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lfunc_lfunctions • Show schema
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{'Lhash': '694225628880009304229819930341', 'a10': [-4.020720133663199, 0.0], 'a2': [-1.8800111088474063, 0.0], 'a3': [-1.8122313978081537, 0.0], 'a4': [1.5344417693896546, 0.0], 'a5': [2.138668284852962, 0.0], 'a6': [3.4070151596813925, 0.0], 'a7': [1.999409847645497, 0.0], 'a8': [0.8752546453627922, 0.0], 'a9': [0.2841826392016947, 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], [1.8800111088474063, 0], [2.0, 0]], [[1.0, 0], [1.8122313978081537, 0], [3.0, 0]], [[1.0, 0], [-2.138668284852962, 0], [5.0, 0]], [[1.0, 0], [-1.999409847645497, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'2.02099558464868064934583892825260', '3.44299713490334917732409548900509', '4.51553463913863125435126342567188', '5.31090897558607048611115367393531', '5.80879315936383684217148861263606', '6.44948371330626029533393124561163', '7.22785354314192252071843797634470', '7.988201699947967511518146676915220'], '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': '0.54764745802591033574501958514', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.60523593121241780221083064845', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.02099558464868064934583892825', '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': 125, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/f/1/12'], '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-c1-0-125', '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': '0.54764745802591033574501958514', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '694225628880009304229819930341', 'Lhash_array': ['694225628880009304229819930341'], 'label': '2-8041-1.1-c1-0-125', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/f/1/12'}