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lfunc_lfunctions • Show schema
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{'Lhash': '1264833123595308693693849357759', 'a10': [-6.151596376809087, -2.238997974378325], 'a2': [-0.8802737555489667, 2.040703944288693], 'a3': [0.0, 0.0], 'a4': [-2.017107427789681, -2.1380089668590974], 'a5': [0.1712687057186934, 2.940570113961204], 'a6': [0.0, 0.0], 'a7': [2.876017381019069, 0.681628640824015], 'a8': [1.9617805361790235, -0.7140297213319552], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.55', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2180324749168053473231671979303', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8802737555489667, -2.040703944288693], [-1.3724832757374672, -1.4547472831460975]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.1712687057186934, -2.940570113961204], [-4.966191788709715, 0.5804645706261512]], 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'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.997777402832915122052052988521', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.50166744937843276642666865480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16585885389045233439465858786', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.34', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/c/55/2'], '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': '2-3e6-81.34-c1-0-8', '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': '2-3e6-81.34-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.4902344708873327, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.997777402832915122052052988521', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1264833123595308693693849357759', 'Lhash_array': ['1264833123595308693693849357759'], 'label': '2-3e6-81.34-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/c/55/2'}