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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_847.600', 'a10': [0.23575893550942723, -0.9718115683235417], 'a2': [0.5326077245747999, -0.8463622225284244], 'a3': [0.9781476007338057, 0.20791169081775934], 'a4': [-0.4326580234465083, -0.9015581150138691], 'a5': [0.9480716290349995, -0.3180568914815749], 'a6': [0.6969375686552934, -0.7171318047589635], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9934817353485502, -0.11399140989054063], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.600', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.24', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^277', 'a^11', 'a^224', 'a^313', 'a^288', 0, 'a^171', 'a^22', 'a^260', 0, 'a^235', 'a^312', 0, 'a^324', 'a^118', 'a^98', 'a^299', 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'191.24925006176476567858058449795', '191.9996275106314159925241849281', '192.20873652193858443255484392851', '192.940813524438999990074628868802', '193.17978364186861892590405633949', '194.10262511542628894661192951879', '194.55630756642087996647678714372', '195.30320839571077865000533771077', '196.181665977301475222485899707410', '196.5795526156513324015690593460', '197.01620624767029867638413126936', '197.58670706024473749017259737529', '198.54130284612371359227344118848', '199.06452770982209644843506805157', '199.80782491529107597867733481841'], 'prelabel': '1-847-847.600-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.47588309619053687, 'root_number': '0.0756930211544569489200794326853-0.997131168176238954346212895765*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.237941548095', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(330)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.83000192640241129109063023141-1.03063600631619770897113143095*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.20134912924', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.10700582268', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.84165197729', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.600', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/600'], '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': '1-847-847.600-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': '1-847-847.600-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.23794154809526843, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20134912924', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_847.600', 'Lhash_array': ['dirichlet_L_847.600'], 'label': '1-847-847.600-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/600'}
Lfunction data - 1-847-847.600-r0-0-0