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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2243.9', 'a10': [-0.5952419772689309, -0.8035465067418149], 'a2': [0.683443141255581, 0.7300037483949682], 'a3': [0.9954638464462174, 0.09514058239521987], 'a4': [-0.06581094534140787, 0.9978321098628117], 'a5': [-0.9934060086830687, -0.11464947410422294], 'a6': [0.6108899564485754, 0.7917155177904862], 'a7': [-0.21548949043964358, -0.9765061594839343], 'a8': [-0.7733992196818433, 0.6339192748256799], 'a9': [0.9818965391629968, 0.18941802020855772], 'algebraic': True, 'analytic_conductor': 10.416448208334975, 'analytic_normalization': 0, 'bad_lfactors': [[2243, [1]]], 'bad_primes': [2243], 'central_character': '2243.9', 'coeff_info': ['x^1121 - 1', '0.999984292127087 + 0.00560495308532831*I', '\\\\zeta_{1121}'], 'conductor': 2243, 'conductor_radical': 2243, 'conjugate': 'dirichlet_L_2243.997', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^146', 'a^17', 'a^292', 'a^581', 'a^163', 'a^802', 'a^438', 'a^34', 'a^727', 'a^144', 'a^309', 'a^1008', 'a^948', 'a^598', 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'199.73612402683743895605743645558'], 'prelabel': '1-2243-2243.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.416448208334975, 'root_angle': -0.022111849610776568, 'root_number': '0.997588178052727120249751368318-0.0694105684275846595299325657348*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0110559248054', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(1121)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.67395889114497073357023418103+0.413404555163745136640716969039*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.609874757889', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.14242825126', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.15148716827', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 10.416448208334975, 'bad_primes': [2243], 'central_character': '2243.9', 'conductor': 2243, 'conductor_radical': 2243, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2243/9'], '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': '1-2243-2243.9-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': '1-2243-2243.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.416448208334975, 'root_angle': -0.011055924805388284, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.609874757889', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2243.9', 'Lhash_array': ['dirichlet_L_2243.9'], 'label': '1-2243-2243.9-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2243/9'}
Lfunction data - 1-2243-2243.9-r0-0-0