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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2268.1103', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.5971585917027862, 0.8021231927550437], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 10.532547720242409, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.1103', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 2268, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_2268.695', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^19', 0, 0, 0, 0, 0, 'a^80', 0, 'a^52', 0, 0, 0, 'a^21', 0, 'a^33', 0, 0, 0, 'a^76', 0, 'a^38', 0, 0, 0, 'a^11', 0, 'a^31', 0, 0, 0, 0, 0, 'a^48', 0, 0, 0, 'a^7', 0, 'a^35', 0, 0, 0, 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'194.4137465016676517933147875466', '195.0472516429076064278829081165', '195.44261270530782415415109543155', '196.2868709102793220672112378169', '196.675687758493311785496582200', '197.464959606608273864374236271006', '197.69167869326387353626715834016', '198.66397740420679378497756211083', '198.95138403749199883346806158104', '199.3914690341092408732558774746', '199.944325786596579593525499843936'], 'prelabel': '1-2268-2268.1103-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.532547720242409, 'root_angle': -0.16440746418129404, 'root_number': '0.512242433682293553146081849836-0.858840898615826918146895917774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.164407464181', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.797947235621457367255261472647+0.0547912824392689219716628692806*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.305146539375', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.86328662435', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.62991872062', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 10.532547720242409, 'bad_primes': [2, 3, 7], 'central_character': '2268.1103', 'conductor': 2268, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2268/1103'], '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': '1-2268-2268.1103-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': '1-2268-2268.1103-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.532547720242409, 'root_angle': -0.16440746418129404, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.305146539375', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2268.1103', 'Lhash_array': ['dirichlet_L_2268.1103'], 'factors': ['1-2268-2268.1103-r0-0-0'], 'label': '1-2268-2268.1103-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2268/1103'}
Lfunction data - 1-2268-2268.1103-r0-0-0