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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.228', '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': '287.228', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 'a^5', 'a^14', 'a^4', 'a^27', 0, 'a^6', 'a^10', 'a^26', 'a^11', 'a^19', 'a^27', 0, 'a^9', 'a^28', 'a^11', 'a^2', 'a^13', 'a^18', 0, 'a^3', 'a^22', 'a^11', 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'196.23091873407327152268927847017', '196.840491239669054877464584193', '197.601880394871979709010211196776', '198.37319718759702415459590321912', '198.8814014719411820913380085018', '199.39784464845107191688956203341'], 'prelabel': '1-287-287.228-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.1525021546225351, 'root_number': '0.574994175967536636080509324975+0.818157501709428509456279287981*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.152502154623', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08635407407094658017467279462+0.122388091122083301790968062465*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.95238931579', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.77699320961', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.86840923095', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.228', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/228'], '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': '1-287-287.228-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': '1-287-287.228-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': '1.95238931579', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.228', 'Lhash_array': ['dirichlet_L_287.228'], 'factors': ['1-287-287.228-r0-0-0'], 'label': '1-287-287.228-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/228'}
Lfunction data - 1-287-287.228-r0-0-0