Let $\omega$ be a complex number such that
\[\omega + \frac{1}{\omega} = 1.\]Find all possible values of
\[\omega^n + \frac{1}{\omega^n},\]where $n$ is a positive integer.

Enter all possible values, separated by commas.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\omega$ be a complex number such that
\[\omega + \frac{1}{\omega} = 1.\]Find all possible values of
\[\omega^n + \frac{1}{\omega^n},\]where $n$ is a positive integer.

Enter all possible values, separated by commas.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-2,-1,1,2
Let $\omega$ be a complex number such that
\[\omega + \frac{1}{\omega} = 1.\]Find all possible values of
\[\omega^n + \frac{1}{\omega^n},\]where $n$ is a positive integer.

Enter all possible values, separated by commas.
train