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We present a new formalism, alternative to the old TBA-like approach, forsolution of the spectral problem of planar N = 4 SYM. It takes a concise formof a non-linear matrix Riemann-Hilbert problem in terms of a few Q-functions.We demonstrate the formalism for two types of observables - local operators atweak coupling and cusped Wilson lines in a near BPS limit.

Quantum spectral curve for AdS_5/CFT_4