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lfunc_lfunctions • Show schema
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{'Lhash': '2014698832310383093345886228352', 'a10': [3.3134814937736827, 2.0259720287871534], 'a2': [1.422766991605567, -0.9962321726381689], 'a3': [0.0, 0.0], 'a4': [0.34774708395165177, -0.9554272608383542], 'a5': [0.8936698555753921, 2.0497205149082784], 'a6': [0.0, 0.0], 'a7': [0.4290553436859051, -0.9201121538160306], 'a8': [0.44200979827003994, 1.649603024587059], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8936698555753921, -2.0497205149082784]]]], 'bad_primes': [3, 5], 'central_character': '405.8', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2408330546903330750019644692094', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.422766991605567, 0.9962321726381689], [0.6840402866513374, -1.8793852415718169]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8936698555753921, 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'data': '3.59435898151608738190427732832', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74077229322157210929371074742', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '135.83', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/r/a/8/13'], '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': '2-405-135.83-c1-0-9', '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': '2-405-135.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.05004661599587816, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58931714460408427420335443553', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2014698832310383093345886228352', 'Lhash_array': ['2014698832310383093345886228352'], 'label': '2-405-135.83-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/r/a/8/13'}