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lfunc_lfunctions • Show schema
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{'Lhash': '1134171629677008540533382055265', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5176380902050415, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.10342452783194647, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.6967746271587942, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.883405834895576, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5], 'central_character': '5120.1', 'coefficient_field': 'CDF', 'conductor': 5120, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5176380902050415, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.10342452783194647, 0], [7.0, 0]], [[1.0, 0], [-3.131652497587396, 0], [11.0, 0]], [[1.0, 0], [1.3178372451957823, 0], [13.0, 0]], [[1.0, 0], [2.545866059960491, 0], [17.0, 0]], [[1.0, 0], [4.166928677997479, 0], [19.0, 0]], [[1.0, 0], [1.078116022520109, 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'4.31625105663016305580884975014146', '5.32479228029210699216794340255677', '6.22340250490550564792797786823253', '6.70407265517974457862263802450501', '7.63320232523072218050480039390849', '8.367827465123727105824957099273903'], 'prelabel': '2-5120-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.394013280788176, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.894703658462995134499571033242', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26204521631430816005964662059', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.55912454340448730220927197728', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.883405834895576, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 5120, 'conductor_radical': 10, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5120/2/a/r/1/3'], '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': '2-5120-1.1-c1-0-46', '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': '2-5120-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.394013280788176, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.894703658462995134499571033242', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1134171629677008540533382055265', 'Lhash_array': ['1134171629677008540533382055265'], 'label': '2-5120-1.1-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5120/2/a/r/1/3'}