  We present a calculation of the net baryon number density as a function of
imaginary baryon number chemical potential, obtained with highly improved
staggered quarks (HISQ) at temporal lattice extent of $N_\tau=4,6$. We
construct various rational function approximations of the lattice data and
discuss how poles in the complex plane can be determined from them. We compare
our results of the singularities in the chemical potential plane to the
theoretically expected positions of the Lee-Yang edge singularity in the
vicinity of the Roberge-Weiss and chiral phase transitions. We find a
temperature scaling that is in accordance with the expected power law behavior.
