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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_289.84', 'a10': [-0.44573835577653825, -0.8951632913550623], 'a2': [-0.8502171357296141, 0.5264321628773558], 'a3': [0.9829730996839018, -0.18374951781657034], 'a4': [0.44573835577653825, -0.8951632913550623], 'a5': [-0.092268359463302, 0.9957341762950345], 'a6': [-0.7390089172206591, 0.6736956436465572], 'a7': [-0.9324722294043558, 0.3612416661871529], 'a8': [0.092268359463302, 0.9957341762950345], 'a9': [0.9324722294043558, -0.3612416661871529], 'algebraic': True, 'analytic_conductor': 1.3421103576499365, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '289.84', 'coeff_info': ['x^34 - 1', '0.982973099683902 + 0.183749517816570*I', '\\\\zeta_{34}'], 'conductor': 289, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_289.203', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^33', 'a^28', 'a^9', 'a^13', 'a^15', 'a^8', 'a^32', 'a^23', 'a^11', 'a^27', 'a^8', 'a^29', 'a^8', 'a^22', 0, 'a^12', 'a^20', 'a^3', 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'195.755012720542095183261247563759', '196.23804650356036874196775152110', '196.96586960572433024240892305949', '197.46537004721761220469585303378', '198.26373950939808581700248212693', '198.50127832625647713173399521057', '199.31594071407838879110691387890'], 'prelabel': '1-17e2-289.84-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3421103576499365, 'root_angle': 0.36159169550173015, 'root_number': '-0.645097824107904456077047155640+0.764099991710016421694879928604*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.361591695502', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(34)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.705325106606436136234547939150+0.410681287525255286170377928860*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.96267614278', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.72988039784', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.19726615119', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3421103576499365, 'bad_primes': [17], 'central_character': '289.84', 'conductor': 289, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/289/84'], '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': '1-17e2-289.84-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': '1-17e2-289.84-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3421103576499365, 'root_angle': 0.36159169550173015, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96267614278', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_289.84', 'Lhash_array': ['dirichlet_L_289.84'], 'factors': ['1-17e2-289.84-r0-0-0'], 'label': '1-17e2-289.84-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/289/84'}
Lfunction data - 1-17e2-289.84-r0-0-0