Recently Koymans and Pagano have established an asymptotic formula in this setting: $n$ a prime with $n$ congruent to $3$ modulo $4$, within the family of $d$ where $n$ ramifies in $\mathbb{Q}(\sqrt{d})$ and with $d$ congruent $1$ modulo $4$ (in general they consider the principal quadratic form), see https://arxiv.org/pdf/2005.14157.pdf. They also improve upper and lower bounds of Fouvry and Kluners for $n=1$.
Tom
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