This is pretty neat. I'm taking this from a graduate text (Problems in Algebraic Number Theory), that we can find on the uiuc library site; what a great resource! Wikipedia and Wolfram Mathworld also both have articles.

The Kronecker symbol is an extension of the Jacobi Symbol to all integers.

For general n, we write n = $2^c m$, with m odd and define:

where $\left( \frac {a}{m} \right)$ is the Jacobi symbol.

And define: