-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 2, 'A3': 0, 'A4': 2, 'A5': 0, 'A6': 0, 'A7': -5, 'A8': 0, 'A9': -1, 'Lhash': '438098409444898727482532739482', 'a10': [0.0, 0], 'a2': [1.4142135623730951, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.8898223650461363, 0], 'a8': [0.0, 0], 'a9': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.43749800906467, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 2]], [3, [1, 0, 1]], [7, [1, 5, 7]], [11, [1, 6, 11]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '853776.1', 'coefficient_field': '1.1.1.1', 'conductor': 853776, 'conductor_radical': 462, 'degree': 4, 'euler_factors': [[1, -2, 2], [1, 0, 1], [1, 0, 3, 0, 25], [1, 5, 7], [1, 6, 11], [1, 0, -18, 0, 169], [1, 0, -11, 0, 289], [1, 0, 13, 0, 361], [1, 4, 34, 92, 529], [1, -2, 10, -58, 841], [1, 0, 35, 0, 961], [1, 6, 67, 222, 1369], [1, 0, -46, 0, 1681], [1, 0, 85, 0, 1849], [1, 0, -5, 0, 2209], [1, -2, 58, -106, 2809], [1, 0, -37, 0, 3481], [1, 0, 7, 0, 3721], [1, 1, -22, 67, 4489], [1, -2, 62, -142, 5041], [1, 0, 71, 0, 5329], [1, 2, 95, 158, 6241], [1, 0, 21, 0, 6889], [1, 0, 107, 0, 7921], [1, 0, 37, 0, 9409], [1, 0, -35, 0, 10201], [1, 0, -17, 0, 10609], [1, 2, 94, 214, 11449], [1, -7, 188, -763, 11881], [1, 12, 246, 1356, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 0, 'label': '4-924e2-1.1-c1e2-0-0', 'leading_term': '1.01309994699', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/2.0.7.1/17424.15/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [1.0130999469897302, 0.9938129873555732, 0.9356904395721304, 0.8379691121238855, 0.6994491509012885, 0.5186001739070044, 0.2937056856747805, 0.023041494773686305, -0.29491748465722367, -0.6612690559394124, -1.0764425988561837, -1.5399547368456437, -2.050172827317484, -2.6040983202088053, -3.197182739351896, -3.823189314491711, -4.474113014395962, -5.14017079968299, -5.809872245336471, -6.470178227259381, -7.106752117290454, -7.704303931415463, -8.247023229772, -8.719091440226773, -9.105258897627625, -9.391466543107217, -9.5654872435732, -9.617557433470282, -9.540966622381225, -9.33257061217551, -8.99319434320574, -8.527892385961097, -7.946039357775072, -7.261228992659247, -6.490969098550187, -5.656169913636463, -4.780434974062106, -3.8891759295614854, -3.0085850628056376, -2.16451076059508, -1.3812909837044527, -0.6806070338576258, -0.08042384673181578, 0.4059169778036488, 0.7703895763093113, 1.0107087045201557, 1.1304473676119864, 1.1388244960194314, 1.0501599635917576, 0.8830160445419163, 0.6590665838808579, 0.40175611675880657, 0.13482925313585575, -0.11917575722010813, -0.3403676561326289, -0.5127746420991638, -0.6253531629069274, -0.6726520604470809, -0.655072765130273, -0.5786938928339217, -0.4546604855259179, -0.2981720071730987, -0.12713645199105802, 0.03941223215780988, 0.18301247513936733, 0.2874530539695494, 0.3402898248811727, 0.3340671508858055, 0.2671285565413586, 0.14393073955070482, -0.025186157959672915, -0.2247739470228096, -0.4355513877820441, -0.6360859742820494, -0.8047485033697198, -0.921774868814995, -0.9712511230292661, -0.9428351611322354, -0.8330426852559718, -0.6459561820271458, -0.39326167857259847, -0.09357567094882478, 0.22891086046588516, 0.5463787161143253, 0.8297636818455899, 1.0513737826692728, 1.18750478983322, 1.220806150029758, 1.1421607966643463, 0.9518772318516531, 0.6600488134262404, 0.2860090276088561, -0.14310366225189844, -0.5945698823002725, -1.0329184691630173, -1.4231086539567677, -1.7337671506090622, -1.9401637423565092, -2.0266220609069903, -1.988107069222619, -1.830804354122423, -1.571602558345222, -1.2365002127926026, -0.8580709525175836, -0.4722247501578433, -0.11458578953810204, 