-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '5391356396013073394620327639975', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.19164096485107301, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]]], 'bad_primes': [2, 3], 'central_character': '24.1', 'coefficient_field': '1.1.1.1', 'conductor': 24, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, 0, 7], [1, -4, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 8, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, 2, 61], [1, 4, 67], [1, -8, 71], [1, -10, 73], [1, 8, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97], [1, 18, 101], [1, -16, 103], [1, 12, 107], [1, 2, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 2, 5], 1]], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, -2, 17], 1]], [[[1, 4, 19], 1]], [[[1, 8, 23], 1]], [[[1, -6, 29], 1]], [[[1, -8, 31], 1]], [[[1, -6, 37], 1]], [[[1, 6, 41], 1]], [[[1, -4, 43], 1]], [[[1, 0, 47], 1]], [[[1, 2, 53], 1]], [[[1, -4, 59], 1]], [[[1, 2, 61], 1]], [[[1, 4, 67], 1]], [[[1, -8, 71], 1]], [[[1, -10, 73], 1]], [[[1, 8, 79], 1]], [[[1, 4, 83], 1]], [[[1, 6, 89], 1]], [[[1, -2, 97], 1]], [[[1, 18, 101], 1]], [[[1, -16, 103], 1]], [[[1, 12, 107], 1]], [[[1, 2, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-24-1.1-c1-0-0', '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/24/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.5391289118749109, 0.5494900679493764, 0.5801277845029248, 0.6298742017898519, 0.697187177361571, 0.780398414983652, 0.8777438437959396, 0.9872277294945799, 1.106416653300369, 1.23223307614437, 1.360786539044795, 1.487263558496433, 1.6058915629287331, 1.7099911461219441, 1.7921301903435474, 1.84439090950352, 1.85875566574032, 1.8276092419517713, 1.7443442467515053, 1.6040430084308934, 1.4041946079210497, 1.145390957299842, 0.8319327961728251, 0.4722672054312474, 0.07917492014620255, -0.33036954330129203, -0.7357274507169698, -1.1135524289010474, -1.4391756356909677, -1.6883762901743407, -1.8394435424932742, -1.8753835513396828, -1.7860782505287884, -1.570166603870432, -1.2364023736212886, -0.8042510561064175, -0.30352737440298305, 0.22705462061632933, 0.742446235920661, 1.1948470798156523, 1.5380735878976006, 1.732347344025776, 1.74902544730585, 1.5747233664337663, 1.214266389567749, 0.6919616786617614, 0.05081442316160879, -0.6504857224826721, -1.3427232817868129, -1.9530882261259201, -2.4132257431635282, -2.6675158221973727, -2.6805477488563856, -2.4427318236417763, -1.973113762903251, -1.3187303601686482, -0.5502498449571104, 0.2458644891902457, 0.9779053926087944, 1.5609497232076759, 1.9287773501790733, 2.043945162102631, 1.9043791754332648, 1.5452112498427022, 1.0351906447606531, 0.4677770826538238, -0.052134167382198913, -0.42412388409640106, -0.5684848744257247, -0.4402089791140285, -0.03829082989887089, 0.5915258179559655, 1.361502293462057, 2.1539220315929835, 2.8388815977451807, 3.2952581949464244, 3.4315007028776074, 3.202659293318358, 2.6204530844612295, 1.7541655907146017, 0.7216298893041307, -0.328707335738122, -1.241969134304042, -1.8832825802496271, -2.161787989989254, -2.0476949960317876, -1.5788742221445875, -0.8552344425931256, -0.021358177800191894, 0.7598455828965839, 1.337811425612767, 1.6035416073077828, 1.5115824341040252, 1.0900807109303694, 0.43639551240408875, -0.30146136374546867, -0.9543666499139003, -1.3669842441556492, -1.4309886963452634, -1.1095680691234682, -0.4476410755693185, 0.4350194849209806, 1.3670410200204859, 2.160791519777359, 2.652665686153988, 2.7397289703718335, 2.4044958505002882, 1.721828577935236, 0.8456191358841865, -0.0226769562044887, -0.6774045312749958, -0.9547283027480602, -0.7710208593688845, -0.14458854367351254, 0.8048944318933183, 1.8799968820951614, 2.847645621167943, 3.490713185982291, 3.6574651116269634, 3.2972949569122756, 2.4739666838549037, 1.3525954474687225, 0.16273020346612832, -0.8542796684287545, -1.501383138954034, -1.67190631754046, -1.3741628981567084, -0.7281017228946659, 0.06573823193051644, 0.7777397025581797, 1.208566559177415, 1.2413638318806584, 0.8731558712078311, 0.21673354000180203, -0.5282940842598872, -1.1285846024524269, -1.3809930676403828, -1.170695066629867, -0.5077485181355486, 0.46854234914322956, 1.5199346488477194, 2.367534911643296, 2.76362096492696, 2.5583535674620577, 1.7433828954836412, 0.4598845180892108, -1.0323246741692835, -2.4175719298581666, -3.4031591076357595, -3.7935592685570723, -3.5399761792740296, -2.751457967820295, -1.6639532901932226, -0.5751999413582809, 0.23703176481728933, 0.5908275672705083, 0.4488521862393854, -0.07411005969219348, -0.7473487977962121, -1.2942127727604906, -1.4759896692020638, -1.1653349729618376, -0.387433609951244, 