The Spectroscopic Monte Carlo Method is applied to the nucleus {}¹⁷⁰Yb using the Monopole plus Quadrupole Pairing plus Quadrupole interaction for yrast states up to J^\pi =12⁺. The unusually small statistical errors in the Monte Carlo calculations of the yrast energies (\approx 40\div 70KeV) despite moderately strong sign oscillations, are discussed. Energy levels, expectation values of pairing potential and the pairing strength to J=12 for the neutron intruder orbit and to J=10 for the proton intruder orbit are evaluated. It is shown that the Hartree-Fock-Bogoliubov wave functions obtained with variation after projection to good particle number and to good z-component of the angular momentum and reprojected to good J²,J_z after variation, give excitation energies in reasonable agreement with the Monte Carlo values. The intrinsic HFB wave functions have a considerable angular momentum dependence. Wave functions which are projected to good angular momentum after variation (PAV), lead to excitation energies larger than the corresponding Monte Carlo values.

PACS numbers: 21.60.-n, 02.70.Ss, 21.60.Ka, 21.10.Re