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We developed an efficient numerical algorithm for computing the spectrum ofanomalous dimensions of the planar ${\cal N}=4$ Super-Yang--Mills at finitecoupling. The method is based on the Quantum Spectral Curve formalism. Incontrast to Thermodynamic Bethe Ansatz, worked out only for some very specialoperators, this method is applicable for generic states/operators and is muchfaster and precise due to its Q-quadratic convergence rate.  To demonstrate the method we evaluate the dimensions $\Delta$ of twistoperators in $sl(2)$ sector directly for any value of the spin $S$ includingnon-integer values. In particular, we compute the BFKL pomeron intercept in awide range of the 't Hooft coupling constant with up to $20$ significantfigures precision, confirming two previously known from the perturbation theoryorders and giving prediction for several new coefficients. Furthermore, weexplore numerically a rich branch cut structure for complexified spin $S$.

Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4