  We compute the finite size spectrum for the spin 1/2 XXZ chain with twisted
boundary conditions, for anisotropy in the regime $0< \gamma <\pi/2$, and
arbitrary twist $\theta$. The string hypothesis is employed for treating
complex excitations. The Bethe Ansatz equtions are solved within a coupled
non-linear integral equation approach, with one equation for each type of
string. The root-of-unity quantum group invariant periodic chain reduces to the
XXZ_1/2 chain with a set of twist boundary conditions ($\pi/\gamma\in Z$,
$\theta$ an integer multiple of $\gamma$). For this model, the restricted
Hilbert space corresponds to an unitary conformal field theory, and we recover
all primary states in the Kac table in terms of states with specific twist and
strings.
