$3\mathrm{.}15.$ Consider a continuous$-$time ideal lowpass filter $S$ whose frequency response is

$H(j)=\{\begin{array}{cc}1,& ||100\\ 0,& ||>100\end{array}$

When the input to this filter is a signal $x(t)$ with fundamental period $T=\frac{}{6}$ and Fourier series coefficients $a_k,$ it is found that

$x(t)Sy(t)=x(t)$

For what values of $k$ is it guaranteed that $a_k=0?$