Trigonometry · Superchallenge problem

A pointer starts aimed along the positive $x$-axis. On its $1$st move it rotates $1^\circ$ counterclockwise, on its $2$nd move $2^\circ$ counterclockwise, on its $3$rd move $3^\circ$, and so on: on the $k$th move it rotates $k^\circ$. After how many moves does it FIRST point along the positive $x$-axis again?