How to prove a generalized Gauss sum formula

Question

I read the wikipedia article on quadratic Gauss sum. link

First let me write a definition of a generalized Gauss sum.

Let $G(a, c)= \sum_{n=0}^{c-1}\exp (\frac{an^2}{c})$, where $a$ and $c$ are relatively prime integers.

(Here is another question. Is the function $e(x)$ defined in the article equal to $\exp(2\pi i/x)$ or $\exp(\pi i/x)$?)

In the article, a formula is given according to values of $a$ and $c$.

For example, if $a$ is odd and $4|c$, then

$G(a, c)=(1+i)\epsilon_a^{-1} \sqrt{c} \big(\frac{c}{a}\big)$, where $\big(\frac{c}{a}\big)$ is the Jacobi symbol.

I would like to prove it but I don't know how to do it. Could you give me a guide?