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lfunc_lfunctions • Show schema
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{'Lhash': '1973311697239370927808987529373', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.36534102436639504, 0.9308737486442042], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.9555728057861407, -0.2947551744109042], 'a8': [0.0, 0.0], 'a9': [-0.7330518718298263, 0.6801727377709194], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.36534102436639504, -0.9308737486442042]]], [7, [[1.0, 0], [-0.9555728057861407, 0.2947551744109042]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.221', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '2620429379803558321127443989484', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.36534102436639504, -0.9308737486442042]], [[1.0, 0], [0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], 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'6.24818407639563623620885601400036', '7.44032358348053150852922398315460', '8.122516548400894825485095697460490', '8.710344682811374315385849237885025', '9.904766474933104848514331809084744', '10.92203632131786625418748884954419'], 'prelabel': '2-588-147.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': -0.272108843537415, 'root_number': '0.65632780710351820757022637180935 - 0.75447585092081442621596822944542*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1360544217687075', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55666845176746133258904324933', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69671423820908542755360543616', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08989798739970360267810482275', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2934502274282054, 'bad_primes': [2, 3, 7], 'central_character': '147.74', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/1/z/a/221/1'], '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': '2-588-147.74-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': '2-588-147.74-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5417104645732861, 'root_angle': -0.1360544217687075, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55666845176746133258904324933', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1973311697239370927808987529373', 'Lhash_array': ['1973311697239370927808987529373'], 'label': '2-588-147.74-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/1/z/a/221/1'}