In this talk I will report the results of the study of a 1D integrable alternating spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. I will review both analytical and numerical approaches to analyzing the spectrum of low energy excitations of the model. It turns out that the computation of the density of Bethe states of the continuous theory can be reduced to the calculation of the connection coefficients for a certain class of differential equations whose monodromy properties are similar to those of the conventional confluent hypergeometric equation. The finite size corrections to the scaling are also discussed.