Linear independence measures for Chowla--Selberg periods

We use simultaneous Padé approximations to ${}_3{F}_2$ hypergeometric functions to estimate from below linear forms in $1$, $\pi \sqrt{d}$, ${\mathrm{\Omega }}_D\mathrm{/}\pi$ and $\pi \mathrm{/}{\mathrm{\Omega }}_D$ with integral coefficients, for certain choices of positive integer $d$ and negative integer $D$, where ${\mathrm{\Omega }}_D$ is (the square of) a Chowla–Selberg period attached to the imaginary quadratic field $Q(\sqrt{D})$.