  We compute exactly various 4-point correlation functions of shortest scalar
operators in bi-scalar planar four-dimensional "fishnet" CFT. We apply the OPE
to extract from these functions the exact expressions for the scaling
dimensions and the structure constants of all exchanged operators with an
arbitrary Lorentz spin. In particular, we determine the conformal data of the
simplest unprotected two-magnon operator analogous to the Konishi operator, as
well as of the one-magnon operator. We show that at weak coupling 4-point
correlation functions can be systematically expanded in terms of harmonic
polylogarithm functions and verify our results by explicit calculation of
Feynman graphs at a few orders in the coupling. At strong coupling we obtain
that the correlation functions exhibit the scaling behaviour typical for
semiclassical description hinting at the existence of the holographic dual.
