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If <math>a</math> and <math>p</math> are coprime, then there exist numbers <math>p'\in\mathbb{Z}[i]</math> (see<ref>{{cite journal |last1=Eisenstein |first1=G.
|title=Beiträge zur Theorie der elliptischen Functionen |language=German|journal=Journal für die reine und angewandte Mathematik|date=1846 |volume=30| url=https://gdz.sub.uni-goettingen.de/id/PPN243919689_0030?tify=%7B%22pages%22%3A%5B202%5D%2C%22view%22%3A%22scan%22%7D}} Eisenstein uses <math>\varphi=\operatorname{sl}</math> and <math>\omega=2\varpi</math>.</ref> for these numbers) such that<ref>{{
:<math>\left(\frac{a}{p}\right)_4=\prod_{p'} \frac{\operatorname{sl}(2\varpi ap'/p)}{\operatorname{sl}(2\varpi p'/p)}.</math>
This theorem is analogous to
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