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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_64.53', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9238795325112867, -0.3826834323650898], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.3826834323650898, 0.9238795325112867], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.7071067811865476, -0.7071067811865476], 'algebraic': True, 'analytic_conductor': 0.2972147504830309, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]]], 'bad_primes': [2], 'central_character': '64.53', 'coeff_info': ['x^16 - 1', '0.923879532511287 + 0.382683432365090*I', '\\\\zeta_{16}'], 'conductor': 64, 'conductor_radical': 2, 'conjugate': 'dirichlet_L_64.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^15', 0, 'a^5', 0, 'a^2', 0, 'a^14', 0, 'a^9', 0, 'a^11', 0, 'a^4', 0, 'a^12', 0, 'a^3', 0, 'a^1', 0, 'a^6', 0, 'a^10', 0, 'a^13', 0, 'a^7', 0, 'a^8', 0, 'a^8', 0, 'a^7', 0, 'a^13', 0, 'a^10', 0, 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  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.2972147504830309, 'bad_primes': [2], 'central_character': '64.53', 'conductor': 64, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/64/53'], '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': '1-2e6-64.53-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2e6-64.53-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2972147504830309, 'root_angle': 0.015625, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27752717835', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_64.53', 'Lhash_array': ['dirichlet_L_64.53'], 'factors': ['1-2e6-64.53-r0-0-0'], 'label': '1-2e6-64.53-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/64/53'}