Detailed results of the quantum 3D calculation of the intermolecular vibrational levels of the endohedral fullerene complex Ne@C-70, for the total angular momentum J=0, are presented. They elucidate, for the first time, the nature of the endohedral vibrations of an atom inside a strongly nonspherical fullerene. The calculations were performed using our recently developed method for accurate highly excited 3D intermolecular vibrational states of atom-large molecule complexes [J. Chem. Phys. 98, 7165 (1993)]. The treatment of the coupled endohedral vibrations of Ne@C-70 involves no dynamical approximations, apart from taking the fullerene to be rigid, producing eigenstates which are essentially exact for the intermolecular potential energy surface (PES) employed. The 3D endohedral PES for Ne@C-70, modeled as a sum of atom-atom Lennard-Jones pair potentials, is anharmonic, especially in the direction of the long (z) axis of C-70 The endohedral vibrational energy level structure of Ne@C-70 which emerged from our calculations is surprisingly simple. The coupling between the vibrational mode parallel to the long (z) axis of C-70 and the modes perpendicular to it, is weak. The two endohedral modes perpendicular to the (z) axis represent an exemplary case of a 2D isotropic, anharmonic oscillator. The fundamental frequencies for the parallel and perpendicular endohedral mode of Ne@C-70, calculated using the present PES, are 9.83 and 54.49 cm(-1), respectively. The wave functions of all endohedral vibrational states of Ne@C-70 up to at least 240 cm(-1) above the ground state, considered in this work, have exceptionally regular nodal patterns, allowing complete and unambiguous quantum number assignment.