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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_105.44', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 11.283817103435627, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '105.44', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 105, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_105.74', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^2', 0, 0, 0, 'a^0', 0, 0, 'a^5', 0, 'a^3', 0, 0, 'a^4', 'a^2', 0, 'a^4', 0, 0, 'a^3', 'a^4', 0, 0, 'a^1', 0, 0, 'a^3', 0, 'a^2', 'a^2', 0, 'a^0', 0, 0, 'a^1', 'a^2', 0, 0, 'a^3', 0, 'a^3', 'a^1', 0, 'a^2', 'a^4', 0, 0, 0, 0, 'a^5', 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'186.158873035262220422486938203212', '186.79134780959060586440198843393', '188.160709445629466706927044320153', '188.64794241170926653838872938103', '189.62733780628362862542976686306', '190.2650119089339844998957147325', '190.95653395795021339378589463000', '191.78333173921004195556399259136', '192.55290254785418343546182400101', '192.98758818737074919362223645705', '194.155977705263632549908620402926', '194.51710067941025423741242490474', '195.40389829831305529294079143320', '196.41101666025447198677319175862', '197.39661766560753477399524331808', '198.02414458834183200660585268964', '199.0474458717965226498134289056', '199.37337317786493387904366034523'], 'prelabel': '1-105-105.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.283817103435627, 'root_angle': 0.8535062863872795, 'root_number': '-0.895953219663104777747250207705+0.444148430342060668918079670489*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.426753143194', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.549377100981931294940818918262-0.272341202321642408462706685630*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.140969649105', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.93424418653', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.38397176178', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.283817103435627, 'bad_primes': [3, 5, 7], 'central_character': '105.44', 'conductor': 105, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/105/44'], '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': '1-105-105.44-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-105-105.44-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.283817103435627, 'root_angle': 0.4267531431936398, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.140969649105', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_105.44', 'Lhash_array': ['dirichlet_L_105.44'], 'label': '1-105-105.44-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/105/44'}