0.6839294161817052, 1.7751906506156565, 2.5931833900404198, 2.9134151269386903, 2.650123476667114, 1.8864976553539923, 0.8548003371811018, -0.1290754916754297, -0.7581741719341265, -0.8269556390321309, -0.2956693354702745, 0.6937011050259733, 1.8561196356301917, 2.846537993707732, 3.363190493077277, 3.240170774015041, 2.500758663357736, 1.354260681100014, 0.13606034067745632, -0.7919359264324926, -1.1506480589559924, -0.8294793678043024, 0.0785364925456044, 1.3037076789141937, 2.4811971933160852, 3.2622897962605104, 3.4208994949398566, 2.9218369878775268, 1.9290739383883033, 0.7511340801797156, -0.2591106918262498, -0.8180475035874413, -0.8014276525927742, -0.28132320260308535, 0.502582284006365, 1.228293484266879, 1.6052943128526458, 1.4786571964586364, 0.8877635659239752, 0.0584464156761233, -0.67059865715046, -0.9639279770527241, -0.6096240383489676, 0.397265694640669, 1.8379528468348345, 3.328017820959579, 4.433586616300466, 4.808660659958354, 4.308493203166247, 3.040733285710373, 1.3359962288556906, -0.3538687180173499, -1.5971522829221627, -2.1168396302226395, -1.8736244240578506, -1.0696652424401096, -0.0720859288739706, 0.7173814800574329, 1.0016097334865186, 0.6879482439225135, -0.08586469780025488, -1.0085066251245827, -1.714116675987714, -1.9207909676386499, -1.5383888397435033, -0.7060235295231108, 0.25544789441600596, 0.9599339643538087, 1.1001362463878543, 0.5666731457091213, -0.5022219209533972, -1.76063525648597, -2.7724696068249863, -3.165759490874535, -2.7685511295487344, -1.6764051454780795, -0.2252749618054132, 1.122618896941145, 1.9404123253656642, 1.9880465612653917, 1.2984159930729802, 0.16588777161793983, -0.960016299525699, -1.6382201880677085, -1.597840977633241, -0.838788903688702, 0.3663449513221194, 1.5707213846695762, 2.316545929739393, 2.3033715391490786, 1.4991580038190238, 0.15265298748014217, -1.2977788609168752, -2.384992193341725], 'positive_zeros': ['4.25303028692796488061253338186834', '6.42897107072744719896577758454500', '8.098990694093691505068092710868270', '9.964671915727173343349228861429439', '11.58204746144152243175303945055362', '12.31725686074733747032880351584204', '14.18198826155077042068868714860043', '15.47325164750050957705309114010867', '16.62726100086658933765837426594319', '17.67075195000178004295107787309645'], 'prelabel': '2-24-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4377681633594122, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 906478665263567321, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.25303028692796488061253338187', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.42897107072744719896577758454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.098990694093691505068092710868', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.19164096485107301, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 24, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 0, 0, 1, 0, 4, 0, -2, 0, 2, 0, 2, 0, -4, 0, 0, 0, -8, 0, -1, 0, -1, 0, 6, 0, 8, 0, -4, 0, 0, 0, 6, 0, 2, 0, -6, 0, 4, 0, -2, 0, 0, 0, -7, 0, -2, 0, -2, 0, -8, 0, 4, 0, 4, 0, -2, 0, 0, 0, 4, 0, -4, 0, 8, 0, 8, 0, 10, 0, 1, 0, 0, 0, -8, 0, 1, 0, -4, 0, -4, 0, -6, 0, -6, 0, 0, 0, -8, 0, 8, 0, 2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, 0, 7], [1, -4, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 8, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, 2, 61], [1, 4, 67], [1, -8, 71], [1, -10, 73], [1, 8, 79], [1, 4, 83], [1, 6, 89], [1, -2, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/24/a', 'ModularForm/GL2/Q/holomorphic/24/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/24/2/a/a'], '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': '2-24-1.1-c1-0-0', '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': '2-24-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4377681633594122, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 906478665263567321, 'z1': {'__RealLiteral__': 0, 'data': '4.25303028692796488061253338187', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9955544
{'Lhash': '5391356396013073394620327639975', 'Lhash_array': ['5391356396013073394620327639975'], 'label': '2-24-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/24/2/a/a'}
-
id: 24545891
{'Lhash': '5391356396013073394620327639975', 'Lhash_array': ['5391356396013073394620327639975'], 'label': '2-24-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/24/2/a/a/1/1'}
-
id: 21991
{'Lhash': '906478665263567321', 'Lhash_array': ['906478665263567321'], 'label': '2-24-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/24/a'}