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lfunc_lfunctions • Show schema
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{'Lhash': '855995882837707606511834838406', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.2568327496616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '5292.1', 'coefficient_field': '1.1.1.1', 'conductor': 5292, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1], [1], [1, 1, 5], [1], [1, -2, 11], [1, 0, 13], [1, 5, 17], [1, 2, 19], [1, -2, 23], [1, -10, 29], [1, 0, 31], [1, -5, 37], [1, 3, 41], [1, 7, 43], [1, -3, 47], [1, -6, 53], [1, 1, 59], [1, -6, 61], [1, -4, 67], [1, -8, 71], [1, 10, 73], [1, 3, 79], [1, -13, 83], [1, -6, 89], [1, -14, 97], [1, 10, 101], [1, 2, 103], [1, 18, 107], [1, -7, 109], [1, -16, 113]], 'euler_factors_factorization': [[1], [1], [[[1, 1, 5], 1]], [1], [[[1, -2, 11], 1]], [[[1, 0, 13], 1]], [[[1, 5, 17], 1]], [[[1, 2, 19], 1]], [[[1, -2, 23], 1]], [[[1, -10, 29], 1]], [[[1, 0, 31], 1]], [[[1, -5, 37], 1]], [[[1, 3, 41], 1]], [[[1, 7, 43], 1]], [[[1, -3, 47], 1]], [[[1, -6, 53], 1]], [[[1, 1, 59], 1]], [[[1, -6, 61], 1]], [[[1, -4, 67], 1]], [[[1, -8, 71], 1]], [[[1, 10, 73], 1]], [[[1, 3, 79], 1]], [[[1, -13, 83], 1]], [[[1, -6, 89], 1]], [[[1, -14, 97], 1]], [[[1, 10, 101], 1]], [[[1, 2, 103], 1]], [[[1, 18, 107], 1]], [[[1, -7, 109], 1]], [[[1, -16, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-5292-1.1-c1-0-11', 'leading_term': '1.586678692109553342920896785120000000000000000000000000000000000000000000000000000000000000', '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/5292/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.5866786921095533, 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2.8542424229761556, 2.8538382874161, 2.7235092849277636, 2.466282351295915, 2.0930901022729205, 1.6221995142822885, 1.0781640550738243, 0.49036021421943377, -0.10880309133936002, -0.6858915507352071, -1.2085428625255852, -1.6475209786520733, -1.9785947216735638], 'positive_zeros': ['0.67526168700081318608927816074164', '1.92056072863143155216859749458689', '2.83109710285122323270485853335342', '3.83480671395287911511255173793603', '4.42843749256593256195863651802715', '5.17261831698512850935825782096819', '6.28089734425250307641247922927335', '6.65724737036948039070918895032017', '7.45880678156365974590710833509793', '8.334513597865881309518697602843883'], 'prelabel': '2-5292-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.500525574879434, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 653547584965732851, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67526168700081318608927816074', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92056072863143155216859749459', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83109710285122323270485853335', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.2568327496616, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 5292, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -5, 0, -2, 0, 0, 0, 2, 0, -4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -3, 0, -7, 0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, -1, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, -10, 0, 0, 0, 0, 0, -3, 0, 0, 0, 13, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 14, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 5, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -5, 37], 'euler41': [1, 3, 41], 'euler43': [1, 7, 43], 'euler47': [1, -3, 47], 'euler5': [1, 1, 5], 'euler53': [1, -6, 53], 'euler59': [1, 1, 59], 'euler61': [1, -6, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -8, 71], 'euler73': [1, 10, 73], 'euler79': [1, 3, 79], 'euler83': [1, -13, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 5], [1, 0, 0], [1, -2, 11], [1, 0, 13], [1, 5, 17], [1, 2, 19], [1, -2, 23], [1, -10, 29], [1, 0, 31], [1, -5, 37], [1, 3, 41], [1, 7, 43], [1, -3, 47], [1, -6, 53], [1, 1, 59], [1, -6, 61], [1, -4, 67], [1, -8, 71], [1, 10, 73], [1, 3, 79], [1, -13, 83], [1, -6, 89], [1, -14, 97]], 'index': 11, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5292/c', 'ModularForm/GL2/Q/holomorphic/5292/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/5292/2/a/c'], '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': '2-5292-1.1-c1-0-11', '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': '2-5292-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.500525574879434, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 653547584965732851, 'z1': {'__RealLiteral__': 0, 'data': '0.67526168700081318608927816074', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21493906
{'Lhash': '855995882837707606511834838406', 'Lhash_array': ['855995882837707606511834838406'], 'label': '2-5292-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5292/2/a/c'}
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id: 24569692
{'Lhash': '855995882837707606511834838406', 'Lhash_array': ['855995882837707606511834838406'], 'label': '2-5292-1.1-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5292/2/a/c/1/1'}
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id: 25387
{'Lhash': '653547584965732851', 'Lhash_array': ['653547584965732851'], 'label': '2-5292-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5292/c'}