This study examines the impact of low and zero magnetic shear, along with rational values ofsafety factor, on linear mode behavior in tokamak plasmas. We focus on how magnetic field linetopology and parallel domain length influence linear mode structures and growth rates asmagnetic shear decreases. Our results show that as magnetic shear is reduced to low values,linear modes can transition between different branches, significantly affecting theircharacteristics. At zero magnetic shear, accurate modeling requires precisely capturingmagnetic topology, as small deviations near rational surfaces can greatly impact growth rates.