  Colored multiple zeta values are special values of multiple polylogarithms
evaluated at Nth roots of unity. In this paper, we define both the finite and
the symmetrized versions of these values and show that they both satisfy the
double shuffle relations. Further, we provide strong evidence for an
isomorphism connecting the two spaces generated by these two kinds of values.
This is a generalization of a recent work of Kaneko and Zagier on finite and
symmetrized multiple zeta values and of the second author on finite and
symmetrized Euler sums.
