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lfunc_lfunctions • Show schema
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{'Lhash': '715516842852241608257988887210', 'a10': [5.534022711943704, 0.0], 'a2': [-1.9943573502797782, 0.0], 'a3': [-0.8226824176296514, 0.0], 'a4': [1.9774612406149785, 0.0], 'a5': [-2.774840081275988, 0.0], 'a6': [1.6407227265456337, 0.0], 'a7': [2.784706412517769, 0.0], 'a8': [0.04495034044570503, 0.0], 'a9': [-2.3231936397230317, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.9943573502797782, 0], [2.0, 0]], [[1.0, 0], [0.8226824176296514, 0], [3.0, 0]], [[1.0, 0], [2.774840081275988, 0], [5.0, 0]], [[1.0, 0], [-2.784706412517769, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'2.52529990408682893501530672734218', '3.31557552739235290077942262771973', '4.52202655781031677522430057089037', '4.96300023361732058580045583582040', '5.73856585660430906078255770819585', '6.92523560282537040083888305065612', '7.38897852189311238877120479935429', '7.912220351626620112506188373536048'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56444326435329976561032657632', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.22773663524541936566046258470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.52529990408682893501530672734', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 135, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/f/1/10'], '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': '2-8041-1.1-c1-0-135', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56444326435329976561032657632', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '715516842852241608257988887210', 'Lhash_array': ['715516842852241608257988887210'], 'label': '2-8041-1.1-c1-0-135', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/f/1/10'}