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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.381', 'a10': [-0.9087264778787534, -0.41739212786308705], 'a2': [0.5228384531415806, 0.8524317872513432], 'a3': [0.9994914186000327, 0.031888934521151754], 'a4': [-0.4532799038330384, 0.8913682341104104], 'a5': [-0.8309154635618966, 0.5563986811753946], 'a6': [0.4953894057817187, 0.8686710174969784], 'a7': [-0.9998728465660103, 0.015946494912164058], 'a8': [-0.9968227806620411, 0.07965139015231544], 'a9': [0.9979661917102114, 0.06374543280437904], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.381', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2259', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^64', 'a^2', 'a^128', 'a^160', 'a^66', 'a^196', 'a^192', 'a^4', 'a^224', 'a^93', 'a^130', 'a^36', 'a^260', 'a^162', 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-0.44275455129549585, 'root_number': '-0.936008179305723953789680325868-0.351978249715495511865963875177*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, '0.965289210302666735871285208463+1.18154742035720785389248507459*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.32244218844', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.51219977308', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.41020557967', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.381', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/381'], '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': '1-4729-4729.381-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': '1-4729-4729.381-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.44275455129549585, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32244218844', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.381', 'Lhash_array': ['dirichlet_L_4729.381'], 'factors': ['1-4729-4729.381-r0-0-0'], 'label': '1-4729-4729.381-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/381'}
Lfunction data - 1-4729-4729.381-r0-0-0