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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.172', 'a10': [-0.10452846326765347, 0.9945218953682733], 'a2': [0.9781476007338057, 0.20791169081775934], 'a3': [0.8660254037844386, -0.5], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [0.10452846326765347, 0.9945218953682733], 'a6': [0.9510565162951535, -0.30901699437494745], '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': '287.172', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.282', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^55', 'a^4', 'a^14', 'a^57', 0, 'a^6', 'a^50', 'a^16', 'a^31', 'a^59', 'a^27', 0, 'a^9', 'a^8', 'a^1', 'a^52', 'a^53', 'a^18', 0, 'a^33', 'a^32', 'a^1', 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'195.93507574215927064456604397814', '196.80008344893609040754807704017', '197.13718352996209466496702198836', '197.95073333011782564093674677314', '198.54798343587493622642993468771', '198.99443317871567544941328899606'], 'prelabel': '1-287-287.172-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.06626244678841749, 'root_number': '0.914575535117525295061429062730+0.404415121582381308182268895775*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0662624467884', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.26107710837445742994405520129+0.302864430662421299351047025564*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.05431779178', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.83441808987', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.74207462862', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.172', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/172'], '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': '1-287-287.172-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': '1-287-287.172-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.06626244678841749, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05431779178', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.172', 'Lhash_array': ['dirichlet_L_287.172'], 'factors': ['1-287-287.172-r0-0-0'], 'label': '1-287-287.172-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/172'}
Lfunction data - 1-287-287.172-r0-0-0