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lfunc_lfunctions • Show schema
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{'Lhash': '1286196798907095302577269918989', 'a10': [0.7071067811865476, 1.224744871391589], 'a2': [0.3826834323650898, -0.6628271480711836], 'a3': [0.5, 0.8660254037844386], 'a4': [0.20710678118654752, 0.3587194676071504], 'a5': [-0.9238795325112867, 1.6002062903825311], 'a6': [0.7653668647301796, -2.060396900318187e-79], 'a7': [0.0, 0.0], 'a8': [1.082392200292394, -5.24504906997025e-80], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9537132391416676, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 13], 'central_character': '1911.1598', 'coefficient_field': 'CDF', 'conductor': 1911, 'conductor_radical': 273, 'conjugate': '2827304502989604204959410000095', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3826834323650898, 0.6628271480711836], [-0.5, -0.8660254037844386]], 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'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01463037107821888795359710354', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91933131029070183671142782695', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54053410250692369725038128313', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9537132391416676, 'bad_primes': [3, 7, 13], 'central_character': '273.233', 'conductor': 1911, 'conductor_radical': 273, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1911/1/w/f/1598/3'], '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': '2-1911-273.233-c0-0-6', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1911-273.233-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9765824282372009, 'root_angle': -0.2384410718008522, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01463037107821888795359710354', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1286196798907095302577269918989', 'Lhash_array': ['1286196798907095302577269918989'], 'label': '2-1911-273.233-c0-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1911/1/w/f/1598/3'}