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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4033.755', 'a10': [2.9010907910729803e-30, -1.0], 'a2': [0.766044443118978, 0.6427876096865394], 'a3': [-0.17364817766693036, -0.984807753012208], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [-0.6427876096865394, -0.766044443118978], 'a6': [0.5, -0.8660254037844386], 'a7': [0.766044443118978, -0.6427876096865394], 'a8': [-0.5, 0.8660254037844386], 'a9': [-0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.755', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.1485', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^4', 'a^26', 'a^8', 'a^23', 'a^30', 'a^32', 'a^12', 'a^16', 'a^27', 'a^27', 'a^34', 'a^20', 'a^0', 'a^13', 'a^16', 'a^10', 'a^20', 'a^32', 'a^31', 'a^22', 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'1-4033-4033.755-r0-0-0', 'leading_term': '1.03389829048568012781464947649+0.776690342362999295122930411662*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4033/755', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.293133234817342, 2.03077613079397, 1.7994837202948002, 0.14057718562830335, -1.655266279198345, -1.5024408668067546, 1.0603653496019738, 3.8765821433053045, 4.157630701275668, 1.5839487893023612, -1.126600314255409, -1.220903985814945, 0.9046686820729173, 2.313701981241011, 1.2751958823617142, -0.6813438261558438, -1.1053484138854512, -0.07746100660896531, 0.11304479803957736, -1.438909638782399, -2.756345238399873, -1.9241707792717402, -0.04399346573080255, 0.44978203857625804, -0.4263770607156554, -0.45491646599465185, 0.672938577542022, 0.3586317111101821, 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{'__RealLiteral__': 0, 'data': '1.76789697496', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.97156986891', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.755', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/755'], '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': '1-4033-4033.755-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': '1-4033-4033.755-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.20508219244899645, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.958520501192', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4033.755', 'Lhash_array': ['dirichlet_L_4033.755'], 'label': '1-4033-4033.755-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/755'}
Lfunction data - 1-4033-4033.755-r0-0-0