Associated to a hyperbolic knot there is a Chern-Simons Invariant. The value is an element of the additive real numbers modulo the subgroup generated by 1/2. Thus all Chern-Simons invariants are given as reals between 0 and 1/2.

There is a naturally defined complex
volume for hyperbolic manifolds, with the imaginary part given by
2π^{2} 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 T ^{2},* Comm. Math. Phys.

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.