A twist on my last problem?

Algebra Level 3

Given that \( C= \omega^{-1} + \omega^1 + \omega^3 + \omega^5 + \cdots + \omega^{2013} \), where \( \omega \) is the 2016th root of unity (other than 1 or \(-1\) ), find the exact value of \( C \).

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