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\subsection{Studying Larmor Precession}  We examined the relationship between precession frequency and magnetic field as discussed in the Methods section. We can see by Eq.~\ref{eq:precession} that precession frequency should vary linearly with magnetic field, which is what we see in Fig.~\ref{fig:precession}. The slope of the line is $\frac{\gamma}{2\pi}$, where $\gamma$ is the gyromagnetic ratio for protons. Our slope was $42.1\pm0.7~\frac{rad}{s\cdot \mu T}$, which agrees with the know value $\frac{\gamma}{2\pi}=42.5~\frac{rad}{s\cdot \mu T}$. The intercept represents the frequency without any extra applied field ($1847\pm7~Hz$), field, which we found to be $1847\pm7~Hz$,  agreeing within uncertainty with the value of $1852/pm18Hz$  we previously found for precession frequency.