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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_260.63', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.8660254037844386, 0.5], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.5, 0.8660254037844386], 'algebraic': True, 'analytic_conductor': 27.940880446602506, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '260.63', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 260, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_260.227', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^13', 0, 0, 0, 'a^8', 0, 'a^2', 0, 'a^7', 0, 0, 0, 0, 0, 'a^11', 0, 'a^11', 0, 'a^9', 0, 'a^7', 0, 0, 0, 'a^15', 0, 'a^10', 0, 'a^9', 0, 'a^8', 0, 0, 0, 'a^10', 0, 0, 0, 'a^7', 0, 'a^11', 0, 0, 0, 'a^0', 0, 'a^4', 0, 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'186.01068098244280437170267486785', '186.77704900978564231646444052736', '187.08303586558711057792332859959', '188.05894360670695952710195941255', '188.54448085910900111836036817614', '189.41103695195751809701354181725', '190.4172431126160744029914993235', '191.09380229024305176915953795382', '191.35770458572561910687117499143', '192.21447870876942314220122563717', '192.873816669084872052554438069260', '193.631143902046359494258151735088', '194.29659740706084860376843290785', '194.809876878526316369675920833466', '196.040506377147584518498584811354', '196.54919853707330300329461201071', '197.17829791521503264020357812920', '197.78857296402687869701701221392', '198.46629380134043864239022796765', '199.064865797720808015840218474044', '199.91090035639621326230985095851'], 'prelabel': '1-260-260.63-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.3305837188767172, 'root_number': '0.507462126022619804056332398079-0.861674062887239711005734274206*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.165291859438', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.31281080470176200120749454500-0.131292636977302571007323278954*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.60087705056', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.46719053514', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.44140664429', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 27.940880446602506, 'bad_primes': [2, 5, 13], 'central_character': '260.63', 'conductor': 260, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/260/63'], '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': '1-260-260.63-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': '1-260-260.63-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 27.940880446602506, 'root_angle': -0.1652918594383586, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60087705056', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_260.63', 'Lhash_array': ['dirichlet_L_260.63'], 'label': '1-260-260.63-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/260/63'}
Lfunction data - 1-260-260.63-r1-0-0