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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4176.347', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8660254037844386, 0.5], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 19.393262469017767, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [29, [1]]], 'bad_primes': [2, 3, 29], 'central_character': '4176.347', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 4176, 'conductor_radical': 174, 'conjugate': 'dirichlet_L_4176.3827', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^5', 0, 'a^4', 0, 0, 0, 'a^13', 0, 'a^17', 0, 0, 0, 'a^0', 0, 'a^9', 0, 0, 0, 'a^2', 0, 'a^10', 0, 0, 0, 0, 0, 'a^8', 0, 0, 0, 'a^9', 0, 'a^9', 0, 0, 0, 'a^14', 0, 'a^19', 0, 0, 0, 'a^10', 0, 'a^8', 0, 0, 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'prelabel': '1-4176-4176.347-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.393262469017767, 'root_angle': -0.034722222222222224, 'root_number': '0.976296007119933365970886489605-0.216439613938102879759553669618*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.867007567010762400046326912905+0.121108509745051916170672740658*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.435801340677', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.79163112591', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.59140454294', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 19.393262469017767, 'bad_primes': [2, 3, 29], 'central_character': '4176.347', 'conductor': 4176, 'conductor_radical': 174, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4176/347'], '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': '1-4176-4176.347-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': '1-4176-4176.347-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.393262469017767, 'root_angle': -0.034722222222222224, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.435801340677', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4176.347', 'Lhash_array': ['dirichlet_L_4176.347'], 'factors': ['1-4176-4176.347-r0-0-0'], 'label': '1-4176-4176.347-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4176/347'}
Lfunction data - 1-4176-4176.347-r0-0-0