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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': -3, 'A6': 1, 'A7': -1, 'A8': 1, 'A9': 1, 'Lhash': '2072621391150258976', 'a10': [-0.9486832980505138, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 567.4009866828144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [13, [1, -1]], [911, [1, 1]]], 'bad_primes': [2, 3, 13, 911], 'central_character': '71058.1', 'coefficient_field': '1.1.1.1', 'conductor': 71058, 'conductor_radical': 71058, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, 3, 5], [1, 1, 7], [1, -6, 11], [1, -1], [1, 3, 17], [1, -2, 19], [1, 0, 23], [1, 3, 29], [1, 4, 31], [1, -5, 37], [1, 3, 41], [1, 7, 43], [1, -6, 47], [1, 12, 53], [1, 0, 59], [1, 1, 61], [1, -8, 67], [1, -3, 71], [1, 16, 73], [1, 10, 79], [1, -18, 83], [1, -15, 89], [1, -17, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-71058-1.1-c1-0-0', 'leading_term': '3.62509786573', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/71058/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.625097865728374, 2.753219375223043, 0.4797191599160364, -2.068767162925715, -3.267061491166984, -2.181396158047756, 0.2729297457053964, 1.762675255621135, 0.685957327012852, -2.028218898640161, -3.725363675691545, -2.897800866963367, -0.8121899759278539, 0.2384446271128726, -0.1498028945040614, -0.3856316149457571, 0.3254680315580356, 0.6501377328676183, -0.3787311306042774, -0.9396732946090185, 1.314884105639773, 4.989416398527066, 5.73200557714048, 2.194942663801982, -1.515920339813258, -1.404810365714366, 0.8130618464686041, 0.8854936673284306, -1.029553649350528, -1.116265487987131, 0.9545325427931358, 1.104903414307084, -1.729959682056415, -3.016617668229226, -0.3831892733629843, 1.696221271525394, -0.4280222220049981, -2.607045326473445, -0.06397026203497246, 3.055237971142915, -0.303667468016422, -7.518601399314048, -9.320654552992137, -4.256824055090998, -0.1316031093832869, -0.7832778602821, -1.677299850849235, -0.1261628659310075, 0.414789574560475, -1.219874563226943, -1.052668115774173, 1.568070374914404, 2.07325977184026, -0.2036973031381623, -0.4631412746307991, 1.996073468395045, 2.384810671327648, -0.02467021007072882, -0.9237086699995405, 0.02673336429172704, -0.6135579483575356, -1.806872486616843, -0.3418211003825667, 1.364274730655661, 0.248893857766227, 0.09549551795912053, 3.244046857284299, 3.313523521851123, -2.058604335812913, -2.991395083306926, 4.90296084461212, 9.002357562065104, 0.5805009494723831, -8.828064370685409, -7.162505662015324, -0.9372775381762126, -0.1368744378963862, -1.55408305241643, 0.04041693124543718, 1.295603655595278, 0.1669359182887456, -0.03721679941172203, -0.5398001631824699, -4.739907679002803, -7.544789656872753, -3.305586097804051, 1.985178151048156, 1.420910291541497, -0.6759744170401764, 0.2018184233132884, 0.06450838371499021, -2.244591204887519, -1.714984949399451, 0.740725634975903, 0.07160801060441613, -1.088765479438011, 1.235032715995861, 2.575308829270789, 0.3615197482802411, 0.01927533590378871, 1.744414978369519, -0.2000393825906107, -2.581092840220789, 0.8726057031158357, 3.887497997614074, -0.06968722901440132, -3.076866260928244, 0.3396772831539674, 1.999604615177359, -0.5922495832310269, 0.2075504571479502, 1.993939047848694, -2.965329488444568, -7.4237991153074, -3.022553464546, 0.2949848363858042, -5.076374083445138, -7.806184203031348, -1.64731915669281, 2.633005672150099, 0.5035426299479311], 'positive_zeros': ['0.5446364892804807', '1.472019532921817', '2.068861026475902', '3.141420937414807', '3.440139802540520', '3.906006088563652', '4.427949185215730', '4.894829273949457', '5.875747154140817', '6.401677092863249', '6.868133976505911', '7.388964558341185', '7.862624721562807', '8.528300552246470', '8.967746360888631', '9.503751541747471', '9.988547338416024', '11.02820133232489', '11.11450404733104', '11.76828957001725', '12.07758223521279', '12.60709939328898', '13.22648927484265', '13.55695635272430', '14.24734568423390', '14.73887538631240', '14.87416935545151', '15.53478493832401', '16.04052638837686', '16.23687534531902', '16.91116281451999', '17.36433056237518', '18.01209802984711', '18.82750610615406', '18.97858741880948', '19.49573058354757'], 'prelabel': '2-71058-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.820180240351128, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2072621391150258976, 'z1': {'__RealLiteral__': 0, 'data': '0.5446364892804807', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.472019532921817', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.068861026475902', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 567.4009866828144, 'bad_primes': [2, 3, 13, 911], 'central_character': '1.1', 'conductor': 71058, 'conductor_radical': 71058, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, -3, 1, -1, 1, 1, -3, 6, 1, 1, -1, -3, 1, -3, 1, 2, -3, -1, 6, 0, 1, 4, 1, 1, -1, -3, -3, -4, 1, 6, -3, 3, 1, 5, 2, 1, -3, -3, -1, -7, 6, -3, 0, 6, 1, -6, 4, -3, 1, -12, 1, -18, -1, 2, -3, 0, -3, -1, -4, -1, 1, -3, 6, 8, -3, 0, 3, 3, 1, -16, 5, 4, 2, -6, 1, -10, -3, 1, -3, 18, -1, 9, -7, -3, 6, 15, -3, -1, 0, -4, 6, -6, 1, 17, -6, 6, 4], 'euler11': [1, -6, 11], 'euler13': [1, -1, 0], 'euler17': [1, 3, 17], 'euler19': [1, -2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -5, 37], 'euler41': [1, 3, 41], 'euler43': [1, 7, 43], 'euler47': [1, -6, 47], 'euler5': [1, 3, 5], 'euler53': [1, 12, 53], 'euler59': [1, 0, 59], 'euler61': [1, 1, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 7], 'euler71': [1, -3, 71], 'euler73': [1, 16, 73], 'euler79': [1, 10, 79], 'euler83': [1, -18, 83], 'euler89': [1, -15, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 3, 5], [1, 1, 7], [1, -6, 11], [1, -1, 0], [1, 3, 17], [1, -2, 19], [1, 0, 23], [1, 3, 29], [1, 4, 31], [1, -5, 37], [1, 3, 41], [1, 7, 43], [1, -6, 47], [1, 12, 53], [1, 0, 59], [1, 1, 61], [1, -8, 67], [1, -3, 71], [1, 16, 73], [1, 10, 79], [1, -18, 83], [1, -15, 89], [1, -17, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/71058/j'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '2-71058-1.1-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': '2-71058-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.820180240351128, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2072621391150258976, 'z1': {'__RealLiteral__': 0, 'data': '0.5446364892804807', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2072621391150258976', 'Lhash_array': ['2072621391150258976'], 'label': '2-71058-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/71058/j'}