  The stability of Trojan type orbits around Neptune is studied. As the first
part of our investigation, we present in this paper a global view of the
stability of Trojans on inclined orbits. Using the frequency analysis method
based on the FFT technique, we construct high resolution dynamical maps on the
plane of initial semimajor axis $a_0$ versus inclination $i_0$. These maps show
three most stable regions, with $i_0$ in the range of $(0^\circ,12^\circ),
(22^\circ,36^\circ)$ and $(51^\circ,59^\circ)$ respectively, where the Trojans
are most probably expected to be found. The similarity between the maps for the
leading and trailing triangular Lagrange points $L_4$ and $L_5$ confirms the
dynamical symmetry between these two points. By computing the power spectrum
and the proper frequencies of the Trojan motion, we figure out the mechanisms
that trigger chaos in the motion. The Kozai resonance found at high inclination
varies the eccentricity and inclination of orbits, while the $\nu_8$ secular
resonance around $i_0\sim44^\circ$ pumps up the eccentricity. Both mechanisms
lead to eccentric orbits and encounters with Uranus that introduce strong
perturbation and drive the objects away from the Trojan like orbits. This
explains the clearance of Trojan at high inclination ($>60^\circ$) and an
unstable gap around $44^\circ$ on the dynamical map. An empirical theory is
derived from the numerical results, with which the main secular resonances are
located on the initial plane of $(a_0,i_0)$. The fine structures in the
dynamical maps can be explained by these secular resonances.
