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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