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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2793.269', 'a10': [-0.12434370464748518, -0.9922392066001721], 'a2': [0.6982368180860729, 0.7158668492597184], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.024930691738072875, 0.9996891820008162], 'a5': [-0.7971325072229225, -0.6038044103254774], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.7330518718298263, 0.6801727377709194], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 300.1495349513877, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [19, [1]]], 'bad_primes': [3, 7, 19], 'central_character': '2793.269', 'coeff_info': ['x^126 - 1', '0.998756921218922 + 0.0498458856606972*I', '\\\\zeta_{126}'], 'conductor': 2793, 'conductor_radical': 399, 'conjugate': 'dirichlet_L_2793.488', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^16', 0, 'a^32', 'a^76', 0, 0, 'a^48', 0, 'a^92', 'a^51', 0, 'a^86', 0, 0, 'a^64', 'a^94', 0, 0, 'a^108', 0, 'a^67', 'a^53', 0, 'a^26', 'a^102', 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'-0.609984988635329506229676137471+0.792412969126299025851314106057*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.354412270982', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(126)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.957671598614058629276603484874+0.311807458012650037858777991231*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.56422197648', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.17324331262', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.98423282706', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 300.1495349513877, 'bad_primes': [3, 7, 19], 'central_character': '2793.269', 'conductor': 2793, 'conductor_radical': 399, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2793/269'], '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': '1-2793-2793.269-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2793-2793.269-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 300.1495349513877, 'root_angle': 0.35441227098167927, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56422197648', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2793.269', 'Lhash_array': ['dirichlet_L_2793.269'], 'label': '1-2793-2793.269-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2793/269'}
Lfunction data - 1-2793-2793.269-r1-0-0