Ridge Through the Spectrum

A three-feature design matrix $X$ produces the Gram matrix $G = X^\top X$. The matrix itself was not saved to disk, but a diagnostics job logged three scalar summaries of it:

For any $3\times3$ matrix these three numbers are the coefficients of the characteristic polynomial:

$\det(G - \lambda I) \;=\; -\left(\lambda^{3} \;-\; \operatorname{tr}(G)\,\lambda^{2} \;+\; M_2\,\lambda \;-\; \det(G)\right)$

For this particular $G$, all three eigenvalues turn out to be distinct positive integers.

The training pipeline now switches to ridge regression, which replaces $G$ by

$G + \lambda I \qquad \text{with ridge strength } \lambda = 0.5$

What is $\det(G + 0.5\,I)$?

Round your answer to 2 decimal places.