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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_675.121', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.9612616959383189, 0.27563735581699916], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.848048096156426, 0.5299192642332049], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.766044443118978, 0.6427876096865394], 'a8': [0.6691306063588582, 0.7431448254773942], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.1346868215007166, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '675.121', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 675, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_675.106', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 0, 'a^4', 0, 0, 'a^5', 'a^6', 0, 0, 'a^17', 0, 'a^43', 'a^7', 0, 'a^8', 'a^21', 0, 'a^6', 0, 0, 'a^19', 'a^22', 0, 0, 'a^0', 0, 'a^9', 'a^29', 0, 'a^31', 'a^10', 0, 'a^23', 0, 0, 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'199.360408071766678828458404239511', '199.95161505386707112683204987977'], 'prelabel': '1-675-675.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1346868215007166, 'root_angle': 0.4096296296296296, 'root_number': '0.280108269370426918635869658393+0.959968414808687522227483313164*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.204814814815', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.84785264979467799590029507421+0.707534159607881259749349154211*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.75612751826', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.50770265345', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.81652924862', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1346868215007166, 'bad_primes': [3, 5], 'central_character': '675.121', 'conductor': 675, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/675/121'], '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': '1-675-675.121-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': '1-675-675.121-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1346868215007166, 'root_angle': 0.2048148148148148, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75612751826', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_675.121', 'Lhash_array': ['dirichlet_L_675.121'], 'label': '1-675-675.121-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/675/121'}
Lfunction data - 1-675-675.121-r0-0-0