9. (16 points) Given complex numbers $a_{1}, a_{2}, a_{3}$ satisfy
$$
\begin{array}{l}
a_{1}^{2}+a_{2}^{2}+a_{3}^{2}=a_{1}^{3}+a_{2}^{3}+a_{3}^{3} \\
=a_{1}^{4}+a_{2}^{4}+a_{3}^{4}=0 .
\end{array}
$$

Find all possible values of $a_{1}+a_{2}+a_{3}$.