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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1022', 'a10': [-0.23434981142250366, -0.9721523367694165], 'a2': [0.9334851442746663, -0.35861606966016646], 'a3': [0.4814741573567515, 0.8764602876329344], 'a4': [0.7427890291629893, -0.6695255470518686], 'a5': [0.129867382596718, -0.9915313726440922], 'a6': [0.7637617168088325, 0.6454982880978266], 'a7': [0.4907648134188302, -0.8712920853020419], 'a8': [0.4532799038330384, -0.8913682341104104], 'a9': [-0.5363652715952123, 0.8439859568894462], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1022', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1837', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2226', 'a^402', 'a^2088', 'a^1822', 'a^264', 'a^1966', 'a^1950', 'a^804', 'a^1684', 'a^2145', 'a^126', 'a^1720', 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21.961383672410207, 'root_angle': -0.27379655746176007, 'root_number': '-0.148961705668088278269599840273-0.988842965411826063474572659842*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.24560818854717825423926702833-0.969164019481027232406341654377*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.794491595191', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.41807160802', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.49759688136', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1022', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1022'], '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': '1-4729-4729.1022-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': '1-4729-4729.1022-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.27379655746176007, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.794491595191', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1022', 'Lhash_array': ['dirichlet_L_4729.1022'], 'factors': ['1-4729-4729.1022-r0-0-0'], 'label': '1-4729-4729.1022-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1022'}
Lfunction data - 1-4729-4729.1022-r0-0-0