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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_225.203', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.4067366430758002, 0.9135454576426009], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.6691306063588582, 0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8660254037844386, 0.5], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.203', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 225, 'conductor_radical': 15, 'conjugate': 'dirichlet_L_225.92', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 0, 0, 'a^5', 'a^33', 0, 0, 'a^26', 0, 'a^19', 'a^16', 0, 'a^44', 'a^3', 0, 'a^18', 0, 0, 'a^37', 'a^1', 0, 0, 'a^30', 0, 'a^27', 'a^32', 0, 'a^28', 'a^55', 0, 'a^14', 0, 0, 'a^9', 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'-0.747798090498531878105720508059+0.663926212652241594900990021760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.384444444444', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.880985720896730072029810365332+0.778646773630570284136590886078*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.03799317154', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.63477640634', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.9323620694', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.0448956071669055, 'bad_primes': [3, 5], 'central_character': '225.203', 'conductor': 225, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/225/203'], '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': '1-15e2-225.203-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': '1-15e2-225.203-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0448956071669055, 'root_angle': 0.3844444444444444, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03799317154', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_225.203', 'Lhash_array': ['dirichlet_L_225.203'], 'factors': ['1-15e2-225.203-r0-0-0'], 'label': '1-15e2-225.203-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/225/203'}
Lfunction data - 1-15e2-225.203-r0-0-0