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lfunc_lfunctions • Show schema
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{'Lhash': '963521631093052609443222981033', 'a10': [-1.4811943040920157, 1.6751308705666461], 'a2': [1.0, 0.0], 'a3': [0.0, 1.0], 'a4': [1.0, 0.0], 'a5': [-1.4811943040920157, 1.6751308705666461], 'a6': [0.0, 1.0], 'a7': [-4.156325174658662, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [1.4811943040920157, -1.6751308705666461]]], [13, [[1.0, 0], [-3.2872577376173853, -1.4811943040920157]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.259', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '3307549089298400144305201900247', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [1.4811943040920157, -1.6751308705666461]], [[1.0, 0], [4.156325174658662, 0], [7.0, 0]], 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['0.76008454610409127593912148589637', '3.05962999417242321438888322324901', '3.71303323600269579325293815272955', '5.30420236931194683124524284282659', '6.22787786056799646866515609644889', '6.97207226366128418102649005259011', '8.386800954775169190001059129645881', '8.836465852067409726634021695398002', '10.35614755357082609311148178194807', '11.23958296023922447335098493402620'], 'prelabel': '2-390-65.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.6347797776728719, 'root_number': '-0.4108837068644229 - 0.9116877642226812*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.317389888836', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76008454610409127593912148590', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.05962999417242321438888322325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71303323600269579325293815273', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.64', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/f/b/259/4'], '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': '2-390-65.64-c1-0-2', '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': '2-390-65.64-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': -0.31738988883643593, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.76008454610409127593912148590', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '963521631093052609443222981033', 'Lhash_array': ['963521631093052609443222981033'], 'label': '2-390-65.64-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/f/b/259/4'}