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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_6003.1066', 'a10': [0.45217190728268575, 0.8919308080026939], 'a2': [0.3526477751855643, -0.9357561363179361], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.7512790933133434, -0.6599846391775195], 'a5': [-0.6751723096548833, 0.7376600519719706], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5463487845069707, -0.8375577625858146], 'a8': [-0.8825215767863213, 0.4702719069927368], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 27.87781479921304, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [23, [1]], [29, [1]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1066', 'coeff_info': ['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}'], 'conductor': 6003, 'conductor_radical': 2001, 'conjugate': 'dirichlet_L_6003.1222', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^373', 0, 'a^284', 'a^170', 0, 'a^304', 'a^195', 0, 'a^81', 'a^1', 0, 'a^92', 'a^215', 0, 'a^106', 'a^189', 0, 'a^207', 'a^454', 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False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.7303144026662787, 'root_number': '-0.662052446151236111071051927187-0.749457509499480970715987036850*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(462)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.756912375343902163562717252692-0.340843144879469526999633820382*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.250995861435', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.51353365519', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.03674521744', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.87781479921304, 'bad_primes': [3, 23, 29], 'central_character': '6003.1066', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/6003/1066'], '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': '1-6003-6003.1066-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': '1-6003-6003.1066-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.87781479921304, 'root_angle': -0.36515720133313934, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.250995861435', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_6003.1066', 'Lhash_array': ['dirichlet_L_6003.1066'], 'label': '1-6003-6003.1066-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/6003/1066'}
Lfunction data - 1-6003-6003.1066-r0-0-0