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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1064', 'a10': [-0.40527927995539337, 0.9141929256118961], 'a2': [-0.7533711667168278, -0.6575955331050582], 'a3': [0.6515676231958488, -0.7585905564946828], 'a4': [0.1351362296805486, 0.9908270280062641], 'a5': [-0.2958434602924771, -0.9552364351312054], 'a6': [-0.9897180218885506, 0.14303229407729687], 'a7': [0.09289105287030068, 0.9956762788661017], 'a8': [0.5497556886765316, -0.8353254951022341], 'a9': [-0.1509192648058248, -0.9885460917481134], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1064', 'coeff_info': ['x^1182 - 1', '0.999985871574519 + 0.00531569857584313*I', '\\\\zeta_{1182}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.4689', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^726', 'a^1020', 'a^270', 'a^830', 'a^564', 'a^278', 'a^996', 'a^858', 'a^374', 'a^741', 'a^108', 'a^236', 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'0.995424269982600866155109259717+0.0955537687880815102497586494691*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(1182)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.695361541983043766759576334656-0.346659462887341263300948560694*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.915654474965', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.65284992652', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.34391536837', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1064', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1064'], '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': '1-4729-4729.1064-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': '1-4729-4729.1064-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.015231092850956415, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.915654474965', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1064', 'Lhash_array': ['dirichlet_L_4729.1064'], 'label': '1-4729-4729.1064-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1064'}
Lfunction data - 1-4729-4729.1064-r0-0-0