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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_2675.234', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.5237615037995126, 0.851864946536523], 'a3': [-0.053322498847817576, 0.9985773435826714], 'a4': [-0.45134777427534634, 0.8923481308641213], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.8785813075865162, 0.4775928035047926], 'a7': [-0.7175072570443312, 0.696551029062997], 'a8': [-0.9965586817815493, 0.08289025133162993], 'a9': [-0.994313422233249, -0.10649327850528746], 'algebraic': True, 'analytic_conductor': 287.4686738256219, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [107, [1]]], 'bad_primes': [5, 107], 'central_character': '2675.234', 'coeff_info': ['x^530 - 1', '0.999929729520755 + 0.0118547889289482*I', '\\\\zeta_{530}'], 'conductor': 2675, 'conductor_radical': 535, 'conjugate': 'dirichlet_L_2675.1589', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^86', 'a^137', 'a^172', 0, 'a^223', 'a^200', 'a^258', 'a^274', 0, 'a^196', 'a^309', 'a^409', 'a^286', 0, 'a^344', 'a^268', 'a^360', 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False, 'root_analytic_conductor': 287.4686738256219, 'root_angle': 0.3137509457570888, 'root_number': '-0.389933159783137777264641879462+0.920843163031326384807851098369*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.313750945757', 'prec': 40}, 'spectral_label': 'r1-0', 'st_group': 'mu(530)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.522618572576112352074240637360+0.682405546269428811004460807162*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.235084302161', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.37439467975', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.98041416053', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 287.4686738256219, 'bad_primes': [5, 107], 'central_character': '2675.234', 'conductor': 2675, 'conductor_radical': 535, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2675/234'], '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': '1-2675-2675.234-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2675-2675.234-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 287.4686738256219, 'root_angle': 0.3137509457570888, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.235084302161', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_2675.234', 'Lhash_array': ['dirichlet_L_2675.234'], 'factors': ['1-2675-2675.234-r1-0-0'], 'label': '1-2675-2675.234-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2675/234'}