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\end{equation*}  where  \begin{eqnarray*} \begin{align*}  g_K= g_I &=& 1\\ &= 1\notag\\  \mu^2_{el} S &=& &=  3.8 \;\mathrm{Debye}^2\\ \;\mathrm{Debye}^2\notag\\  Z_{rot} &=& &=  .8556\; T_{ex}-0.10\\ T_{ex}-0.10\notag\\  F(T) &=& \frac{1}{e^{h\nu/k_BT}-1}.\\  \end{eqnarray*} &= \frac{1}{e^{h\nu/k_BT}-1}.\notag\\  \end{align*}  {\bf where $\epsilon_0$ is the vacuum permittivity, $\mu_{el}$ is the permanent electric dipole moment, S is the line strength, Z$_{rot}$ is the rotational partition function, g$_K$ is the K-level degeneracy, g$_I$ is the reduced nuclear spin degeneracy, E$_u$ is the energy of the upper-transition state, T$_{ex}$ is the excitation temperature and T$_{bg}$ is the background temperature.} The dipole moment line strength ($\mu^2_{el}$ S) is taken from the JPL spectral line catalog \citep{Pickett1998}. The partition function (Z$_{rot}$) is a linear fit to JPL data between T=37 to 75 K. T$_{bg}$ was taken to be the cosmic microwave background temperature, 2.725 K. The uncertainty in the fit amplitudes and derived column densities is dominated by our flux-calibration uncertainty. Since the relationships are linear, we estimate the uncertainty in both as 20\%.