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lfunc_lfunctions • Show schema
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{'Lhash': '2244757296653218883541863801966', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.36327126400268045], 'a8': [0.0, 0.0], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2260764507227501, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [151, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 151], 'central_character': '453.8', 'coefficient_field': 'CDF', 'conductor': 453, 'conductor_radical': 453, 'conjugate': '3151572432420479994010532348967', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.5, -0.36327126400268045], [0.30901699437494745, -0.9510565162951535]], [[1.0, 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{'__RealLiteral__': 0, 'data': '4.18206251790532487468604274879', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2260764507227501, 'bad_primes': [3, 151], 'central_character': '453.8', 'conductor': 453, 'conductor_radical': 453, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/453/1/j/a/8/1'], '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': '2-453-453.8-c0-0-0', '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': '2-453-453.8-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.47547497381329135, 'root_angle': -0.13362232530201906, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77080127303932958247840334988', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2244757296653218883541863801966', 'Lhash_array': ['2244757296653218883541863801966'], 'label': '2-453-453.8-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/453/1/j/a/8/1'}