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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_25.11', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.30901699437494745, -0.9510565162951535], 'a3': [-0.8090169943749475, -0.5877852522924731], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [1.0, 0.0], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]]], 'bad_primes': [5], 'central_character': '25.11', 'coeff_info': ['x^5 - 1', '0.309016994374947 + 0.951056516295154*I', '\\\\zeta_{5}'], 'conductor': 25, 'conductor_radical': 5, 'conjugate': 'dirichlet_L_25.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^3', 'a^3', 0, 'a^2', 'a^0', 'a^2', 'a^1', 0, 'a^4', 'a^1', 'a^1', 'a^4', 0, 'a^1', 'a^2', 'a^0', 'a^2', 0, 'a^3', 'a^3', 'a^4', 'a^0', 0, 'a^0', 'a^4', 'a^3', 'a^3', 0, 'a^2', 'a^0', 'a^2', 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'199.172676002538489217965917045589', '199.738478960277815788650444521720'], 'prelabel': '1-5e2-25.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': -0.56, 'root_number': '-0.187381314585724630542550734447-0.982287250728688681085641742865*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.28', 'prec': 17}, 'spectral_label': 'r0-0', 'st_group': 'mu(5)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.689339964895652399779757911300-0.523112699284459236944960385672*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.73898283151', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.44236786102', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.13806006101', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.11', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/11'], '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': '1-5e2-25.11-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': '1-5e2-25.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': -0.28, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73898283151', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_25.11', 'Lhash_array': ['dirichlet_L_25.11'], 'label': '1-5e2-25.11-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/25/11'}
Lfunction data - 1-5e2-25.11-r0-0-0