3.0578503889470885, -2.719536541615307, -2.3426585838816316, -1.942646493504836, -1.535594094383369, -1.137542553719519, -0.7637693559397037, -0.42811518361882095, -0.14237965454589294, 0.0841860718534418, 0.24526608566978889, 0.3377276303262841, 0.36171821507036217, 0.3206070612000785, 0.22077336246449536, 0.07125117725851386, -0.11675226214525729, -0.3304417814933784, -0.5560947650415785, -0.7797647196139327, -0.9879932783957768, -1.1684952621258946, -1.310782386020361, -1.4066938862612652, -1.4508066412283958, -1.4407030988484537, -1.3770822362735933, -1.2637065508570842, -1.107186341058491, -0.916610878327418, -0.7030440781774734, -0.4789095392698089, -0.25729594960396973, -0.05121852266448459, 0.12712494678421585, 0.2670638167245632, 0.36009155239049506, 0.40039437061304495, 0.38524099202279183, 0.31520956969393066, 0.19423591462962778, 0.029476211018648266, -0.16901293570586826, -0.3887645320913037, -0.6155393922891605, -0.834082149367012, -1.0289576749432645, -1.185425210303983, -1.2903043173040447, -1.3327858809149955, -1.3051429469374551, -1.2033001447056817, -1.0272266861394903, -0.7811261874005181, -0.4734064535037533, -0.11642342922712863, 0.27399479312538894, 0.6792262999118556, 1.0787072683684082, 1.4509187565739818, 1.7744614347896606, 2.029165304989862, 2.197178026772909, 2.2639748794439125, 2.219235752311733, 2.057539827048312, 1.7788366025909614, 1.388662272037908, 0.8980827159114705, 0.32335793810189467, -0.3146630338333062, -0.9913936586121859, -1.6795714035847118, -2.3504811561497565, -2.9752828753077387, -3.5263790630651615, -3.978754041744372, -4.311216874077827, -4.507483150113039, -4.557037695856656, -4.455730256433865, -4.206068920281598, -3.8171908748295413, -3.304506286288438, -2.6890278542351607, -1.9964150346506921, -1.2557771786078877, -0.49829306698654147, 0.24428520758398503, 0.9411689630541193, 1.5640319267312592, 2.0883939713212785, 2.4948169432630714, 2.7698487565476353, 2.9066642713513318, 2.905366757222533, 2.7729311915719537, 2.522789369853288, 2.1740758215377345, 1.7505718181790304, 1.2794013284619854, 0.7895466963375051, 0.31026229456669596, -0.13052918806285518, -0.5077712472199071], 'positive_zeros': ['1.23297886210285181777321436747754', '2.62344002697790795187697994636405', '3.72455677823649494894558967993045', '4.42303895506447824218553717817987', '5.45001030587274355240973905662151', '6.51780423833610446264208059382368', '6.88655912806536134012016034995716', '8.155207854629156628630531146508857', '8.500775704585080846252634260999327'], 'prelabel': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, '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': 1242217629414449617, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23297886210285181777321436748', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62344002697790795187697994636', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72455677823649494894558967993', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.762974500266903, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, -3, 3, 0, 0, 1, 0, 2, 3, 0, -1, -3, 0, -1, 0, 0, -1, -1, 0, 0, -2, 0, 3, 6, 0, 4, -5, 0, 3, 0, 0, 1, 1, 0, 0, -5, 0, 4, -1, 0, 1, -3, 0, 2, 0, 0, -2, -10, 0, 0, -9, 0, -6, 11, 0, 14, -4, 0, 7, 0, 0, 2, 3, 0, 0, -5, 0, 2, -1, 0, 1, -3, 0, 5, 0, 0, 5, -8, 0, 0, -4, 0, 3, -10, 0, -6, 1, 0, 3, 0, 0, -17, -2, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 19], 'euler2': [1, 1, 2], 'euler23': [1, 1, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -1, 37], 'euler41': [1, 5, 41], 'euler43': [1, -4, 43], 'euler47': [1, 3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -11, 59], 'euler61': [1, -14, 61], 'euler67': [1, -2, 67], 'euler7': [1, 3, 7], 'euler71': [1, 5, 71], 'euler73': [1, -2, 73], 'euler79': [1, -5, 79], 'euler83': [1, 8, 83], 'euler89': [1, 10, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 0, 0], [1, 3, 7], [1, -1, 0], [1, -2, 13], [1, 3, 17], [1, 1, 19], [1, 1, 23], [1, -6, 29], [1, -4, 31], [1, -1, 37], [1, 5, 41], [1, -4, 43], [1, 3, 47], [1, 10, 53], [1, -11, 59], [1, -14, 61], [1, -2, 67], [1, 5, 71], [1, -2, 73], [1, -5, 79], [1, 8, 83], [1, 10, 89], [1, 17, 97]], 'index': 38, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2475/b', 'ModularForm/GL2/Q/holomorphic/2475/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/2475/2/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': '2-2475-1.1-c1-0-38', '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': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1242217629414449617, 'z1': {'__RealLiteral__': 0, 'data': '1.23297886210285181777321436748', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20667334
{'Lhash': '1562986394613399396267125880591', 'Lhash_array': ['1562986394613399396267125880591'], 'label': '2-2475-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/b'}
-
id: 24557381
{'Lhash': '1562986394613399396267125880591', 'Lhash_array': ['1562986394613399396267125880591'], 'label': '2-2475-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/b/1/1'}
-
id: 27833
{'Lhash': '1242217629414449617', 'Lhash_array': ['1242217629414449617'], 'label': '2-2475-1.1-c1-0-38', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2475/b'}