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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.107', 'a10': [0.6691306063588582, 0.7431448254773942], 'a2': [-0.10452846326765347, 0.9945218953682733], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.9781476007338057, -0.20791169081775934], 'a5': [0.6691306063588582, -0.7431448254773942], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.107', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.228', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^25', 'a^16', 'a^26', 'a^3', 0, 'a^24', 'a^20', 'a^4', 'a^19', 'a^11', 'a^3', 0, 'a^21', 'a^2', 'a^19', 'a^28', 'a^17', 'a^12', 0, 'a^27', 'a^8', 'a^19', 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{'__RealLiteral__': 0, 'data': '3.92860111931', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.107', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/107'], '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': '1-287-287.107-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': '1-287-287.107-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.1525021546225351, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.804381686479', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.107', 'Lhash_array': ['dirichlet_L_287.107'], 'label': '1-287-287.107-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/107'}
Lfunction data - 1-287-287.107-r0-0-0