arbitrary initial parameters guess of $C_i = k_{xi} = k_{yi} = b_y = 1$. We were then able to fit to the entire field using the result of our $B_x$ fit as an initial guess. Figure 3 shows plots of the fits for both the C-shaped and canted solenoid LGB’s. Figure 4 plots the residuals for each component of both LGB’s.\
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The quality of each fit is quantified in Table 3. We used as many terms in the series as was necessary to drive the average residual between each component of the fit field and the true field below 10% of the magnitude of the true field. For instance, using 7 terms for the C-shaped LGB fit yields an average residual of $0.000$ $T$ in $B_x$, $0.036$ $T$ in $B_y$, and $0.007$ $T$ in $B_z$, each of which is less than 10% of the magnitude of the true $B_x$, $B_y$, and $B_z$ components. Looking to Table 3, the maximum residual is simply the magnitude of the maximum difference between the fit field and the true field. To calculate the average residual between the fit field and the true field, we simply summed the absolute values of the residuals for 