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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.422', 'a10': [-0.589074657562223, -0.8080786148747842], 'a2': [-0.7533711667168278, -0.6575955331050582], 'a3': [0.6515676231958488, -0.7585905564946828], 'a4': [0.1351362296805486, 0.9908270280062641], 'a5': [0.9751807495903484, 0.2214102654088247], 'a6': [-0.9897180218885506, 0.14303229407729687], 'a7': [-0.9087264778787534, -0.41739212786308705], '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': '4729.422', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1087', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^242', 'a^340', 'a^90', 'a^14', 'a^188', 'a^224', 'a^332', 'a^286', 'a^256', 'a^247', 'a^36', 'a^210', 'a^72', 'a^354', 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'0.0921083944719446778464224763927+0.995748986275055482223232711813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(394)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.550046151330198503206520541972-0.501638051025222557526611893552*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.138135090644', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.891857223206', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '2.06194932026', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.422', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/422'], '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': '1-4729-4729.422-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': '1-4729-4729.422-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.2353196857457703, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.138135090644', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.422', 'Lhash_array': ['dirichlet_L_4729.422'], 'factors': ['1-4729-4729.422-r0-0-0'], 'label': '1-4729-4729.422-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/422'}
Lfunction data - 1-4729-4729.422-r0-0-0