The colored Jones polynomial of a cable of the figure-eight knot

We study the asymptotic behavior of $N$-dimensional colored Jones polynomial a cable figure-eight knot, evaluated at $\exp(\xi/N)$ for real number $\xi$. show that if $\xi$ is sufficiently large, grows exponentially when $N$ goes to infinity. Moreover growth rate related Chern-Simons invariant knot exterior associated with an $\mathrm{SL}(2;\mathbb{R})$ representation.