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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_288.85', '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': [-0.25881904510252074, 0.9659258262890683], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 1.337466377173639, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '288.85', 'coeff_info': ['x^24 - 1', '0.965925826289068 + 0.258819045102521*I', '\\\\zeta_{24}'], 'conductor': 288, 'conductor_radical': 6, 'conjugate': 'dirichlet_L_288.61', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^31', 0, 'a^14', 0, 0, 0, 'a^11', 0, 'a^25', 0, 0, 0, 'a^12', 0, 'a^9', 0, 0, 0, 'a^34', 0, 'a^14', 0, 0, 0, 'a^29', 0, 'a^16', 0, 0, 0, 'a^21', 0, 'a^15', 0, 0, 0, 'a^34', 0, 'a^11', 0, 0, 0, 'a^20', 0, 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'-0.915311479119447142408175816731+0.402746689858737234818584299645*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.434027777778', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(24)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.662197797672818519202519025368+0.186018047901863568268630791927*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.05060441237', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.31469658961', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.16699123703', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.337466377173639, 'bad_primes': [2, 3], 'central_character': '288.85', 'conductor': 288, 'conductor_radical': 6, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/288/85'], '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': '1-288-288.85-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-288-288.85-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.337466377173639, 'root_angle': 0.4340277777777778, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.05060441237', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_288.85', 'Lhash_array': ['dirichlet_L_288.85'], 'factors': ['1-288-288.85-r0-0-0'], 'label': '1-288-288.85-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/288/85'}