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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.499', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.848048096156426, -0.5299192642332049], 'a3': [-0.5591929034707468, -0.8290375725550417], 'a4': [0.4383711467890774, 0.898794046299167], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.03489949670250097, 0.9993908270190958], 'a7': [0.10452846326765347, 0.9945218953682733], 'a8': [0.10452846326765347, -0.9945218953682733], 'a9': [-0.374606593415912, 0.9271838545667874], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.499', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.289', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^53', 'a^59', 'a^16', 0, 'a^22', 'a^21', 'a^69', 'a^28', 0, 0, 'a^75', 'a^13', 'a^74', 0, 'a^32', 'a^17', 'a^81', 0, 0, 'a^80', 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47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.547426018047800376954907703433-0.0531796618639127072841117097970*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44364826224', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.9190736645', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.04825701923', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.499', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/499'], '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': '1-1045-1045.499-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': '1-1045-1045.499-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.25998648431453586, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44364826224', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.499', 'Lhash_array': ['dirichlet_L_1045.499'], 'label': '1-1045-1045.499-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/499'}
Lfunction data - 1-1045-1045.499-r0-0-0