2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98465R.M. Kashaev conjectured that the asymptotic behavior of his link invariant, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots $6_3$, $8_9$ and $8_{20}$ and for the Whitehead link, the colored Jones polynomials are related to the hyperbolic volumes and the Chern-Simons invariants and propose a complexification of Kashaev's conjecture.14 pages, 9 figures. Added some calculationsGeometric Topology57M27text