Can $300$…$04$ be a perfect square?

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$300…04$ is divisible by $4$ and always $1$ mod $3$. Sometimes, $300$$04$ is $1$ mod $11$, which is a quadratic residue modulo $11$. But when I tried to check if there is any perfect square form of $300$$04$, I didn’t succeed. Can $300$$04$ be a perfect square?