The discrete-time Fourier transform of a signal $ x[n]$ is $X (\Omega)=(1+\cos \Omega) e^{-j \Omega}$ Consider that $ x_{p}[n]$ is a periodic signal of period $ \mathrm{N}=5$ such that
$\qquad \begin{array}{r}x_{p}[n]=x[n], \text { for } n=0,1,2 \\
=0, \text { for } n=3,4\end{array}$
Note that $x_{p}[n]=\sum_{k=0}^{N-1} a_{k} e^{j \frac{2 \pi}{N} k n}.$ The magnitude of the Fourier series coefficient $a_{3}$ is_____________ (Round off to $3$ decimal places).
