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lfunc_lfunctions • Show schema
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{'Lhash': '1563112404345282921381804858871', 'a10': [0.0, 0.0], 'a2': [0.6180339887498949, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.618033988749895, 0.0], 'a5': [0.0, 0.0], 'a6': [0.6180339887498949, 0.0], 'a7': [-0.7639320225002103, 0.0], 'a8': [-2.23606797749979, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.46423983431198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '9075.1', 'coefficient_field': 'CDF', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7639320225002103, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.2360679774997898, 0], [13.0, 0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], [[1.0, 0], [5.0, 0], [19.0, 0]], [[1.0, 0], [2.381966011250105, 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[0]], 'group': 'GL2', 'index': 262, 'label': '2-9075-1.1-c1-0-262', '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/9075/2/a/bc/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.2834969010588605e-60, 0.23884180129314955, 0.4759092044338638, 0.7093800683962828, 0.9373408452216972, 1.157750773413114, 1.36841714450223, 1.5669840996094053, 1.7509365404145911, 1.9176198360195016, 2.0642751443791663, 2.1880893949027835, 2.2862583259019207, 2.3560604457279855, 2.3949393845873086, 2.4005918122862, 2.3710579004427044, 2.3048111926229966, 2.2008447029130758, 2.0587500876090568, 1.8787868249865012, 1.6619384963210453, 1.4099534907341569, 1.1253677602902397, 0.8115076320870788, 0.47247114061761997, 0.1130868732040935, -0.26115008287187447, -0.6441648511515984, 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'7.54022256928087440928849863933137'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23307826625401211238811328081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48609794171826852903278564832', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08801349628430757443220575255', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.46423983431198, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'index': 262, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9075/2/a/bc/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-9075-1.1-c1-0-262', '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': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23307826625401211238811328081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1563112404345282921381804858871', 'Lhash_array': ['1563112404345282921381804858871'], 'label': '2-9075-1.1-c1-0-262', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/bc/1/2'}