7. Let $x_{1}, x_{2}$ be the roots of the equation $x^{2}-6 x+1=0$, and let $a_{n}=x_{1}^{n}+x_{2}^{n}(\bmod 5)$, with $0 \leqslant a_{n}<5$, then $a_{20 \times 2}=$ $\qquad$ .
7. 4

Hint: First prove that $a_{n}$ is a sequence with a period of 6.