\[\large{\begin{cases} a &=& 100 + 85i \\ b &=& 208 + 39i \\ c &=& 188 + 22i \\ \end{cases} } \]

Given that \(a\), \(b\), & \(c\) are Gaussian integers as shown above, if \(d\) is the greatest common divisor (GCD) of \(a\), \(b\), & \(c\), what is the value of \(ādā^{2}\)?

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