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lfunc_lfunctions • Show schema
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{'Lhash': '2412744312695864457946989382352', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.8660254037844386, 0.5], 'a4': [0.0, 0.0], 'a5': [-1.0, -2.0], 'a6': [0.0, 0.0], 'a7': [3.232050807568877, 1.8660254037844386], 'a8': [0.0, 0.0], 'a9': [0.6339745962155614, 0.36602540378443865], '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': '260.197', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '2323293445932893381130259329709', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.8660254037844386, -0.5], [2.598076211353316, 1.5]], [[1.0, 0], [1.0, 2.0]], [[1.0, 0], [-3.232050807568877, -1.8660254037844386], [3.5, 6.06217782649107]], [[1.0, 0], [0.5980762113533159, -2.232050807568877], 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'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.0027496144566160736, 'root_number': '0.9999626912538094 - 0.00863806115042915*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00137480722831', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90331966258010760259918966033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34057032696346975032708691445', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34664307617958722339205963536', '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': '65.2', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/bk/b/197/1'], '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': '2-260-65.2-c1-0-4', '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': '2-260-65.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.0013748072283080368, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90331966258010760259918966033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2412744312695864457946989382352', 'Lhash_array': ['2412744312695864457946989382352'], 'label': '2-260-65.2-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/bk/b/197/1'}