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lfunc_lfunctions • Show schema
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{'Lhash': '2339898368301455971878777447786', 'a10': [0.1501683474320005, 0.26009920744088016], 'a2': [-2.0536451458980234, 0.0], 'a3': [0.0, 0.0], 'a4': [2.2174583852705134, 0.0], 'a5': [-0.07312283124080547, -0.12665245890235985], 'a6': [0.0, 0.0], 'a7': [-2.3303539672252174, -1.2527770701276786], 'a8': [-0.4465823573456119, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.3303539672252174, 1.2527770701276786]]]], 'bad_primes': [3, 7], 'central_character': '189.37', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '748357470789638035394474958280', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0536451458980234, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.07312283124080547, 0.12665245890235985], [-2.5, 4.330127018922194]], [[1.0, 0], [2.3303539672252174, 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'12.62362434516931202091723302524201'], 'prelabel': '2-189-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.5289275855048519, 'root_number': '-0.09075364820261647 + 0.995873373144355*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.264463792752', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84585434494345503365220949432', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.76889846405000270772698489281', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.76832140419754963255405264580', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '63.58', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/h/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': '2-189-63.58-c1-0-2', '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': '2-189-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.26446379275242593, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84585434494345503365220949432', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2339898368301455971878777447786', 'Lhash_array': ['2339898368301455971878777447786'], 'label': '2-189-63.58-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/h/b/37/1'}