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lfunc_lfunctions • Show schema
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{'Lhash': '2232577012714294905877404722414', 'a10': [-3.8206167146017913, 3.040825168992868], 'a2': [1.5441415022035736, 1.5441415022035736], 'a3': [-1.7320396300983532, -0.006222521093584401], 'a4': [0.0, 2.7687459576550175], 'a5': [-0.2525000281697365, 2.221765904809569], 'a6': [-2.6649058232272522, -2.6841227293651335], 'a7': [0.7071067811865476, -0.7071067811865476], 'a8': [-1.1870525378663437, 1.1870525378663437], 'a9': [2.9999225604624797, 0.02155530626642225], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7320396300983532, 0.006222521093584401]]], [5, [[1.0, 0], [0.2525000281697365, -2.221765904809569]]], [7, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.8', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '4575304218601963009218387446211', 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0.9156578079301484, 'root_angle': -0.536627411808821, 'root_number': '-0.11481464413506395 - 0.993386932414625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.268313705904', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76119272322542106218804930515', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.16339290432771893384852888771', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92644268719996325673704644914', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8384292212234444, 'bad_primes': [3, 5, 7], 'central_character': '15.8', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/2/j/a/8/11'], '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': '2-105-15.8-c1-0-1', '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': '2-105-15.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9156578079301484, 'root_angle': -0.2683137059044105, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76119272322542106218804930515', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2232577012714294905877404722414', 'Lhash_array': ['2232577012714294905877404722414'], 'label': '2-105-15.8-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/2/j/a/8/11'}