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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -3, 'Lhash': '1015148891321640216', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 1614.255727262205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1, -1]], [19, [1]]], 'bad_primes': [2, 5, 7, 19], 'central_character': '202160.1', 'coefficient_field': '1.1.1.1', 'conductor': 202160, 'conductor_radical': 1330, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, 1], [1, -1], [1, 4, 11], [1, -6, 13], [1, -2, 17], [1], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, -10, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -2, 53], [1, 8, 59], [1, 14, 61], [1, 12, 67], [1, 16, 71], [1, -2, 73], [1, 8, 79], [1, 8, 83], [1, 10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-202160-1.1-c1-0-4', 'leading_term': '1.08312155142', '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/202160/bj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.08312155142456, 0.3284000695733887, -1.354490309422826, -2.460443988464877, -1.695562156791437, 0.3769641738243547, 1.334935133008234, -0.4674149717900621, -3.422165851545556, -4.136781685044103, -1.782239647911589, 0.6055159640981245, 0.4112524057758171, -0.6304394712943929, 0.7288003095373407, 3.60141783042423, 3.911831998640695, 1.181604377099082, -0.1496376718606167, 2.043546211582246, 3.783676737497946, 1.750484150068507, -0.9226888305790181, -0.4447339554725376, 0.6471753108313213, -1.290031701077981, -3.041091122035447, 0.2153785132165509, 5.204905834886439, 5.187757571633363, 1.360088149479867, -0.05486665123405854, 0.919746698658903, 0.04283428944719244, -1.379217825024658, 0.03941908386845261, 0.8054081947851045, -3.088172925885614, -6.265934847462512, -2.813148099022579, 1.893265256102123, 0.7810622435501884, -2.162856316091984, -1.038699741282521, 0.6920102650292306, -0.6295293196691021, -1.045614229147393, 0.5011479445041844, -1.343388927221002, -5.282761592309965, -3.777063443507775, 1.266053762575143, 1.639997050166207, -0.7713950070571214, 0.3685825779978015, 1.488998472445241, -1.592104451612952, -2.707843729385808, 1.146486655997345, 2.477661356884848, -0.4353085931135677, -0.5508261682963046, 1.351612061990898, -0.6153874432451159, -2.570553261745893, 0.1910781266865553, 1.783867700504733, -0.07816650594799476, 1.754858091180586, 5.975995224376502, 3.863030601971614, -1.248282659035531, -1.162868603214483, 0.124413980554421, -1.530231800143046, -0.5244225668596622, 2.377976325674305, -0.2689997096695638, -4.137910950932698, -1.680454154794789, 0.914821147705101, -1.446803824810997, -2.062956471190056, 0.01257408926945145, -0.8372076105488304, -0.8240596228226786, 2.680513011730572, 0.8169112030060651, -6.062544614027606, -5.7007160478525, 0.2475722765347826, 0.9642520273229221, -0.7870616250572086, 0.260208516034052, -0.2054649407473515, -1.065850134331074, 1.959188219887317, 1.963677628489424, -3.270826324694174, -2.851637563861891, 2.662435851892691, 2.290781685033902, -0.3823448367246463, 1.678872783934803, 2.221791020017228, -0.1335665575987355, 0.8236694649468558, 0.1961112893195851, -5.420403092574526, -5.643672015816607, 0.1823996232479144, 1.254996354886895, -0.219016359711336, 1.46688575355138, 1.053528792604809, -0.3853047026867155, 2.422260456560674, 1.554069290797494, -5.200567732130345, -5.083698302203827, 0.7041197981819804], 'positive_zeros': ['0.3043144232943374', '1.204331615727472', '1.708227492175900', '2.661869776370674', '3.076938540575836', '3.423453593928067', '4.385113020606207', '4.538498162173575', '5.387988237122233', '5.815199764830554', '6.128753993004905', '6.739948175006333', '7.654769763662970', '7.771833181037930', '8.255490350915346', '8.745562192202627', '9.080330674674257', '9.874070948152094', '10.30389051729763', '10.85479225550729', '11.16573382824689', '11.65286518092157', '11.89965425857242', '12.67704653267931', '13.14800247121950', '13.46210434436383', '13.89391783678777', '14.43360978627006', '14.96083520698593', '15.30958772931747', '15.70388894856047', '16.23680636636147', '16.73448874110261', '16.86382949302867', '17.67164525856659', '18.15085721748377', '18.28642207397281', '18.78792824248224', '19.23678434141309', '19.85489766491630'], 'prelabel': '2-202160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.17780142394809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1015148891321640216, 'z1': {'__RealLiteral__': 0, 'data': '0.3043144232943374', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.204331615727472', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.708227492175900', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1614.255727262205, 'bad_primes': [2, 5, 7, 19], 'central_character': '1.1', 'conductor': 202160, 'conductor_radical': 1330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 1, 0, -3, 0, -4, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 8, 0, 0, 0, -1, 0, 10, 0, 0, 0, -2, 0, -4, 0, 3, 0, -8, 0, 1, 0, 0, 0, 2, 0, 4, 0, 0, 0, -8, 0, -14, 0, -3, 0, -6, 0, -12, 0, 0, 0, -16, 0, 2, 0, 0, 0, -4, 0, -8, 0, 9, 0, -8, 0, -2, 0, 0, 0, -10, 0, 6, 0, 0, 0, 0, 0, -2, 0, 12, 0], 'euler11': [1, 4, 11], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 3], 'euler31': [1, -8, 31], 'euler37': [1, -10, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 8, 59], 'euler61': [1, 14, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 16, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 8, 83], 'euler89': [1, 10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, 1, 0], [1, -1, 0], [1, 4, 11], [1, -6, 13], [1, -2, 17], [1, 0, 0], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, -10, 37], [1, 2, 41], [1, 4, 43], [1, 8, 47], [1, -2, 53], [1, 8, 59], [1, 14, 61], [1, 12, 67], [1, 16, 71], [1, -2, 73], [1, 8, 79], [1, 8, 83], [1, 10, 89], [1, 2, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/202160/bj'], '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': '2-202160-1.1-c1-0-4', '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': '2-202160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 40.17780142394809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1015148891321640216, 'z1': {'__RealLiteral__': 0, 'data': '0.3043144232943374', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1015148891321640216', 'Lhash_array': ['1015148891321640216'], 'label': '2-202160-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/202160/bj'}