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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.242', 'a10': [-0.6871003849303381, -0.7265624962992387], 'a2': [0.00797350092461664, -0.9999682111362367], 'a3': [0.8033559396470452, -0.5954991471310542], 'a4': [-0.9998728465660103, -0.015946494912164058], 'a5': [0.7210608041484818, -0.6928717895258435], 'a6': [-0.589074657562223, -0.8080786148747842], 'a7': [0.9495672539760007, 0.3135634388389013], 'a8': [-0.023918475057802948, 0.9997139123523836], 'a9': [0.29076153153237394, -0.9567955538049643], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.242', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2599', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^296', 'a^354', 'a^198', 'a^346', 'a^256', 'a^20', 'a^100', 'a^314', 'a^248', 'a^307', 'a^158', 'a^68', 'a^316', 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0.49574251555744525, 'root_number': '-0.999642225006859631181537369572+0.0267473733913261293517313993501*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, '0.982199435828972028271519558129-1.29641047157822525248327571651*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.691620446724', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.40966064274', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.05620028519', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.242', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/242'], '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': '1-4729-4729.242-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': '1-4729-4729.242-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.49574251555744525, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.691620446724', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.242', 'Lhash_array': ['dirichlet_L_4729.242'], 'factors': ['1-4729-4729.242-r0-0-0'], 'label': '1-4729-4729.242-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/242'}
Lfunction data - 1-4729-4729.242-r0-0-0