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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_315.59', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, 0.0], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.4628538500336679, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '315.59', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 315, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_315.299', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 0, 'a^2', 0, 0, 0, 'a^0', 0, 0, 'a^3', 0, 'a^4', 0, 0, 'a^4', 'a^1', 0, 'a^5', 0, 0, 'a^1', 'a^0', 0, 0, 'a^2', 0, 0, 'a^5', 0, 'a^5', 'a^2', 0, 'a^5', 0, 0, 'a^5', 'a^3', 0, 0, 'a^4', 0, 'a^5', 'a^5', 0, 'a^4', 'a^1', 0, 0, 0, 0, 'a^0', 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'199.84974421197212930345059833199'], 'prelabel': '1-315-315.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4628538500336679, 'root_angle': -0.28538260250160946, 'root_number': '-0.220488676025866133748366361683-0.975389534362738918162781408250*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.285382602502', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.677835355439196267070056369493-0.354598171553880407150253238068*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.69009698425', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.32018449', 'prec': 34}, 'z3': {'__RealLiteral__': 0, 'data': '3.17656671876', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.4628538500336679, 'bad_primes': [3, 5, 7], 'central_character': '315.59', 'conductor': 315, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/315/59'], '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': '1-315-315.59-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': '1-315-315.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4628538500336679, 'root_angle': -0.28538260250160946, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69009698425', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_315.59', 'Lhash_array': ['dirichlet_L_315.59'], 'factors': ['1-315-315.59-r0-0-0'], 'label': '1-315-315.59-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/315/59'}
Lfunction data - 1-315-315.59-r0-0-0