Accelerator physics needs advanced modeling and simulation techniques, in particular for beam stability studies. A deeper understanding of the effects of magnetic fields nonlinearities will greatly help in the improvement of future colliders design and performance. This paper presents a study of quadrupole tracking using realistic field maps and measured or simulated longitudinal harmonics. The main goal is to describe the effect of the longitudinal dependence of high order non-homogeneity of the field in the case of the HL-LHC inner triplet.