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lfunc_lfunctions • Show schema
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{'Lhash': '1981736440561283500726784513307', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.3478035900811167, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.811296381478361, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.4075986524470787, 0.0], 'a8': [0.0, 0.0], 'a9': [2.5121816975977795, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.790315019405732, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [241, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 241], 'central_character': '3856.1', 'coefficient_field': 'CDF', 'conductor': 3856, 'conductor_radical': 482, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.3478035900811167, 0], [3.0, 0]], [[1.0, 0], [3.811296381478361, 0], [5.0, 0]], [[1.0, 0], [0.4075986524470787, 0], [7.0, 0]], [[1.0, 0], [-4.859985287678896, 0], [11.0, 0]], [[1.0, 0], [2.7873345068352915, 0], [13.0, 0]], [[1.0, 0], [1.0486889062005351, 0], [17.0, 0]], [[1.0, 0], [-2.7146837259916867, 0], 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'4.02811421613778133390050268573583', '4.65830405606779159802024547359194', '6.07208196815888007250097057486183', '6.94004442839650220618005636946407', '7.69979696282387216811114804088715', '7.994037935151349139661849805888228'], 'prelabel': '2-3856-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.54890214541631, 'root_angle': 1.0, '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': '1.56331440241063995892356136996', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73194970994956366794305130973', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53227230922997156708043131728', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.790315019405732, 'bad_primes': [2, 241], 'central_character': '1.1', 'conductor': 3856, 'conductor_radical': 482, 'degree': 2, 'index': 96, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3856/2/a/h/1/6'], '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': '2-3856-1.1-c1-0-96', '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': '2-3856-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.54890214541631, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56331440241063995892356136996', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1981736440561283500726784513307', 'Lhash_array': ['1981736440561283500726784513307'], 'label': '2-3856-1.1-c1-0-96', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3856/2/a/h/1/6'}