There is a naturally defined complex volume for hyperbolic manifolds, with the imaginary part given by 2π2 times the Chern-Simons invariant. The values of the complex volumes are also available from KnotInfo.
The initial data is for knots having 7 or fewer tetrahedra in their decompositions (see tetrahedral enumeration). Initial data for knots with 6 or fewer tetrahedra was taken from "The simplest hyperbolic knots" by by Callahan, Dean, and Weeks. Initial data for knots with 7 tetrahedra was taken from "The next simplest hyperbolic knots" by Champanerkar, Kofman, and Patterson.
Walter Neumann provided us with a complete set of data for knots of 12 crossings or less, using the program Snap.
R. Meyerhoff, Geometric invariants of 3-manifolds, Math. Intelligencer 14 (1992), 37-153.
P. Kirk and E. Klassen, Chern-Simons invariants of 3-manifolds decomposed along tori and the circle bundle over the representation space of T2, Comm. Math. Phys. 153 (1993), no. 3, 521--557.
W.D. Neumann, Extended Bloch group and the Cheeger-Chern-Simons class, Geom. Topol. 8 (2004), 413--474.
W.D. Neumann, D. Zagier, Volumes of hyperbolic 3-manifolds, Topology 24 (1985) 307-332.