  We determine the generalized form factors, which correspond to the second
Mellin moment (i.e., the first $x$-moment) of the generalized parton
distributions of the nucleon at leading twist. The results are obtained using
lattice QCD with $N_f=2$ nonperturbatively improved Wilson fermions, employing
a range of quark masses down to an almost physical value with a pion mass of
about 150 MeV. We also present results for the isovector quark angular momentum
and for the first $x$-moment of the transverse quark spin density. We compare
two different fit strategies and find that directly fitting the ground state
matrix elements to the functional form expected from Lorentz invariance and
parametrized in terms of form factors yields comparable, and usually more
stable results than the traditional approach where the form factors are
determined from an overdetermined linear system based on the fitted matrix
elements.
