Compute the sum of the geometric series $-1 + 2 - 4 + 8 - \cdots + 512$.
The first term is $-1$, the common ratio is $-2$, and there are 10 terms, so the sum equals \[\frac{(-1)((-2)^{10}-1)}{-2-1} = \frac{-1023}{-3} = \boxed{341}.\]