  We study the asymptotic behavior of the $N$-dimensional colored Jones
polynomial of the figure-eight knot evaluated at
$\exp\bigl((\kappa+2p\pi\i/N\bigr)$, where $\kappa:=\arccosh(3/2)$ and $p$ is a
positive integer. We can prove that it grows exponentially with growth rate
determined by the Chern--Simons invariant of an affine representation from the
fundamental group of the knot complement to the Lie group $\SL(2;\C)$.
