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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_828.463', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.7860530947427875, 0.6181589862206052], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5800569095711982, -0.8145759520503357], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 88.98095772994952, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '828.463', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 828, 'conductor_radical': 138, 'conjugate': 'dirichlet_L_828.583', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^26', 0, 'a^43', 0, 0, 0, 'a^91', 0, 'a^56', 0, 0, 0, 'a^6', 0, 'a^93', 0, 0, 0, 0, 0, 'a^52', 0, 0, 0, 'a^28', 0, 'a^35', 0, 0, 0, 'a^69', 0, 'a^18', 0, 0, 0, 'a^26', 0, 'a^97', 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'196.9731895956358910167543293181', '197.75336286511560741368271658021', '198.204572781836823263801775329941', '198.83703226783880490686250605925', '199.37784555738696500085449913522', '199.984990567856775368044023914819'], 'prelabel': '1-828-828.463-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 88.98095772994952, 'root_angle': -0.06140869659921469, 'root_number': '0.926481800512144271560869342049-0.376339571822809123239776606761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0614086965992', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.769178309795380210285268591758+0.0265392407765372957808810010624*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.383611296022', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.82738797178', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.2830046869', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 88.98095772994952, 'bad_primes': [2, 3, 23], 'central_character': '828.463', 'conductor': 828, 'conductor_radical': 138, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/828/463'], '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': '1-828-828.463-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-828-828.463-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 88.98095772994952, 'root_angle': -0.06140869659921469, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.383611296022', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_828.463', 'Lhash_array': ['dirichlet_L_828.463'], 'factors': ['1-828-828.463-r1-0-0'], 'label': '1-828-828.463-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/828/463'}
Lfunction data - 1-828-828.463-r1-0-0