Define the Jacobi symbol $\left(\frac{a}{n}\right)$, where $a, n \in \mathbb{Z}$ and $n$ is odd and positive.

State and prove the Law of Quadratic Reciprocity for the Jacobi symbol. [You may use Quadratic Reciprocity for the Legendre symbol without proof but should state it clearly.]

Compute the Jacobi symbol $\left(\frac{503}{2019}\right)$.