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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1084', 'a10': [-0.982742504593294, 0.18497883572371057], 'a2': [0.4532799038330384, -0.8913682341104104], 'a3': [-0.9979661917102114, -0.06374543280437904], 'a4': [-0.589074657562223, -0.8080786148747842], 'a5': [-0.6103416861215312, -0.7921382620365754], 'a6': [-0.5091786732784713, 0.8606608383552581], 'a7': [0.47212908190508035, -0.8815294266327506], 'a8': [-0.9873113120936072, 0.15879664043045638], 'a9': [0.9918730395931648, 0.12723157362941068], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1084', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1095', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1950', 'a^1206', 'a^1536', 'a^1526', 'a^792', 'a^1958', 'a^1122', 'a^48', 'a^1112', 'a^525', 'a^378', 'a^1220', 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21.961383672410207, 'root_angle': 0.4746621246937625, 'root_number': '-0.987354015253027325601391229501+0.158530907282222677820911264186*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, '0.573538293365596969940868112038-0.648056439788690083846471166465*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.489154337005', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '0.995494835535', 'prec': 47}, 'z3': {'__RealLiteral__': 0, 'data': '1.91718453475', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1084', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1084'], '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': '1-4729-4729.1084-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': '1-4729-4729.1084-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.4746621246937625, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.489154337005', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1084', 'Lhash_array': ['dirichlet_L_4729.1084'], 'factors': ['1-4729-4729.1084-r0-0-0'], 'label': '1-4729-4729.1084-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1084'}
Lfunction data - 1-4729-4729.1084-r0-0-0