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lfunc_lfunctions • Show schema
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{'Lhash': '3080799607904366290242246729530', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.8660254037844386, 0.5], 'a4': [0.0, 0.0], 'a5': [-1.0, -2.0], 'a6': [0.0, 0.0], 'a7': [2.232050807568877, -3.866025403784439], 'a8': [0.0, 0.0], 'a9': [0.6339745962155614, 0.36602540378443865], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 2.0]]], [13, [[1.0, 0], [-3.0, -2.0]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.37', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1868013271469416055573850224215', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.8660254037844386, -0.5], [2.598076211353316, 1.5]], [[1.0, 0], [1.0, 2.0]], [[1.0, 0], [-2.232050807568877, 3.866025403784439], [-3.5, -6.06217782649107]], [[1.0, 0], [2.866025403784439, 0.7679491924311227], 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1.4408714212424685, 'root_angle': 0.18441742735438274, 'root_number': '0.836810785799743 + 0.5474921997336735*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0922087136772', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43032236749597662862668088796', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96304883255103036573203004353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.80972659012944149074876397327', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '65.37', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/bf/b/37/1'], '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': '2-260-65.37-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': 0, 'prelabel': '2-260-65.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.09220871367719137, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43032236749597662862668088796', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3080799607904366290242246729530', 'Lhash_array': ['3080799607904366290242246729530'], 'label': '2-260-65.37-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/bf/b/37/1'}