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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_260.179', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.5, 0.8660254037844386], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 27.940880446602506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.179', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 260, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_260.199', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^8', 0, 0, 0, 'a^7', 0, 'a^4', 0, 'a^8', 0, 0, 0, 0, 0, 'a^1', 0, 'a^4', 0, 'a^3', 0, 'a^8', 0, 0, 0, 'a^0', 0, 'a^2', 0, 'a^0', 0, 'a^4', 0, 0, 0, 'a^2', 0, 0, 0, 'a^5', 0, 'a^4', 0, 0, 0, 'a^3', 0, 'a^2', 0, 'a^3', 0, 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{'__RealLiteral__': 0, 'data': '-0.418707618059', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.679863695953903570459798405651+0.380979823297988294679053524195*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.83444993314', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.28770032081', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.64122514273', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.940880446602506, 'bad_primes': [2, 5, 13], 'central_character': '260.179', 'conductor': 260, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/260/179'], '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': '1-260-260.179-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-260-260.179-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.41870761805923334, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83444993314', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_260.179', 'Lhash_array': ['dirichlet_L_260.179'], 'factors': ['1-260-260.179-r1-0-0'], 'label': '1-260-260.179-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/260/179'}
Lfunction data - 1-260-260.179-r1-0-0