0.18314010099221698, 0.39642120482571247, 0.510418783474663, 0.5214768136330644, 0.43739347215216307, 0.2764139973532654, 0.0650258587816298, -0.16522424282173886, -0.38155200749036033, -0.5539695025987169, -0.6590634120794303, -0.6830600380679958, -0.6237839851998278, -0.4912313505112986, -0.30663101163380313, -0.10004348469874759, 0.09327366291567973, 0.23734284181655624, 0.3002707839131165, 0.25879603372382126, 0.10199319325446278, -0.16638341240275184, -0.5272974265444481, -0.9477584253529224, -1.384041592579665, -1.7865227836486048, -2.105632936212603, -2.2982621664139447, -2.3338407737745155, -2.1993092621618637, -1.9022703525149591, -1.4717896339411136, -0.9565632254291612, -0.42047526779775296, 0.06410833525957878, 0.4246590381284757, 0.5975200430413905, 0.5366037091144764, 0.22066254102293079, -0.3418625899984535, -1.11119220229391, -2.0182000218454306, -2.970082589006751, -3.859301221222164, -4.574968384942742, -5.015499276430374, -5.101116817107352, -4.784720350357565, -4.0597245481359066, -2.96374485210394, -1.5774274221139588, -0.01825340499661826, 1.5702682600131905, 3.0330358233072214, 4.219948977140312, 5.002857032813269, 5.290915807843359, 5.042492736317899, 4.272070773543611, 3.051113238407355, 1.5025121607438172, -0.21102051845429906, -1.903531851263209, -3.3856597112552254, -4.4855484773352705, -5.068468393570201, -5.052823839541539, -4.420580973788736, -3.2207392249194484, -1.5652509246310062, 0.3823294075639967, 2.424313841462058, 4.350558112246972, 5.96188964272673, 7.092565226035176, 7.629097625236638, 7.523176903061107, 6.79708558503798, 5.540890312524808, 3.9016813396187997, 2.066103828066911, 0.2382590637325258, -1.3843583021868422, -2.6339580048870412, -3.3917592497082487, -3.601134180842761, -3.2729839103683545, -2.482715438532466, -1.3592504775133585, -0.06751216460469887, 1.2133294196466708, 2.3130280184803955, 3.0918446072732837, 3.4577534918060704, 3.3770627557235136, 2.8771163950158796, 2.040801070894881, 0.9936761508178188, -0.11446533059258883, -1.1310492341429992, -1.922227087688904, -2.3914756021074948, -2.492730126003215, -2.236248434724419, -1.6864076738898113, -0.9517578834728952, -0.16873606886632372, 0.5186649702769764, 0.9804041114780441, 1.1200299094664596, 0.8896519202674038, 0.29809020735648084, -0.5890040282964166, -1.657140946862959, -2.7580414219312317, -3.7296894095693016, -4.418620471529297, -4.7013532173153845, -4.501978471262245, -3.803449583748048, -2.6509926002405293, -1.1471532815762249, 0.5608367318538742, 2.2996258784150863, 3.891676273137809, 5.177551132860244, 6.035522026460011, 6.3958713986662765, 6.248043091724228, 5.639823654313928, 4.668868818542311, 3.4679575530980022, 2.1862061258172134, 0.9689857376191886, -0.060609983132445096, -0.8162150431146247, -1.2567020469856287, -1.38782776830864, -1.257127295875157, -0.9431619457688732, -0.541019468260484, -0.14644456530719294, 0.1589221560640623, 0.319003427710692, 0.3098643567873958, 0.1406725520195869, -0.150773842326265, -0.5069018815357154, -0.8618941143857367, -1.1538254827238383, -1.3353326958601055], 'positive_zeros': ['0.34559870785058827821464289393644', '2.05810142864732361546642741249749', '2.56441439605749691831116722252834', '3.06419486027480802927699159185343', '3.41132652410486665374980615055422', '3.96942376784484647534584462004723', '4.47637194710682231002839543900395', '5.14437926980385986395867403480450', '5.48264148375570867199907669293120', '5.93247645442844181763325675629622', '6.17324608575687128870111201303132', '6.82887139876270587854125304670974', '7.05290258881509115254089049460952', '7.66657287289099020522924014999403', '8.148360787377756783960579641537938'], 