If $z^2 + z + 1 = 0,$ find
\[z^{49} + z^{50} + z^{51} + z^{52} + z^{53}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $z^2 + z + 1 = 0,$ find
\[z^{49} + z^{50} + z^{51} + z^{52} + z^{53}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-1
If $z^2 + z + 1 = 0,$ find
\[z^{49} + z^{50} + z^{51} + z^{52} + z^{53}.\]
train