Approximately,
\[
\begin{alignedat}{4}
A^\prime_{\mathbf{7}}&{}\approx{}&-0.207106781187&{}:{}&0.500000000000&{}:{}&0.707106781187&,\\B^\prime_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&-0.207106781187&{}:{}&0.707106781187&,\\C^\prime_{\mathbf{7}}&{}\approx{}&1.558260083544&{}:{}&1.558260083544&{}:{}&-2.116520167087&,
\\
A^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.757076375334&{}:{}&0.221742536459&{}:{}&0.021181088207&,\\B^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.221742536459&{}:{}&0.757076375334&{}:{}&0.021181088207&,\\C^{\prime\prime}_{\mathbf{7}}&{}\approx{}&0.146446609407&{}:{}&0.146446609407&{}:{}&0.707106781187&,
\\
A^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-1.294545023646&{}:{}&0.536218105897&{}:{}&1.758326917749&,\\B^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&0.536218105897&{}:{}&-1.294545023646&{}:{}&1.758326917749&,\\C^{\prime\prime\prime}_{\mathbf{7}}&{}\approx{}&-0.707106781187&{}:{}&-0.707106781187&{}:{}&2.414213562373&,
\\
A^*_{\mathbf{7}}&{}\approx{}&0.000000000000&{}:{}&0.675576651179&{}:{}&0.324423348821&,\\B^*_{\mathbf{7}}&{}\approx{}&0.675576651179&{}:{}&0.000000000000&{}:{}&0.324423348821&,\\C^*_{\mathbf{7}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&.
\end{alignedat}
\]