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lfunc_lfunctions • Show schema
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{'Lhash': '1264167289084878447068444337377', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.271330370297698, 1.271330370297698], 'a6': [0, 0], 'a7': [0, 0.15894165103667743], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '1152.865', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '1756720146966865557835725415315', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.271330370297698, -1.271330370297698], [0, 5.0]], [[1.0, 0], [0, -0.15894165103667743], [-7.0, 0]], [[1.0, 0], [-3.7979326519318133, -3.7979326519318133], [0, 11.0]], [[1.0, 0], [-4.212146214304909, 4.212146214304909], [0, -13.0]], [[1.0, 0], [3.053204563268231, 0], [17.0, 0]], [[1.0, 0], 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-0.45905038247974356, -1.2242527897934317, -1.9783698083768602], 'positive_zeros': ['0.997252152018289728472507164929886', '2.14163664663664782010807357065397', '3.67880576484288635016962254215282', '4.36196111504773499221150372404442', '5.60669306153293526584838384314484', '6.32604237750801891687825335406346', '6.99303375124325256222142254107119', '8.399888304026330515510494738994142', '9.094699989510457135688956135952301', '9.219172782856626451711334234547045'], 'prelabel': '2-1152-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.22660817189402938, 'root_number': '0.75711511984860209823630756760962525490746412927713980046 - 0.6532814824381882639283215867135935767918805941746347638*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1133040859470147', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.997252152018289728472507164930', 'prec': 107}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '16.5', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/k/f/865/3'], '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': '2-1152-16.5-c1-0-6', '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': '2-1152-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': -0.11330408594701469, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.997252152018289728472507164930', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1264167289084878447068444337377', 'Lhash_array': ['1264167289084878447068444337377'], 'label': '2-1152-16.5-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/k/f/865/3'}