  A new approach is presented to explore the singularity structure of lattice
QCD at imaginary chemical potential. Our method can be seen as a combination of
the Taylor expansion and analytic continuation approaches. Its novelty lies in
using rational (Pad\'e) approximants for studying Lee Yang edge singularities.
The motivation for using rational approximants will be exhibited. We will
provide some confidence in our approach based on numerical experiments
performed on well-motivated "toy models". Our focus lies in identifying
singularities of the net-baryon number density in the complex $\mu_B$ plane. To
this end we have found signatures of the Roberge-Weiss critical point(and
Chiral singularities -- subject to some caveats). In this contribution we will
discuss the setup, simulation parameters and results obtained for 2+1 flavor
QCD in the complex $\mu_B/T$ plane.
