  We employ the analytic Bethe Anzats to construct eigenvalues of transfer
matrices with finite-dimensional atypical representations in the auxiliary
space for the putative long-range spin chain encoding anomalous dimensions of
all composite single-trace gauge invariant operators of the maximally
supersymmetric Yang-Mills theory. They obey an infinite fusion hierarchy which
can be reduced to a finite set of integral relations for a minimal set of
transfer matrices. This set is used to derive a finite systems of functional
equations for eigenvalues of nested Baxter polynomials.
