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lfunc_lfunctions • Show schema
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{'Lhash': '2859953902782612884879498134677', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.461767498255581, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 19], 'central_character': '684.1', 'coefficient_field': '1.1.1.1', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1], [1], [1, -1, 5], [1, 3, 7], [1, 5, 11], [1, 4, 13], [1, -3, 17], [1, 1], [1, 8, 23], [1, -2, 29], [1, -4, 31], [1, -10, 37], [1, 10, 41], [1, -1, 43], [1, -1, 47], [1, -4, 53], [1, 6, 59], [1, 13, 61], [1, 12, 67], [1, 2, 71], [1, -9, 73], [1, -8, 79], [1, -12, 83], [1, 12, 89], [1, 8, 97], [1, -10, 101], [1, 6, 103], [1, 2, 107], [1, 0, 109], [1, -10, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -1, 5], 1]], [[[1, 3, 7], 1]], [[[1, 5, 11], 1]], [[[1, 4, 13], 1]], [[[1, -3, 17], 1]], [[[1, 1], 1]], [[[1, 8, 23], 1]], [[[1, -2, 29], 1]], [[[1, -4, 31], 1]], [[[1, -10, 37], 1]], [[[1, 10, 41], 1]], [[[1, -1, 43], 1]], [[[1, -1, 47], 1]], [[[1, -4, 53], 1]], [[[1, 6, 59], 1]], [[[1, 13, 61], 1]], [[[1, 12, 67], 1]], [[[1, 2, 71], 1]], [[[1, -9, 73], 1]], [[[1, -8, 79], 1]], [[[1, -12, 83], 1]], [[[1, 12, 89], 1]], [[[1, 8, 97], 1]], [[[1, -10, 101], 1]], [[[1, 6, 103], 1]], [[[1, 2, 107], 1]], [[[1, 0, 109], 1]], [[[1, -10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-684-1.1-c1-0-6', '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/684/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [4.187551582050563e-121, 0.266312007395736, 0.5376458501537574, 0.8170643175545392, 1.104132997050342, 1.3940485842530013, 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4.048651576423084, 3.967785513276604, 3.1197572154673923, 1.8488570442165189, 0.5914996224633183, -0.2809273487033202, -0.5908805759616248, -0.409122041332449], 'positive_zeros': ['2.25610582463945759407900622793818', '3.16174551478824360442184908445214', '4.55834684131140031321784081524763', '5.65147980657085516848049895381461', '6.33560598867710411281522365718144', '7.53862789028003683931489821584924', '8.146906664648363880391573042939637', '9.559628331745101664415344236204651', '9.954901377829594152119131032207005'], 'prelabel': '2-684-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.337042468218235, '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': 1126715890451893956, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25610582463945759407900622794', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16174551478824360442184908445', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.55834684131140031321784081525', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.461767498255581, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -3, 0, 0, 0, -5, 0, -4, 0, 0, 0, 3, 0, -1, 0, 0, 0, -8, 0, -4, 0, 0, 0, 2, 0, 4, 0, 0, 0, -3, 0, 10, 0, 0, 0, -10, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 4, 0, -5, 0, 0, 0, -6, 0, -13, 0, 0, 0, -4, 0, -12, 0, 0, 0, -2, 0, 9, 0, 0, 0, 15, 0, 8, 0, 0, 0, 12, 0, 3, 0, 0, 0, -12, 0, 12, 0, 0, 0, -1, 0, -8, 0, 0, 0], 'euler11': [1, 5, 11], 'euler13': [1, 4, 13], 'euler17': [1, -3, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -10, 37], 'euler41': [1, 10, 41], 'euler43': [1, -1, 43], 'euler47': [1, -1, 47], 'euler5': [1, -1, 5], 'euler53': [1, -4, 53], 'euler59': [1, 6, 59], 'euler61': [1, 13, 61], 'euler67': [1, 12, 67], 'euler7': [1, 3, 7], 'euler71': [1, 2, 71], 'euler73': [1, -9, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 12, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 5], [1, 3, 7], [1, 5, 11], [1, 4, 13], [1, -3, 17], [1, 1, 0], [1, 8, 23], [1, -2, 29], [1, -4, 31], [1, -10, 37], [1, 10, 41], [1, -1, 43], [1, -1, 47], [1, -4, 53], [1, 6, 59], [1, 13, 61], [1, 12, 67], [1, 2, 71], [1, -9, 73], [1, -8, 79], [1, -12, 83], [1, 12, 89], [1, 8, 97]], 'index': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/684/b', 'ModularForm/GL2/Q/holomorphic/684/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/684/2/a/b'], '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': '2-684-1.1-c1-0-6', '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': '2-684-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.337042468218235, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1126715890451893956, 'z1': {'__RealLiteral__': 0, 'data': '2.25610582463945759407900622794', 'prec': 103}}
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lfunc_instances • Show schema
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id: 13086890
{'Lhash': '2859953902782612884879498134677', 'Lhash_array': ['2859953902782612884879498134677'], 'label': '2-684-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/2/a/b'}
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id: 24550176
{'Lhash': '2859953902782612884879498134677', 'Lhash_array': ['2859953902782612884879498134677'], 'label': '2-684-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/2/a/b/1/1'}
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id: 94912
{'Lhash': '1126715890451893956', 'Lhash_array': ['1126715890451893956'], 'label': '2-684-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/684/b'}