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lfunc_lfunctions • Show schema
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{'Lhash': '716570158997915401176444845697', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7842950954560696, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.25005076864406, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.384881203243555, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.61494531562012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 17], 'central_character': '8092.1', 'coefficient_field': 'CDF', 'conductor': 8092, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7842950954560696, 0], [3.0, 0]], [[1.0, 0], [2.25005076864406, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.874131651603377, 0], [11.0, 0]], [[1.0, 0], [0.9557219122451819, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.332888616648942, 0], [19.0, 0]], [[1.0, 0], [7.478450342600859, 0], 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'3.66966331569954263288393651192549', '3.95254128236184582132069761017234', '4.92623940664378513336403147966568', '5.90174660743413613759005023128211', '6.44411827281486004994123875724580', '7.25291682891599682480908869451946', '7.915692526646267823399556601557950'], 'prelabel': '2-8092-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.038342199460043, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56527418428145990102978702320', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82158724925294201897239912465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82548047412272707017762659063', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.61494531562012, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 8092, 'conductor_radical': 238, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8092/2/a/u/1/8'], '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': '2-8092-1.1-c1-0-19', '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': '2-8092-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.038342199460043, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56527418428145990102978702320', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '716570158997915401176444845697', 'Lhash_array': ['716570158997915401176444845697'], 'label': '2-8092-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8092/2/a/u/1/8'}