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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.239', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [0.24192189559966773, 0.9702957262759965], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.882947592858927, 0.46947156278589075], 'a5': [-0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6156614753256583, -0.7880107536067219], 'a8': [-0.6691306063588582, -0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.239', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.830', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 0, 'a^38', 'a^35', 0, 'a^58', 'a^57', 0, 'a^54', 'a^88', 0, 'a^11', 'a^77', 0, 'a^76', 'a^12', 0, 'a^54', 'a^73', 0, 'a^17', 'a^2', 0, 'a^70', 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'194.78411124566200387237524714862', '195.239681579293538406187808038870', '195.82053731737875219669132483473', '196.74508814414838574873052659592', '197.15717004664687825340579477598', '197.92712457528786542882016387682', '198.10928364579929733970906387071', '198.87237621126318792694493297026', '199.51949132858436795704140163120'], 'prelabel': '1-837-837.239-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.3180906996450292, 'root_number': '-0.414894167304547506852693029927+0.909869677446537473395052689622*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.318090699645', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.799499784120384643396688633471+0.551642881627428740750182653762*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.980133138108', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.96517094218', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.01222306499', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.239', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/239'], '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': '1-837-837.239-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': '1-837-837.239-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': 0.3180906996450292, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.980133138108', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.239', 'Lhash_array': ['dirichlet_L_837.239'], 'factors': ['1-837-837.239-r0-0-0'], 'label': '1-837-837.239-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/239'}
Lfunction data - 1-837-837.239-r0-0-0