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lfunc_lfunctions • Show schema
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{'Lhash': '1872090689411285846762976177564', 'a10': [-1.4584588620258865, -1.6949624620557695], 'a2': [-0.5938201855735016, 0.8045977797666684], 'a3': [2.0610432917219024, -0.389970430738875], 'a4': [-0.2947551744109042, -0.9555728057861407], 'a5': [-0.4977007216583881, 2.1799756860251263], 'a6': [-0.9101197672181706, 1.8898831700719654], 'a7': [1.433216953208131, -2.2239355127873655], 'a8': [0.9438833303083676, 0.3302790619551671], 'a9': [1.3032012675685785, -0.511468807389333], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.9126696990427408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5938201855735016, -0.8045977797666684]]], [5, [[1.0, 0], [0.4977007216583881, -2.1799756860251263]]], [7, [[1.0, 0], [-1.433216953208131, 2.2239355127873655]]]], 'bad_primes': [2, 5, 7], 'central_character': '490.103', 'coefficient_field': 'CDF', 'conductor': 490, 'conductor_radical': 70, 'conjugate': 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'root_angle': -0.17871867762625548, 'root_number': '0.8464779924369552 - 0.5324237112675411*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0893593388131', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47681915590481501345240859392', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.66850523152209863465375837963', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91441721893593292864013633092', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.9126696990427408, 'bad_primes': [2, 5, 7], 'central_character': '245.103', 'conductor': 490, 'conductor_radical': 70, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/490/2/w/a/103/11'], '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': '2-490-245.103-c1-0-14', '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': '2-490-245.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9780469405559467, 'root_angle': -0.08935933881312774, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47681915590481501345240859392', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1872090689411285846762976177564', 'Lhash_array': ['1872090689411285846762976177564'], 'label': '2-490-245.103-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/490/2/w/a/103/11'}