'prelabel': '4-924e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.716280019947559, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 778196762996606452, 'z1': {'__RealLiteral__': 0, 'data': '0.34559870785058827821464289393644', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '2.05810142864732361546642741249749', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.56441439605749691831116722252834', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 54.43749800906467, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 853776, 'conductor_radical': 462, 'degree': 4, 'dirichlet_coefficients': [1, 2, 0, 2, 0, 0, -5, 0, -1, 0, -6, 0, 0, -10, 0, -4, 0, -2, 0, 0, 0, -12, -4, 0, -3, 0, 0, -10, 2, 0, 0, -8, 0, 0, 0, -2, -6, 0, 0, 0, 0, 0, 0, -12, 0, -8, 0, 0, 18, -6, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 5, -8, 0, 0, -1, 0, 0, 0, 2, 0, 0, -12, 0, 0, 30, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 36, 6, -6], 'euler11': [1, 6, 11, 0, 0], 'euler13': [1, 0, -18, 0, 169], 'euler17': [1, 0, -11, 0, 289], 'euler19': [1, 0, 13, 0, 361], 'euler2': [1, -2, 2, 0, 0], 'euler23': [1, 4, 34, 92, 529], 'euler29': [1, -2, 10, -58, 841], 'euler3': [1, 0, 1, 0, 0], 'euler31': [1, 0, 35, 0, 961], 'euler37': [1, 6, 67, 222, 1369], 'euler41': [1, 0, -46, 0, 1681], 'euler43': [1, 0, 85, 0, 1849], 'euler47': [1, 0, -5, 0, 2209], 'euler5': [1, 0, 3, 0, 25], 'euler53': [1, -2, 58, -106, 2809], 'euler59': [1, 0, -37, 0, 3481], 'euler61': [1, 0, 7, 0, 3721], 'euler67': [1, 1, -22, 67, 4489], 'euler7': [1, 5, 7, 0, 0], 'euler71': [1, -2, 62, -142, 5041], 'euler73': [1, 0, 71, 0, 5329], 'euler79': [1, 2, 95, 158, 6241], 'euler83': [1, 0, 21, 0, 6889], 'euler89': [1, 0, 107, 0, 7921], 'euler97': [1, 0, 37, 0, 9409], 'euler_factors': [[1, -2, 2, 0, 0], [1, 0, 1, 0, 0], [1, 0, 3, 0, 25], [1, 5, 7, 0, 0], [1, 6, 11, 0, 0], [1, 0, -18, 0, 169], [1, 0, -11, 0, 289], [1, 0, 13, 0, 361], [1, 4, 34, 92, 529], [1, -2, 10, -58, 841], [1, 0, 35, 0, 961], [1, 6, 67, 222, 1369], [1, 0, -46, 0, 1681], [1, 0, 85, 0, 1849], [1, 0, -5, 0, 2209], [1, -2, 58, -106, 2809], [1, 0, -37, 0, 3481], [1, 0, 7, 0, 3721], [1, 1, -22, 67, 4489], [1, -2, 62, -142, 5041], [1, 0, 71, 0, 5329], [1, 2, 95, 158, 6241], [1, 0, 21, 0, 6889], [1, 0, 107, 0, 7921], [1, 0, 37, 0, 9409]], 'index': 0, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/17424.15/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/17424.1/c', 'EllipticCurve/2.0.7.1/17424.1/c', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/17424.15/c'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-924e2-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-924e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.716280019947559, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 778196762996606452, 'z1': {'__RealLiteral__': 0, 'data': '0.34559870785058827821464289393644', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9603510
{'Lhash': '438098409444898727482532739482', 'Lhash_array': ['438098409444898727482532739482'], 'label': '4-924e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/17424.15/c'}
-
id: 9603259
{'Lhash': '438098409444898727482532739482', 'Lhash_array': ['438098409444898727482532739482'], 'label': '4-924e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/17424.1/c'}
-
id: 9603066
{'Lhash': '438098409444898727482532739482', 'Lhash_array': ['438098409444898727482532739482'], 'label': '4-924e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/17424.1/c'}
-
id: 9602962
{'Lhash': '438098409444898727482532739482', 'Lhash_array': ['438098409444898727482532739482'], 'label': '4-924e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/17424.15/c'}