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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_297.146', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.9902680687415704, -0.13917310096006544], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9612616959383189, 0.27563735581699916], 'a5': [0.374606593415912, -0.9271838545667874], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5591929034707468, 0.8290375725550417], 'a8': [-0.9135454576426009, -0.4067366430758002], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 31.917082664003633, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '297.146', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 297, 'conductor_radical': 33, 'conjugate': 'dirichlet_L_297.59', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^47', 0, 'a^4', 'a^73', 0, 'a^14', 'a^51', 0, 'a^30', 0, 0, 'a^52', 'a^61', 0, 'a^8', 'a^3', 0, 'a^6', 'a^77', 0, 0, 'a^85', 0, 'a^56', 'a^9', 0, 'a^18', 'a^29', 0, 'a^22', 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'199.66366188604263316661060210865'], 'prelabel': '1-297-297.146-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 31.917082664003633, 'root_angle': -0.05193188525031988, 'root_number': '0.947235574927067454418723611540-0.320538243572569634330080476158*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0519318852503', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.866379081611668875431556565418-0.100395129089979410946884496174*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.866849749014', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.92022719408', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.15039093073', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 31.917082664003633, 'bad_primes': [3, 11], 'central_character': '297.146', 'conductor': 297, 'conductor_radical': 33, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/297/146'], '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': '1-297-297.146-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': '1-297-297.146-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 31.917082664003633, 'root_angle': -0.05193188525031988, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.866849749014', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_297.146', 'Lhash_array': ['dirichlet_L_297.146'], 'factors': ['1-297-297.146-r1-0-0'], 'label': '1-297-297.146-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/297/146'}
Lfunction data - 1-297-297.146-r1-0-0