  Let $\Bbb Z$ be the set of integers, and let $p$ be a prime of the form
$4k+1$. Suppose $q\in\Bbb Z$, $2\nmid q$, $p\nmid q$, $p=c^2+d^2$, $c,d\in\Bbb
Z$ and $c\equiv 1\pmod 4$. In this paper we continue to discuss congruences for
$q^{[p/8]}\pmod p$ and present new reciprocity laws, but we assume
$4p=x^2+qy^2$ or $p=x^2+2qy^2$, where $[\cdot]$ is the greatest integer
function and $x,y\in\Bbb Z$.
