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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.593', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.6427876096865394, 0.766044443118978], 'a3': [-0.3420201433256687, -0.9396926207859084], 'a4': [-0.17364817766693036, -0.984807753012208], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9396926207859084, 0.3420201433256687], 'a7': [0.8660254037844386, -0.5], 'a8': [0.8660254037844386, 0.5], 'a9': [-0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.593', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.252', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^25', 'a^26', 0, 'a^2', 'a^33', 'a^3', 'a^14', 0, 0, 'a^15', 'a^11', 'a^10', 0, 'a^16', 'a^13', 'a^27', 0, 0, 'a^22', 0, 'a^17', 'a^28', 0, 'a^24', 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{'__RealLiteral__': 0, 'data': '-0.3443068428', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.607107028879834996609871482588-0.0686299723597595892547447076098*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.261521763143', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.63714369613', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.10957638408', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.593', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/593'], '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': '1-1045-1045.593-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': '1-1045-1045.593-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.3443068427997558, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.261521763143', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.593', 'Lhash_array': ['dirichlet_L_1045.593'], 'label': '1-1045-1045.593-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/593'}
Lfunction data - 1-1045-1045.593-r0-0-0