Approximately,
\[
\begin{alignedat}{4}
A^\prime_{\mathbf{a}}&{}\approx{}&-1.198926561037&{}:{}&0.839915207551&{}:{}&1.359011353486&,\\B^\prime_{\mathbf{a}}&{}\approx{}&-0.199576037755&{}:{}&0.876655225327&{}:{}&0.322920812428&,\\C^\prime_{\mathbf{a}}&{}\approx{}&-0.338909579091&{}:{}&0.338909579091&{}:{}&1.000000000000&,
\\
A^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.251216481318&{}:{}&0.677353438913&{}:{}&0.573863042405&,\\B^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.586162603175&{}:{}&0.482947614758&{}:{}&1.103214988417&,\\C^{\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.391445299440&{}:{}&0.869601363923&{}:{}&0.521843935517&,
\\
A^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.157648462322&{}:{}&0.692484678091&{}:{}&0.465163784231&,\\B^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.565724688594&{}:{}&0.396321830444&{}:{}&1.169402858151&,\\C^{\prime\prime\prime}_{\mathbf{a}}&{}\approx{}&-0.311451084882&{}:{}&0.958413981388&{}:{}&0.353037103494&,
\\
A^*_{\mathbf{a}}&{}\approx{}&0.000000000000&{}:{}&0.690983005625&{}:{}&0.309016994375&,\\B^*_{\mathbf{a}}&{}\approx{}&-0.951056516295&{}:{}&0.000000000000&{}:{}&1.951056516295&,\\C^*_{\mathbf{a}}&{}\approx{}&-0.278768257918&{}:{}&1.278768257918&{}:{}&0.000000000000&.
\end{alignedat}
\]