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lfunc_lfunctions • Show schema
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{'Lhash': '1653439185099309719077392214532', 'a10': [-2.3608787636011512, 0], 'a2': [-2.3608787636011512, 0], 'a3': [0, 2.848624152860972], 'a4': [3.5737485364228996, 0], 'a5': [1.0, 0], 'a6': [0, -6.725256267970788], 'a7': [0, -0.8163968504326622], 'a8': [-3.7154294988892165, 0], 'a9': [-5.114659564262889, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.344367011223804, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [3.2272981484944654, -0.764556512446396]]], [19, [[1.0, 0], [2.177934147581954, 3.7757916850372544]]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.626', 'coefficient_field': 'CDF', 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': '333521508120296488373755642231', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.3608787636011512, 0], [2.0, 0]], [[1.0, 0], [0, -2.848624152860972], [-3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0.8163968504326622], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.344367011223804, 'bad_primes': [5, 11, 19], 'central_character': '209.208', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1045/2/f/b/626/3'], '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': '2-1045-209.208-c1-0-51', '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': '2-1045-209.208-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.888661802846398, 'root_angle': 0.12970878818273474, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30433353228533355930398307613', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1653439185099309719077392214532', 'Lhash_array': ['1653439185099309719077392214532'], 'label': '2-1045-209.208-c1-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1045/2/f/b/626/3'}