  We utilize the eigenvalue filtering technique combined with the stochastic
estimate of the mode number to determine the eigenvalue spectrum. Simulations
of (2 + 1)-flavor QCD are performed using the Highly Improved Staggered Quarks
(HISQ/tree) action on $N_{\tau}$ = 8 lattices with aspect ratios
$N_{\sigma}/N_{\tau}$ ranging from 5 to 7. The strange quark mass is fixed to
its physical value $m_{s}^{\rm phy}$, and the light quark masses $m_{l}$ are
varied from $m_{s}^{\rm phy}/40$ to $m_{s}^{\rm phy}/160$ which correspond to
pion mass $m_{\pi}$ ranging from 110 MeV to 55 MeV in the continuum limit. We
compute the chiral condensate and $\chi_{\pi} - \chi_{\delta}$ through the
eigenvalue spectrum obtained from the the eigenvalue filtering method. We
compare these results with those obtained from a direct calculation of the
observables which involves inversions of the fermion matrix using the
stochastic "noise vector" method. We find that these approaches yield
consistent results. Furthermore, we also investigate the quark mass and
temperature dependences of the Dirac eigenvalue density at zero eigenvalues to
gain more insights about the $U_A(1)$ symmetry breaking in QCD.
