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lfunc_lfunctions • Show schema
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{'Lhash': '1141462566677371078043613011165', 'a10': [4.7161064298922595, 2.1640199834380947], 'a2': [-1.3639820487882122, -1.8773602317993254], 'a3': [-0.9510565162951535, -0.30901699437494745], 'a4': [-1.046000421775233, 3.219258277976006], 'a5': [-1.9490193097262225, 1.096049145939323], 'a6': [0.7170877994199611, 2.2069693149840446], 'a7': [0.0, 1.0], 'a8': [3.0564946353211586, -0.9931153084460587], 'a9': [0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.192146106117222, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.9510565162951535, 0.30901699437494745]]], [5, [[1.0, 0], [1.9490193097262225, -1.096049145939323]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 7], 'central_character': '525.64', 'coefficient_field': 'CDF', 'conductor': 525, 'conductor_radical': 105, 'conjugate': '713731277150410058175329813511', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.900455193625010494317581568973', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.63191443058749882262338763331', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.90080817059457192634569642360', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.192146106117222, 'bad_primes': [3, 5, 7], 'central_character': '25.14', 'conductor': 525, 'conductor_radical': 105, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/525/2/z/b/64/2'], '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': '2-525-25.14-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': '2-525-25.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0474731026602577, 'root_angle': 0.3169353914232161, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.900455193625010494317581568973', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1141462566677371078043613011165', 'Lhash_array': ['1141462566677371078043613011165'], 'label': '2-525-25.14-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/525/2/z/b/64/2'}