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lfunc_lfunctions • Show schema
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{'Lhash': '1169721996555433309558763234695', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.5336702156975233, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.5336702156975233, 0.0], 'a7': [-1.9239248658793502, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.715196100877359, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 67.15418809989684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 29], 'central_character': '8410.1', 'coefficient_field': 'CDF', 'conductor': 8410, 'conductor_radical': 290, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.5336702156975233, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.9239248658793502, 0], [7.0, 0]], [[1.0, 0], [-2.0908723790921133, 0], [11.0, 0]], [[1.0, 0], [6.178983573990179, 0], [13.0, 0]], [[1.0, 0], [-4.262932556476116, 0], [17.0, 0]], [[1.0, 0], [-2.9277645649640283, 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'6.25782648515929395413398386352567', '6.92859477299959446110690889609909', '7.40194265222314697493856643771102'], 'prelabel': '2-8410-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.194765896588923, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.922747953059648373534199173726', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.19050039746017029194616536777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17686641436187814526799699260', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 67.15418809989684, 'bad_primes': [2, 5, 29], 'central_character': '1.1', 'conductor': 8410, 'conductor_radical': 290, 'degree': 2, 'index': 116, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8410/2/a/br/1/5'], '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': '2-8410-1.1-c1-0-116', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8410-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.194765896588923, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.922747953059648373534199173726', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1169721996555433309558763234695', 'Lhash_array': ['1169721996555433309558763234695'], 'factors': ['2-8410-1.1-c1-0-116'], 'label': '2-8410-1.1-c1-0-116', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8410/2/a/br/1/5'}