Binary Quadratic Representation

It can be proved that a prime number of form $5n+1$ has a unique representation by the binary quadratic form $x^2+3xy+y^2$

For instance $10000000711={14365}^2+3\times 14365\times 79734+{79734}^2$

Find this representation for the first 100 prime numbers $\equiv 1\text{ modulo }5\text{ and }>{10}^{50}$

Answer format: $\sum x,\sum y$ where $x<y$

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