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A set of coupled non-linear integral equations is derived for a class ofmodels connected with the quantum group $U_q(\hat g)$ ($g$ simply laced Liealgebra), which are solvable using the Bethe Ansatz; these equations describearbitrary excited states of a system with finite spatial length $L$. Theygeneralize the Destri-De Vega equation for the Sine-Gordon/massive Thirringmodel to affine Toda field theory with imaginary coupling constant. As anapplication, the central charge and all the conformal weights of the UVconformal field theory are extracted in a straightforward manner. The quantumgroup truncation for $q$ at a root of unity is discussed in detail; in the UVlimit we recover through this procedure the RCFTs with extended $W(g)$conformal symmetry.Comment: 33 pages, TeX with lanlmac (revised: minor misprints corrected, some  comments added, appendix slightly expanded revised 05/98: more misprints  corrected, important refs added

Nonlinear integral equations for complex affine Toda models associated with simply laced Lie algebras