  Differential cross sections of the exclusive process $e p \to e^\prime \pi^+
n$ were measured with good precision in the range of the photon virtuality $Q^2
= 1.8 - 4.5$ GeV$^2$, and the invariant mass range of the $\pi^+ n$ final state
W = 1.6 - 2.0 GeV using the CEBAF Large Acceptance Spectrometer. Data were
collected with nearly complete coverage in the azimuthal and polar angles of
the $n\pi^+$ center-of-mass system. More than 37,000 cross section points were
measured. The contributions of the isospin $I = {1\over 2}$ resonances
$N(1675){5\over 2}^-$, $N(1680){5\over 2}^+$ and $N(1710){1\over 2}^+$ were
extracted at different values of $Q^2$ using a single-channel, energy-dependent
resonance amplitude analysis. Two different approaches, the unitary isobar
model and the fixed-$t$ dispersion relations, were employed in the analysis. We
observe significant strength of the $N(1675){5\over 2}^-$ in the $A_{1/2}$
amplitude, which is in strong disagreement with quark models that predict both
transverse amplitudes to be strongly suppressed. For the $N(1680){5\over 2}^+$
we observe a slow changeover from the dominance of the $A_{3/2}$ amplitude at
the real photon point ($Q^2=0$) to a $Q^2$ where $A_{1/2}$ begins to dominate.
The scalar amplitude $S_{1/2}$ drops rapidly with $Q^2$ consistent with quark
model prediction. For the $N(1710){1\over 2}^+$ resonance our analysis shows
significant strength for the $A_{1/2}$ amplitude at $Q^2 < 2.5$ GeV$^2$.
