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lfunc_lfunctions • Show schema
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{'Lhash': '2897713181589366993817126998180', 'a10': [-0.35142745259911196, -0.3982604122861612], 'a2': [-0.45048278833957905, 1.340546626346804], 'a3': [-0.09297469459107813, -1.7295536147126795], 'a4': [-1.5941305148195961, -1.2077863642718483], 'a5': [-0.18778731667588874, 0.3252571734996656], 'a6': [2.3604307629534125, 0.6544972217688716], 'a7': [-0.19856475994113829, -2.638289604290916], 'a8': [2.337222295265439, -1.5929193145021987], 'a9': [-2.9827114123313914, 0.32160943821361315], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.45048278833957905, -1.340546626346804]]], [3, [[1.0, 0], [0.09297469459107813, 1.7295536147126795]]], [7, [[1.0, 0], [0.19856475994113829, 2.638289604290916]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.107', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'4.79264951630804086200307463738161', '6.44990847801676697606217747612551', '8.387200754590129763396961822850647', '9.175517677867360678367539461613754', '9.763078121062560517755741813355579', '10.95386335793450735548246783458814', '12.00240445031495050273533835324376', '12.26624176626045530058592222558682'], 'prelabel': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.248397494011223, 'root_number': '0.7106576784752601 + 0.7035379620348527*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.124198747006', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.28589264349944620694813826725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.94168818943820832641508493576', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.79264951630804086200307463738', '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': '168.107', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/v/a/107/11'], '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': '2-168-168.107-c1-0-18', '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': '2-168-168.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.1241987470056115, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28589264349944620694813826725', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2897713181589366993817126998180', 'Lhash_array': ['2897713181589366993817126998180'], 'label': '2-168-168.107-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/v/a/107/11'}