VN-TST 2014 Problem 2

In the Cartesian plane is given a set of points with integer coordinate $$T=\{ (x;y)\mid x,y\in\mathbb{Z} ; \ |x|,|y|\leq 20 ; \ (x;y)\ne (0;0)\}$$ We colour some points of $T$ such that for each point $(x;y)\in T$ then either $(x;y)$ or $(-x;-y)$ is coloured. Denote $N$ to be the number of couples ${(x_1;y_1),(x_2;y_2)}$ such that both $(x_1;y_1)$ and $(x_2;y_2)$ are coloured and $x_1\equiv 2x_2 \pmod {41}, y_1\equiv 2y_2 \pmod {41}$ . Find the all possible values of $N$ .