  The anomalous dimensions of single-trace local Wilson operators with
covariant derivatives in maximally supersymmetric gauge theory are believed to
be generated from a deformed noncompact sl(2) Baxter equation. We perform a
systematic expansion of this equation at strong coupling in the
single-logarithmic limit of large conformal spin to overcome the limitation of
the asymptotic nature of the equation. The analysis is reduced to
Riemann-Hilbert problems for corresponding resolvents of Bethe roots in each
order of the quasiclassical expansion. We explicitly construct the resolvents
in the lowest two orders in strong coupling and find all local conserved
charges of the underlying long-range spin chain.
