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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_5445.344', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8799502578106532, -0.4750658309949949], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.5486249124420699, -0.8360686009221558], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9480716290349995, -0.3180568914815749], 'a8': [0.08557500847883974, -0.9963317308626913], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 585.1465155067333, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1]]], 'bad_primes': [3, 5, 11], 'central_character': '5445.344', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 5445, 'conductor_radical': 165, 'conjugate': 'dirichlet_L_5445.554', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^304', 0, 'a^278', 0, 0, 'a^313', 'a^252', 0, 0, 0, 0, 'a^179', 'a^287', 0, 'a^226', 'a^156', 0, 'a^42', 0, 0, 0, 'a^50', 0, 0, 'a^153', 0, 'a^261', 'a^163', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 585.1465155067333, 'bad_primes': [3, 5, 11], 'central_character': '5445.344', 'conductor': 5445, 'conductor_radical': 165, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5445/344'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-5445-5445.344-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5445-5445.344-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 585.1465155067333, 'root_angle': -0.049816345270890725, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.730388719746', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_5445.344', 'Lhash_array': ['dirichlet_L_5445.344'], 'label': '1-5445-5445.344-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5445/344'}