I will present a simple numerical method based on the
Quantum Spectral Curve in N=4 planar supersymmetric Yang-Mills theory.
It allows for the first time
to obtain the exact spectrum of a non-trivial interacting QFT in 4d
with almost unlimited precision. I will show examples with 80 digits
accuracy and explore numerically the rich cut structure for twist
operators with complexified spin. The method also gives new data for
the generalized quark-antiquark potential in a wide range of the
coupling.Inspired by these numerical results a new analytic method will be
presented which gives a systematic weak coupling expansion for any
operator, and leads to a new analytic result for the BFKL
eigenvalue at next-to-next-to-leading order.