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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5225.1356', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9781476007338057, -0.20791169081775934], 'a3': [-0.9781476007338057, -0.20791169081775934], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9135454576426009, 0.4067366430758002], 'a7': [-0.8090169943749475, -0.5877852522924731], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.9135454576426009, 0.4067366430758002], 'algebraic': True, 'analytic_conductor': 24.264797988653697, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '5225.1356', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 5225, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_5225.4096', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^8', 'a^1', 0, 'a^1', 'a^9', 'a^9', 'a^1', 0, 0, 'a^9', 'a^1', 'a^2', 0, 'a^2', 'a^11', 'a^9', 0, 0, 'a^2', 0, 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'192.81049613858717887720298891795', '193.341142516048915945188014532', '193.43943086772766673749241459080', '194.32046147888065373135127912076', '194.56817179479240313769573752953', '195.22217271456422161955273193542', '195.85819849761095832387819059035', '196.39998804802228160506296152018', '197.03032101985852662578148166655', '197.52690448262772042605753563711', '197.86751872533071797077389313110', '198.60366124737658821777806096083', '199.09649305227914653246244121775', '199.684041194154703916549115598172'], 'prelabel': '1-5225-5225.1356-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.264797988653697, 'root_angle': 0.4446792377333798, 'root_number': '0.172921711800250507877725759047+0.984935572303118263336542285523*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.501339247678774214795548854436-0.0346618041447527536281540155884*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.02371889118', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.22963141664', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.60486684051', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.264797988653697, 'bad_primes': [5, 11, 19], 'central_character': '5225.1356', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5225/1356'], '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': '1-5225-5225.1356-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': '1-5225-5225.1356-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.264797988653697, 'root_angle': 0.2223396188666899, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02371889118', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5225.1356', 'Lhash_array': ['dirichlet_L_5225.1356'], 'label': '1-5225-5225.1356-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5225/1356'}
Lfunction data - 1-5225-5225.1356-r0-0-0