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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_343.172', 'a10': [0.5895128895116598, -0.8077589696806923], 'a2': [0.9963483380212069, -0.08538143429562847], 'a3': [-0.5365483771762629, 0.8438695627580832], 'a4': [0.9854200213552425, -0.17013930031663263], 'a5': [0.6563278071035182, -0.7544758509208144], 'a6': [-0.46253829024083526, 0.8865993063730001], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9672948630390295, -0.2536545839095074], 'a9': [-0.4242316778990373, -0.9055536888925844], 'algebraic': True, 'analytic_conductor': 1.592885303369994, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '343.172', 'coeff_info': ['x^147 - 1', '0.999086667417098 + 0.0427297436149168*I', '\\\\zeta_{147}'], 'conductor': 343, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_343.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^145', 'a^50', 'a^143', 'a^127', 'a^48', 0, 'a^141', 'a^100', 'a^125', 'a^110', 'a^46', 'a^138', 0, 'a^30', 'a^139', 'a^74', 'a^98', 'a^49', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.592885303369994, 'bad_primes': [7], 'central_character': '343.172', 'conductor': 343, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/343/172'], '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': '1-7e3-343.172-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-7e3-343.172-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.592885303369994, 'root_angle': -0.043488824101069, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22735071074', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_343.172', 'Lhash_array': ['dirichlet_L_343.172'], 'factors': ['1-7e3-343.172-r0-0-0'], 'label': '1-7e3-343.172-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/343/172'}