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lfunc_lfunctions • Show schema
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{'Lhash': '1133869092415037041433853178504', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.33987688662318255, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 3.8844837019393323], 'a8': [0.0, 0.0], 'a9': [-2.8844837019393323, 0.0], '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], [0, -1.0]]], [13, [[1.0, 0], [-3.5446068153161496, -0.6601231133768174]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.181', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2819929881736512652618676609834', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.33987688662318255, 0], [3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -3.8844837019393323], [-7.0, 0]], [[1.0, 0], [0, -1.5446068153161499], [-11.0, 0]], [[1.0, 0], [-3.5446068153161496, -0.6601231133768174]], 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'5.67626480644896880904916524832461', '6.76723577313674734978808031094718', '7.937729835859477063608209308651254', '8.806296291302671338372418577886191', '9.936873445749874374708830575235269', '11.19406063249565506796310157419582', '11.30438393746008789850740416108422'], 'prelabel': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.44139157548106817, 'root_number': '0.183085210261465 - 0.9830970479985763*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.220695787741', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.894464998644653211329237356339', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.20869582271191960041843794520', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42694601665224417265258606945', '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': '13.12', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/f/a/181/4'], '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': '2-260-13.12-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': '2-260-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.22069578774053408, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.894464998644653211329237356339', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1133869092415037041433853178504', 'Lhash_array': ['1133869092415037041433853178504'], 'label': '2-260-13.12-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/f/a/181/4'}