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lfunc_lfunctions • Show schema
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{'Lhash': '2008252357449804012098092129747', 'a10': [3.544300075334989, 9.307448403802349], 'a2': [0.7117460936257927, 1.869068617843771], 'a3': [0.0, 4.449456675074567], 'a4': [-2.9868349964168486, 2.660604574937727], 'a5': [4.979725364251088, 0.0], 'a6': [-8.316339837837363, 3.1668834072415315], 'a7': [0.0, -12.26284473570967], 'a8': [-7.098720656512172, -3.688924645585404], 'a9': [-10.797664703365628, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.7117460936257927, -1.869068617843771]]], [19, [[1.0, 0], [0, 4.358898943540674]]]], 'bad_primes': [2, 19], 'central_character': '76.39', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '4909702827873661384974149232569', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7117460936257927, -1.869068617843771]], [[1.0, 0], [0, -4.449456675074567], [-9.0, 0]], [[1.0, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '5.72808470595039932793024412330', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0708500091382565, 'bad_primes': [2, 19], 'central_character': '4.3', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/3/b/b/39/10'], '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': '2-76-4.3-c2-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-76-4.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4390448252706574, 'root_angle': -0.3658164493672881, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58423177261008336429867314971', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2008252357449804012098092129747', 'Lhash_array': ['2008252357449804012098092129747'], 'label': '2-76-4.3-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/3/b/b/39/10'}