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lfunc_lfunctions • Show schema
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{'Lhash': '2081542364950210361430832611062', 'a10': 0, 'a2': 1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.82362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3234.1', 'coefficient_field': '1.1.1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 0, 5], [1], [1, 1], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, 0, 23], [1, 6, 29], [1, 2, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, -6, 47], [1, 6, 53], [1, 0, 59], [1, 2, 61], [1, 4, 67], [1, 12, 71], [1, -4, 73], [1, -8, 79], [1, 6, 83], [1, -6, 89], [1, 2, 97], [1, 6, 101], [1, 14, 103], [1, 0, 107], [1, 10, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, 1], 1]], [[[1, 0, 5], 1]], [1], [[[1, 1], 1]], [[[1, 2, 13], 1]], [[[1, 0, 17], 1]], [[[1, 2, 19], 1]], [[[1, 0, 23], 1]], [[[1, 6, 29], 1]], [[[1, 2, 31], 1]], [[[1, -2, 37], 1]], [[[1, 0, 41], 1]], [[[1, 4, 43], 1]], [[[1, -6, 47], 1]], [[[1, 6, 53], 1]], [[[1, 0, 59], 1]], [[[1, 2, 61], 1]], [[[1, 4, 67], 1]], [[[1, 12, 71], 1]], [[[1, -4, 73], 1]], [[[1, -8, 79], 1]], [[[1, 6, 83], 1]], [[[1, -6, 89], 1]], [[[1, 2, 97], 1]], [[[1, 6, 101], 1]], [[[1, 14, 103], 1]], [[[1, 0, 107], 1]], [[[1, 10, 109], 1]], [[[1, 18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 61, 'label': '2-3234-1.1-c1-0-61', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3234/2/a/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.502882498256895e-60, 0.21605165401471935, 0.4316328031464453, 0.6462143560384013, 0.8591536456059576, 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-1.4552538943703124, -1.6095610224506043, -1.6889114277834476, -1.6878271786226318, -1.6060334979707034, -1.4485474530641713, -1.2254369978934738, -0.9512609774159348], 'positive_zeros': ['1.64204739427050866177734888707170', '2.60622211031772570676167298328803', '3.71076198654888108453853603433493', '4.44329737475499316523087610458015', '5.28504090410954752716150203642030', '5.86088051722843540343111085134312', '6.64764709700293617110788735405087', '7.43580396718635232825666196861895', '8.019259750876931777400838091871393'], 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 833931581226288680, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64204739427050866177734888707', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60622211031772570676167298329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71076198654888108453853603433', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.82362001368209, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 0, 1, 1, 0, -1, -1, -2, 0, 0, 1, 0, 1, -2, 0, 0, -1, 0, -1, -5, -2, -1, 0, -6, 0, -2, 1, 1, 0, 0, 1, 2, -2, 2, 0, 0, 0, -4, -1, 0, 0, 6, -1, 0, -5, 0, -2, -6, -1, 0, 0, 2, -6, 0, 0, -2, -2, 0, 1, 0, 1, -4, 0, 0, 0, -12, 1, 4, 2, 5, -2, 0, 2, 8, 0, 1, 0, -6, 0, 0, -4, 6, -1, 6, 0, 0, 0, 2, 6, 0, -1, -2, 0, -1, -5], 'euler11': [1, 1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 12, 71], 'euler73': [1, -4, 73], 'euler79': [1, -8, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 5], [1, 0, 0], [1, 1, 0], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, 0, 23], [1, 6, 29], [1, 2, 31], [1, -2, 37], [1, 0, 41], [1, 4, 43], [1, -6, 47], [1, 6, 53], [1, 0, 59], [1, 2, 61], [1, 4, 67], [1, 12, 71], [1, -4, 73], [1, -8, 79], [1, 6, 83], [1, -6, 89], [1, 2, 97]], 'index': 61, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3234/q', 'ModularForm/GL2/Q/holomorphic/3234/2/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/3234/2/a/q'], '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': '2-3234-1.1-c1-0-61', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 833931581226288680, 'z1': {'__RealLiteral__': 0, 'data': '1.64204739427050866177734888707', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20140263
{'Lhash': '2081542364950210361430832611062', 'Lhash_array': ['2081542364950210361430832611062'], 'label': '2-3234-1.1-c1-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/q'}
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id: 24560692
{'Lhash': '2081542364950210361430832611062', 'Lhash_array': ['2081542364950210361430832611062'], 'label': '2-3234-1.1-c1-0-61', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/q/1/1'}
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id: 28866
{'Lhash': '833931581226288680', 'Lhash_array': ['833931581226288680'], 'label': '2-3234-1.1-c1-0-61', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3234/q'}