  A set of coupled non-linear integral equations is derived for a class of
models connected with the quantum group $U_q(\hat g)$ ($g$ simply laced Lie
algebra), which are solvable using the Bethe Ansatz; these equations describe
arbitrary excited states of a system with finite spatial length $L$. They
generalize the Destri-De Vega equation for the Sine-Gordon/massive Thirring
model to affine Toda field theory with imaginary coupling constant. As an
application, the central charge and all the conformal weights of the UV
conformal field theory are extracted in a straightforward manner. The quantum
group truncation for $q$ at a root of unity is discussed in detail; in the UV
limit we recover through this procedure the RCFTs with extended $W(g)$
conformal symmetry.
