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lfunc_lfunctions • Show schema
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{'Lhash': '1811996880705597352107252698835', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.8090169943749475, -0.5877852522924731], 'a6': [0, 0], 'a7': [0.7143466266756998, -2.198532852756478], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.810379600213524, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [11, [[1.0, 0], [-3.148354378117663, 1.043007531030982]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '1980.1081', 'coefficient_field': 'CDF', 'conductor': 1980, 'conductor_radical': 330, 'conjugate': '806505672718129373268444134427', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.7143466266756998, 2.198532852756478], [-5.663118960624632, -4.114496766047312]], [[1.0, 0], 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['1.42941349957106726775409564144891', '2.40770084459948149363213636197284', '3.78791367550993460009848415598823', '4.19353811312852697106253724376393', '5.54889416966868374967402872678152', '6.14982285340747782350088777740060', '7.00216075068797934905031407032753', '7.81905589005106515495016493606148', '8.824788769531758346246031690444485', '9.060396249911950218246453325872947'], 'prelabel': '2-1980-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9762268044231988, 'root_angle': 0.25286890261416883, 'root_number': '-0.01802487057574500022186409331017095760351990638158948050 + 0.9998375388235468937884536925496728477496459946187367182*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.25286890261416883', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42941349957106726775409564145', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40770084459948149363213636197', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78791367550993460009848415599', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.810379600213524, 'bad_primes': [2, 3, 5, 11], 'central_character': '11.3', 'conductor': 1980, 'conductor_radical': 330, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1980/2/z/c/1081/2'], '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': '2-1980-11.3-c1-0-16', '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': '2-1980-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9762268044231988, 'root_angle': 0.25286890261416883, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42941349957106726775409564145', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1811996880705597352107252698835', 'Lhash_array': ['1811996880705597352107252698835'], 'factors': ['2-1980-11.3-c1-0-16'], 'label': '2-1980-11.3-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1980/2/z/c/1081/2'}