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lfunc_lfunctions • Show schema
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{'Lhash': '1009248770803916266553389115366', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.9510565162951535, 0.30901699437494745], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '4000.257', 'coefficient_field': 'CDF', 'conductor': 4000, 'conductor_radical': 10, 'conjugate': '1489014968358614343723586767913', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.9510565162951535, -0.30901699437494745]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.2787682579175257, -0.14203952192020614], [0.5877852522924731, 0.8090169943749475]], [[1.0, 0], [-1.760073510670101, 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'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.20620819117478337, 'root_number': '0.79739992173355657319994892393798 - 0.60345121163132803127805778198472*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10310409558739168', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.796156898929570856522469151921', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.18089425945419952803428963485', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16506333841467406646810723115', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9962600505320096, 'bad_primes': [2, 5], 'central_character': '25.22', 'conductor': 4000, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4000/1/bo/c/257/1'], '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': '2-4000-25.22-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-4000-25.22-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4128906718256757, 'root_angle': -0.10310409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.796156898929570856522469151921', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1009248770803916266553389115366', 'Lhash_array': ['1009248770803916266553389115366'], 'label': '2-4000-25.22-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4000/1/bo/c/257/1'}