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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_547.218', 'a10': [-0.5961324854692254, -0.8028860814388825], 'a2': [0.4493704009671613, 0.8933455337855631], 'a3': [-0.9009688679024191, 0.4338837391175581], 'a4': [-0.5961324854692254, 0.8028860814388825], 'a5': [-0.9851389890168738, 0.17175905309127604], 'a6': [-0.7924768419510905, -0.6099020044000728], 'a7': [0.7709531747949796, 0.6368918293348892], 'a8': [-0.9851389890168738, -0.17175905309127604], 'a9': [0.6234898018587335, -0.7818314824680298], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.218', 'coeff_info': ['x^91 - 1', '0.997617272301248 + 0.0689911444043249*I', '\\\\zeta_{91}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.409', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 'a^39', 'a^32', 'a^43', 'a^55', 'a^10', 'a^48', 'a^78', 'a^59', 'a^28', 'a^71', 'a^26', 'a^26', 'a^82', 'a^64', 'a^50', 'a^3', 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'198.42559815894572230769902750707', '198.76964167860017258525047878651', '199.41853572141349902134951241665'], 'prelabel': '1-547-547.218-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.40009934994811736, 'root_number': '0.308720138357452489177578375706-0.951152919447002166587329674031*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.200049674974', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(91)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.395025655191618467447193703773+0.504694160789720854301156111105*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.21585948368', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.93067957922', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.51844356175', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.218', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/218'], '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': '1-547-547.218-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': '1-547-547.218-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.20004967497405868, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.21585948368', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_547.218', 'Lhash_array': ['dirichlet_L_547.218'], 'label': '1-547-547.218-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/218'}
Lfunction data - 1-547-547.218-r0-0-0