This paper presents results from partial-wave analyses of the photoproduction reactions $gamma p rightarrow eta p$ and $gamma n rightarrow eta n$. World data for the observables DSG, $Sigma$, $T$, $P$, $F$, and $E$ were analyzed as part of this work. The dominant amplitude in the fitting range from threshold to a c.m. energy of 1900 MeV was found to be $S_{11}$ in both reactions, consistent with results of other groups. At c.m. energies above 1600 MeV, our solution deviates from published results, with this work finding higher-order partial waves becoming significant. Data off the proton suggest that the higher-order terms contributing to the reaction include $P_{11}$, $P_{13}$, and $F_{15}$. The final results also hint that $F_{17}$ is needed to fit double-polarization observables above 1900 MeV. Data off the neutron show a contribution from $P_{13}$, as well as strong contributions from $D_{13}$ and $D_{15}$.
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