Show that $G_4(i)\neq 0$, and $G_6(\rho)\neq 0$, $\rho=e^{2\pi i /3}$

Question

Let $G_k$ denote the Eisenstein series of weight $k$. I know that $G_k(i)=0$ if $k \not\equiv 0 \ (mod \ 4)$ and $G_k(\rho)=0$ if $k \not\equiv 0 \ (mod \ 6)$. However, I want to know how to show, that $G_4(i)\neq0$ and $G_6(\rho)\neq0$, without using the $\frac{k}{12}$-formula.