  The link between BFKL physics and twist-two operators involves an analytical
continuation in the spin of the operators away from the physical even integer
values. Typically this is done only after obtaining an analytical result for
integer spin through nested harmonic sums. In this paper we propose analyticity
conditions for the solution of Baxter equation which would work directly for
any value of complex spin and reproduce results from the analytical
continuation of harmonic sums. We carry out explicit contructions up to 2-loop
level. These nonstandard solutions of the Baxter equation have rather
surprising asymptotics. We hope that these analyticity conditions may be used
for incorporating them into the exact TBA/FiNLIE/QSC approaches valid at any
coupling.
