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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_675.347', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9702957262759965, 0.24192189559966773], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.882947592858927, -0.46947156278589075], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.984807753012208, 0.17364817766693036], 'a8': [-0.7431448254773942, 0.6691306063588582], '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': '675.347', 'coeff_info': ['x^180 - 1', '0.999390827019096 + 0.0348994967025010*I', '\\\\zeta_{180}'], 'conductor': 675, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_675.533', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^83', 0, 'a^166', 0, 0, 'a^5', 'a^69', 0, 0, 'a^98', 0, 'a^7', 'a^88', 0, 'a^152', 'a^39', 0, 'a^114', 0, 0, 'a^1', 'a^13', 0, 0, 'a^90', 0, 'a^171', 'a^56', 0, 'a^4', 'a^55', 0, 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'199.35778120097935704463260703809', '199.76319174406400429369303838398'], 'prelabel': '1-675-675.347-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1346868215007166, 'root_angle': 0.24296296296296296, 'root_number': '0.722565084489228041379685027882+0.691302899369787644268636175316*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.121481481481', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(180)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.790060955441747797354084663519+0.140816520482119176183695914996*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.11677408454', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.0727357404', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.2446018866', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.1346868215007166, 'bad_primes': [3, 5], 'central_character': '675.347', 'conductor': 675, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/675/347'], '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': '1-675-675.347-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': '1-675-675.347-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1346868215007166, 'root_angle': 0.12148148148148148, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11677408454', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_675.347', 'Lhash_array': ['dirichlet_L_675.347'], 'label': '1-675-675.347-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/675/347'}
Lfunction data - 1-675-675.347-r0-0-0