A series invariant of a complement of a knot with more than ten crossings

A Cable Knot and BPS-Series

We present the first example of a composite knot, namely, a cable of the figure eight knot, which has more than ten crossings.This cable knot result provides nontrivial evidence for the conjectures for the seriesinvariant and demonstrates the robustness of integrality of the quantuminvariant under the cabling operation.Furthermore, we find interesting effects of the cabling on the series invariant.