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lfunc_lfunctions • Show schema
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{'Lhash': '2355125812474352110452624289791', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.6374586088176875, -2.8361615057632856], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.171221833107733, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '3528.361', 'coefficient_field': 'CDF', 'conductor': 3528, 'conductor_radical': 42, 'conjugate': '114802027485432147309602359704', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.6374586088176875, 2.8361615057632856], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.6374586088176875, 2.8361615057632856], [-5.5, -9.526279441628825]], [[1.0, 0], [6.274917217635375, 0], [13.0, 0]], [[1.0, 0], [-2.0, 3.4641016151377544], [-8.5, 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'-0.6054643436493673635071294605077551469423497523567868621 - 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3535062863872795', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85786668033788830292703780484', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65307693125030121054280548218', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69721416794052783552388272573', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.171221833107733, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 3528, 'conductor_radical': 42, 'degree': 2, 'index': 49, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3528/2/s/bk/361/1'], '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': '2-3528-7.4-c1-0-49', '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': '2-3528-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.307656906122299, 'root_angle': -0.3535062863872795, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85786668033788830292703780484', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2355125812474352110452624289791', 'Lhash_array': ['2355125812474352110452624289791'], 'label': '2-3528-7.4-c1-0-49', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3528/2/s/bk/361/1'}