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lfunc_lfunctions • Show schema
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{'Lhash': '2737220275940225892719074073714', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.13397459621556135, 0.5], 'a4': [0.0, 0.0], 'a5': [-1.0, -2.0], 'a6': [0.0, 0.0], 'a7': [-1.2320508075688772, -2.133974596215561], 'a8': [0.0, 0.0], 'a9': [2.366025403784439, -1.3660254037844386], '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': '260.137', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '1244247791957385930118872087885', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.13397459621556135, -0.5], [-2.598076211353316, 1.5]], [[1.0, 0], [1.0, 2.0]], [[1.0, 0], [1.2320508075688772, 2.133974596215561], [-3.5, 6.06217782649107]], [[1.0, 0], [1.1339745962155614, 4.232050807568878], 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1.4408714212424685, 'root_angle': 0.35516599680618277, 'root_number': '0.43947079375096676 + 0.8982568794280928*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.177582998403', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15928606466751431862994085829', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.47450023298770843653119276078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.94898726315901955375340244502', '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': '65.7', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/bf/b/137/1'], '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': '2-260-65.7-c1-0-5', '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': '2-260-65.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': 0.17758299840309139, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15928606466751431862994085829', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2737220275940225892719074073714', 'Lhash_array': ['2737220275940225892719074073714'], 'label': '2-260-65.7-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/bf/b/137/1'}