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lfunc_lfunctions • Show schema
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{'Lhash': '2421821759426735487333680307226', 'a10': [3.200014593379893, 0.0], 'a2': [2.5642814133194807, 0.0], 'a3': [1.1267601496525175, 0.0], 'a4': [4.575539166695752, 0.0], 'a5': [1.2479186476017277, 0.0], 'a6': [2.889330109023027, 0.0], 'a7': [2.5038432928164345, 0.0], 'a8': [6.6044072144342625, 0.0], 'a9': [-1.7304115651550367, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.5642814133194807, 0], [2.0, 0]], [[1.0, 0], [-1.1267601496525175, 0], [3.0, 0]], [[1.0, 0], [-1.2479186476017277, 0], [5.0, 0]], [[1.0, 0], [-2.5038432928164345, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.7896536715778524, 0], 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'3.58770445103657965574502239626039', '4.17599570516765756930959501161296', '5.15819517075313412821505476611515', '5.90324039932996144543463661478965', '6.40239919969037187005062020484915', '7.70153515466961312643525646464854', '8.116929899811195018990266400315791', '9.228683244034658195551924562857973'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91048050542531803716997485783', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34241904051139675505698096420', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58770445103657965574502239626', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 113, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/t/1/20'], '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': '2-1859-1.1-c1-0-113', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91048050542531803716997485783', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2421821759426735487333680307226', 'Lhash_array': ['2421821759426735487333680307226'], 'label': '2-1859-1.1-c1-0-113', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/t/1/20'}