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lfunc_lfunctions • Show schema
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{'Lhash': '3395090420450205651487639310796', 'a10': [-1.945826201310958, -3.898493749924725], 'a2': [0.08572422190793073, -1.4116130340069406], 'a3': [1.6927283552396108, -0.36697508821145], 'a4': [-1.9853027155565597, -0.2420188579506767], 'a5': [2.6681800766564447, -1.5404744855039947], 'a6': [-0.3729189965207225, -2.420936063185886], 'a7': [-1.463066402379498, 2.204413006273623], 'a8': [-0.5118255049014375, 2.7817323114441455], 'a9': [2.730658569264397, -1.2423782749641579], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.08572422190793073, 1.4116130340069406]]], [3, [[1.0, 0], [-1.6927283552396108, 0.36697508821145]]], [7, [[1.0, 0], [1.463066402379498, -2.204413006273623]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'5.65703079679624852336279359823782', '6.93996238044928832168874163511118', '7.59121981069069050082670022589038', '9.016769800950299651740556021534020', '9.919212152265186950404794782490859', '10.34839354503403884414710988285483', '12.59904419237282548141913315532112', '13.48121572414361865245712883692306'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.46946288223554394, 'root_number': '0.09578809500113883 + 0.9954017484694573*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.234731441118', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.67825410238353480102841831450', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17430984920452054806581695253', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.65703079679624852336279359824', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/13'], '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': '2-168-168.101-c1-0-23', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.23473144111777197, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.67825410238353480102841831450', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3395090420450205651487639310796', 'Lhash_array': ['3395090420450205651487639310796'], 'label': '2-168-168.101-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/13'}