The autoionizing (X2-SIGMA-g+) 8f, 9f, and 10f, upsilon = 1 states of N2 have been studied by using double-resonance ionization spectroscopy via numerous rotational levels of the a 1-PI-g, upsilon' = 5 state. These nf states lie in a complex region of the spectrum that also contains transitions to high vibrational levels of the b'1-SIGMA-u+ valence state and Rydberg states that converge to the X 2-SIGMA-g+, A 2-pi-u, and B 2-SIGMA-u+ states of the ion. A long-range interaction model, which is based on the interaction of the Rydberg electron with the polarizability and quadrupole moment of the N2+ ion core, has been used to interpret the f-state structure and to identify the extent of perturbations due to interactions with nearby states. A generalized least-squares fit of the model to the energies of the unperturbed 8f state yields an effective quadrupole moment of (3.2 +/- 0.1)ea0(2) and an isotropic polarizability of (16.1 +/- 0.4)a0(3) for the X 2-SIGMA-g+, upsilon+ = 1 state of the ion. In addition, a new state that is observed to perturb the 9f, upsilon = 1 state is tentatively identified as the previously unobserved (A 2-PI(u)3d-pi-1-DELTA-u, upsilon = 2 state. The results presented here complete the interpretation of the single-photon absorption spectrum of N2 from the first ionization potential at approximately 125 667 to approximately 126 850 cm-1.