Approximately,
\[
\begin{alignedat}{4}
A^\prime_{\mathbf{b}}&{}\approx{}&1.000000000000&{}:{}&-0.366025403784&{}:{}&0.366025403784&,\\B^\prime_{\mathbf{b}}&{}\approx{}&1.699358737118&{}:{}&-2.398717474236&{}:{}&1.699358737118&,\\C^\prime_{\mathbf{b}}&{}\approx{}&0.366025403784&{}:{}&-0.366025403784&{}:{}&1.000000000000&,
\\
A^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.602317462994&{}:{}&-0.726257150084&{}:{}&1.123939687090&,\\B^{\prime\prime}_{\mathbf{b}}&{}\approx{}&0.683012701892&{}:{}&-0.366025403784&{}:{}&0.683012701892&,\\C^{\prime\prime}_{\mathbf{b}}&{}\approx{}&1.123939687090&{}:{}&-0.726257150084&{}:{}&0.602317462994&,
\\
A^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.430940107676&{}:{}&-0.608290376865&{}:{}&1.177350269190&,\\B^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&0.612004618870&{}:{}&-0.224009237740&{}:{}&0.612004618870&,\\C^{\prime\prime\prime}_{\mathbf{b}}&{}\approx{}&1.177350269190&{}:{}&-0.608290376865&{}:{}&0.430940107676&,
\\
A^*_{\mathbf{b}}&{}\approx{}&0.000000000000&{}:{}&-0.866025403784&{}:{}&1.866025403784&,\\B^*_{\mathbf{b}}&{}\approx{}&0.500000000000&{}:{}&0.000000000000&{}:{}&0.500000000000&,\\C^*_{\mathbf{b}}&{}\approx{}&1.866025403784&{}:{}&-0.866025403784&{}:{}&0.000000000000&.
\end{alignedat}
\]