  In December 2023, the Fermi LAT Catalog announced the discovery of 33 new
millisecond pulsars. Motivated by that, in this work, I study how different
values of the symmetry energy slope $(L)$ affect the properties of static and
slowly rotating neutron stars. For fixed values of angular velocity, I study
how the slope influences the increase of the maximum mass, the radii of the
canonical 1.4 solar mass, its eccentricity, as well the same quantities for the
2.01 $M_\odot$ stars. I show that different slope values cause different
variations not only the absolute quantities but also in relative ones. Indeed,
different slope values predict different values for the eccentricity, which
does not depend on the absolute value of the neutron stars' radii. Therefore,
this quantity can be a powerful tool to constrain the symmetry energy slope.
