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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.51', 'a10': [0.9135454576426009, -0.4067366430758002], 'a2': [0.6691306063588582, -0.7431448254773942], 'a3': [-0.5, 0.8660254037844386], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [0.9135454576426009, 0.4067366430758002], 'a6': [0.30901699437494745, 0.9510565162951535], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.8090169943749475, -0.5877852522924731], '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': '287.51', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.242', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^5', 'a^11', 'a^1', 'a^3', 0, 'a^9', 'a^10', 'a^14', 'a^14', 'a^1', 'a^3', 0, 'a^6', 'a^7', 'a^14', 'a^8', 'a^7', 'a^12', 0, 'a^12', 'a^13', 'a^14', 'a^2', 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'195.68447693750610648251843309582', '196.558960296816467483939095302840', '197.424503929995608413911167562303', '197.901968334443509558834335091265', '198.66429047391781736221604305159', '199.673051051211440515087845453062'], 'prelabel': '1-287-287.51-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.13638499533579698, 'root_number': '0.909604118464970635716127706931-0.415476049455998926406142853932*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0681924976679', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.43996959505268801116080866881-0.255149396198248561778101200219*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.33439679232', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.79557042572', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.88510312354', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.51', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/51'], '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': '1-287-287.51-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': '1-287-287.51-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.06819249766789849, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33439679232', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.51', 'Lhash_array': ['dirichlet_L_287.51'], 'label': '1-287-287.51-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/51'}
Lfunction data - 1-287-287.51-r0-0-0