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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_225.211', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6691306063588582, 0.7431448254773942], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.8090169943749475, 0.5877852522924731], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.211', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 225, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_225.16', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 0, 0, 'a^5', 'a^6', 0, 0, 'a^2', 0, 'a^13', 'a^7', 0, 'a^8', 'a^6', 0, 'a^6', 0, 0, 'a^4', 'a^7', 0, 0, 'a^0', 0, 'a^9', 'a^14', 0, 'a^1', 'a^10', 0, 'a^8', 0, 0, 'a^3', 'a^8', 0, 0, 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'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02887900655241164411497736470+0.836949351407109293175306277645*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.21713228383', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.56142429829', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.63500721337', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'bad_primes': [3, 5], 'central_character': '225.211', 'conductor': 225, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/225/211'], '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': '1-15e2-225.211-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': '1-15e2-225.211-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0448956071669055, 'root_angle': 0.36444444444444446, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21713228383', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_225.211', 'Lhash_array': ['dirichlet_L_225.211'], 'factors': ['1-15e2-225.211-r0-0-0'], 'label': '1-15e2-225.211-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/225/211'}
Lfunction data - 1-15e2-225.211-r0-0-0