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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_147.53', 'a10': [0.8262387743159949, 0.5633200580636221], 'a2': [-0.36534102436639504, -0.9308737486442042], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7330518718298263, 0.6801727377709194], 'a5': [-0.8262387743159949, 0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.9009688679024191, 0.4338837391175581], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 15.797343944809878, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '147.53', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 147, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_147.86', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 0, 'a^16', 'a^17', 0, 0, 'a^3', 0, 'a^4', 'a^1', 0, 'a^36', 0, 0, 'a^32', 'a^19', 0, 'a^14', 'a^33', 0, 'a^30', 'a^23', 0, 'a^34', 'a^23', 0, 0, 'a^33', 0, 'a^28', 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'196.95608456908692667053675189665', '197.92805447462814447260814255404', '198.4361895704469336481749929', '199.13789597991632018577614414808', '199.905816660708243435456491054811'], 'prelabel': '1-147-147.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': -0.4625850340136055, 'root_number': '-0.972494507836751123339749511660-0.232925808418378593274720164517*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.462585034014', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.590823539396049248591056377342-0.263245932615625434722349470612*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.237604510569', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.9887985008', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.51896698088', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 15.797343944809878, 'bad_primes': [3, 7], 'central_character': '147.53', 'conductor': 147, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/147/53'], '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': '1-147-147.53-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': '1-147-147.53-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 15.797343944809878, 'root_angle': -0.4625850340136055, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.237604510569', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_147.53', 'Lhash_array': ['dirichlet_L_147.53'], 'factors': ['1-147-147.53-r1-0-0'], 'label': '1-147-147.53-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/147/53'}
Lfunction data - 1-147-147.53-r1-0-0