Continuous Homomorphism of Matrix Groups - counterexample

Question

Let {${G={\begin{bmatrix} 1 & n \\ 0 & 1 \\ \end{bmatrix}} \in SUT_2(\mathbb R) : n\in\mathbb Z}$}. $$\\$$ For any irrational number r$\in\mathbb R-\mathbb Q$, a function is given with $$\varphi:G\to U(1); \varphi(\begin{bmatrix} 1 & n \\ 0 & 1 \\ \end{bmatrix}) = e^{2\pi rni}$$ I want to show, that $\varphi$ is not a continuous homomorphism of matrix groups. Therefore I want to show that $\varphi$G has limit points in U(1) which are not in $\varphi$G. Such a point is $-1+0i = e^{\pi i}$. My problem is, that im not able to find a series in $\varphi$G which has the limit point -1. $$\\$$ Any Ideas? :)