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

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

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