  We developed a general non-perturbative framework for the BFKL spectrum of
planar N=4 SYM, based on the Quantum Spectral Curve (QSC). It allows one to
study the spectrum in the whole generality, extending previously known methods
to arbitrary values of conformal spin $n$. We show how to apply our approach to
reproduce all known perturbative results for the Balitsky-Fadin-Kuraev-Lipatov
(BFKL) Pomeron eigenvalue and get new predictions. In particular, we re-derived
the Faddeev-Korchemsky Baxter equation for the Lipatov spin chain with non-zero
conformal spin reproducing the corresponding BFKL kernel eigenvalue. We also
get new non-perturbative analytic results for the Pomeron eigenvalue in the
vicinity of $|n|=1,\;\Delta=0$ point and we obtained an explicit formula for
the BFKL intercept function for arbitrary conformal spin up to the 3-loop order
in the small coupling expansion and partial result at the 4-loop order. In
addition, we implemented the numerical algorithm of arXiv:1504.06640 as an
auxiliary file to this arXiv submission. From the numerical result we managed
to deduce an analytic formula for the strong coupling expansion of the
intercept function for arbitrary conformal spin.
