We generalize local operators of the leading twist-2 of $\mathcal{N}=4$ SYM theory to the case of complex Lorentz spin j using principal series representation of $sl(2,R)$. We give the direct computation of correlation function of two such non-local operators in the BFKL regime when $j\to 1$. The correlator appears to have the expected conformal coordinate dependence governed by the anomalous dimension of twist-2 operator in NLO BFKL approximation predicted by Kotikov and Lipatov.