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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3751.1106', 'a10': [0.9352756712299465, -0.3539200740356119], 'a2': [-0.6106478796354381, -0.7919022459222751], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.25421833419348694, 0.9671468547019572], 'a5': [-0.29085400400539907, 0.9567674473737217], 'a6': [0.38048352246492306, -0.9247876994925291], 'a7': [0.3980214108958622, 0.9173761259529634], 'a8': [0.9211236531148501, -0.3892701063173915], 'a9': [-0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1106', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2235', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^213', 'a^55', 'a^96', 'a^98', 'a^268', 'a^61', 'a^309', 'a^110', 'a^311', 0, 'a^151', 'a^206', 'a^274', 'a^153', 'a^192', 'a^196', 'a^323', 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'0.145091256641', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.89283192491', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.47938640864', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1106', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1106'], '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': '1-3751-3751.1106-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': '1-3751-3751.1106-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': -0.2153730488010993, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.145091256641', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3751.1106', 'Lhash_array': ['dirichlet_L_3751.1106'], 'factors': ['1-3751-3751.1106-r0-0-0'], 'label': '1-3751-3751.1106-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1106'}
Lfunction data - 1-3751-3751.1106-r0-0-0