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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_847.601', 'a10': [-0.6548607339452851, 0.7557495743542583], 'a2': [-0.9934817353485502, -0.11399140989054063], 'a3': [0.8090169943749475, 0.5877852522924731], 'a4': [0.9740119169423335, 0.22649676742576438], 'a5': [0.5644432188667692, -0.825471896962774], 'a6': [-0.7367411378764049, -0.6761749002740194], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9418443636395247, -0.33604939321543015], 'a9': [0.30901699437494745, 0.9510565162951535], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.601', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.272', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^57', 'a^11', 'a^4', 'a^93', 'a^68', 0, 'a^61', 'a^22', 'a^40', 0, 'a^15', 'a^92', 0, 'a^104', 'a^8', 'a^98', 'a^79', 'a^56', 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'2.04331214492', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.94117755642', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.601', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/601'], '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': '1-847-847.601-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-847-847.601-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': -0.05330578512396694, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.936216440372', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_847.601', 'Lhash_array': ['dirichlet_L_847.601'], 'factors': ['1-847-847.601-r0-0-0'], 'label': '1-847-847.601-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/601'}