  We find the eigenvalue of the kernel of BFKL equation in the
next-to-next-to-next-to-leading logarithm approximation (NNNLLA) in the planar
N=4 SYM theory by using the quantum spectral curve to compute values at fixed
spin, and reconstructing the general result using the LLL-algorithm, which also
was used for the reconstruction of the general result for the intercept
function for arbitrary conformal spin at fourth order, computed earlier in
paper 1802.06908 up to the rational part. We have found, that a new type of
harmonic sums enter into results. Those sums have the argument multiplied by
factor two with compare to usual harmonic sums and contain the last imagine
index, what reflect their relations with the multiple polylogarithms, generated
by ``fourth root of unity''. The final result contains Catalan number, which
did not appear early in the calculations for the anomalous dimension of twist-2
operators.
