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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_31.10', 'a10': [-0.9781476007338057, -0.20791169081775934], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [-0.5, 0.8660254037844386], 'a6': [-0.5, -0.8660254037844386], 'a7': [0.9135454576426009, 0.4067366430758002], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '31.10', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 31, 'conductor_radical': 31, 'conjugate': 'dirichlet_L_31.28', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^7', 'a^6', 'a^5', 'a^10', 'a^1', 'a^9', 'a^14', 'a^8', 'a^11', 'a^13', 'a^2', 'a^4', 'a^12', 'a^12', 'a^4', 'a^2', 'a^13', 'a^11', 'a^8', 'a^14', 'a^9', 'a^1', 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'unitary', 'types': ['DIR'], 'values': [[1, '0.603451447239357306279679305214+0.534445349439063168378695709422*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.95325943908', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.60098766832', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.87773670743', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.10', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/10'], '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': '1-31-31.10-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': '1-31-31.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.3332196959897036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.95325943908', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_31.10', 'Lhash_array': ['dirichlet_L_31.10'], 'label': '1-31-31.10-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/31/10'}
Lfunction data - 1-31-31.10-r0-0-0