  Result on the locations of the tricritical points of $N_f=2$ lattice QCD with
imaginary chemical potential is presented. Simulations are carried out with
Symanzik improved gauge action and Asqtad fermion action. With imaginary
chemical potential $i\mu_I=i\pi T$, previous studies show that the
Roberge-Weiss (RW) transition endpoints are triple points at both large and
small quark masses, and second order transition points at intermediate quark
masses. The triple and second order endpoints are separated by two tricritical
ones. Our simulations are carried out at 7 values of quark mass $am$ ranging
from 0.024 to 0.070 on lattice volume $12^3\times 4, 16^3\times 4,\,
20^3\times4$. The susceptibility and Binder cumulant of the imaginary part of
Polyakov loop are employed to determine the nature of RW transition endpoints.
The simulations suggest that the two tricritical points are within the range
$0.024-0.026$ and $0.040-0.050$, respectively.
