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In this work we investigate the magnetic field dependence of the precession frequency of vortex states in spin-valve nanocontacts with an amorphous CoFeB free layer and an artificial antiferromagnet as polarizer. The nanocontacts have radii between 70 and 90 nm. We show that the excitation frequency in these devices responds to small, in-plane magnetic fields along the easy and hard axis directions. The characteristics of the frequency response depend on the generated magnetic configuration under the nanocontact. This, in turn, results from the combined effect of the applied magnetic field and the current-generated Oersted field. Taking also into account the relative large nanocontact radii, a variety of vortex excitation modes can arise with distinctive frequency versus field responses, some of which could be considered for magnetic field sensing applications.