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lfunc_lfunctions • Show schema
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{'Lhash': '2166746940825229503355785752554', 'a10': [4.106066838477494, 0.0], 'a2': [1.8793852415718169, 0.0], 'a3': [0.0, 0.0], 'a4': [1.532088886237956, 0.0], 'a5': [2.184792530904095, 0.0], 'a6': [0.0, 0.0], 'a7': [0.532088886237956, 0.0], 'a8': [-0.8793852415718167, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.03203738086476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 11], 'central_character': '8019.1', 'coefficient_field': 'CDF', 'conductor': 8019, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8793852415718169, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.184792530904095, 0], [5.0, 0]], [[1.0, 0], [-0.532088886237956, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.573977952239538, 0], [13.0, 0]], [[1.0, 0], [5.879385241571817, 0], [17.0, 0]], [[1.0, 0], [1.2908593693815895, 0], [19.0, 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'5.28986116686070574746411051716086', '6.01586391537007199087811592237000', '6.57885790577834128580569096996259', '7.08361744491534830394306838592582'], 'prelabel': '2-8019-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.00200208578233, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70926195312424864611206945710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49734751074547972988331473650', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99255420674316744521429238946', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.03203738086476, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 8019, 'conductor_radical': 33, 'degree': 2, 'index': 341, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8019/2/a/b/1/3'], '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': '2-8019-1.1-c1-0-341', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8019-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.00200208578233, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70926195312424864611206945710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2166746940825229503355785752554', 'Lhash_array': ['2166746940825229503355785752554'], 'label': '2-8019-1.1-c1-0-341', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8019/2/a/b/1/3'}