Heegner decompositions

Consider the field $F_d$ of numbers $a+b\times \sqrt{-d}$ where $a,b,d$ are integers and $d$ is a squarefree positive number. For some d, it can be proved that the factorization of the elements of $F_d$ is unique The surprising fact about these special values is that there are only 9 of them: $\{1,2,3,7,11,19,43,67,163\}$ They are called the Heegner numbers.

Can you find the smallest prime number $p>{10}^{50}$ such as $p\text{ can be written }p=x^2+h\times y^2$ for each Heegner number h.

Answer format: $p\mathrm{mod}{10}^{50},\sum x,\sum y$

Example : 2372241,680483,159290 // For $p>{10}^{10}$
$$10002372241={23220}^2+1\times {97279}^2$$ $$10002372241={90979}^2+2\times {29370}^2$$ $$10002372241={79729}^2+3\times {34860}^2$$ $$10002372241={95703}^2+7\times {10976}^2$$ $$10002372241={82865}^2+11\times {16884}^2$$ $$10002372241={52279}^2+19\times {19560}^2$$ $$10002372241={90313}^2+43\times {6552}^2$$ $$10002372241={44273}^2+67\times {10956}^2$$ $$10002372241={47063}^2+163\times {6912}^2$$
For the equation $x^2+y^2=p$ , we assume $x<y$

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