6. Let the expansion of $\left(1+x+x^{2}\right)^{100}$ be $a_{0}+a_{1} x+a_{2} x^{2}+\cdots+a_{200} x^{200}$. Find the value of $a_{0}+a_{3}+a_{6}+\cdots+a_{198}$.
6. Consider the cube root of unity $\omega$. Let $a_{0}+a_{3}+a_{6}+\cdots+a_{198}=A, a_{1}+a_{4}+\cdots+a_{199}=B, a_{2}+a_{5}+$ $\cdots+a_{2 m}=C$, then $A+B+C=3^{1 \omega 0}, A+\omega B+\omega^{2} C=0, A+\omega^{2} B+\omega C=0$, from which we find $A=3^{9}$.