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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_152.123', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.17364817766693036, -0.984807753012208], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 16.334668568783, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '152.123', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 152, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_152.131', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^14', 0, 'a^11', 0, 'a^21', 0, 'a^10', 0, 'a^6', 0, 'a^13', 0, 'a^25', 0, 'a^8', 0, 0, 0, 'a^17', 0, 'a^25', 0, 'a^4', 0, 'a^6', 0, 'a^19', 0, 'a^21', 0, 'a^2', 0, 'a^14', 0, 'a^9', 0, 'a^9', 0, 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'195.244152297118697515686304777820', '195.90125619591762490946501340593', '196.53324668100902886335666062408', '196.89836877480216136486743086438', '198.30097250951680795347340873274', '198.83694006601538994548983404794', '199.598830415362799176021536863199'], 'prelabel': '1-152-152.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.334668568783, 'root_angle': 0.28029332098734944, 'root_number': '-0.189191341026241170278507689556+0.981940240788965993484513698907*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.280293320987', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.752730540147431125513155659736-0.162428373112845500545016227553*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.55105761304', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.85729215636', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.64951442009', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 16.334668568783, 'bad_primes': [2, 19], 'central_character': '152.123', 'conductor': 152, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/152/123'], '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': '1-152-152.123-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': '1-152-152.123-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.334668568783, 'root_angle': 0.28029332098734944, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55105761304', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_152.123', 'Lhash_array': ['dirichlet_L_152.123'], 'factors': ['1-152-152.123-r1-0-0'], 'label': '1-152-152.123-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/152/123'}
Lfunction data - 1-152-152.123-r1-0-0