I am looking for upper and lower bounds for the following expression:

$$\prod_{\substack{p\le n \\ p \equiv 1\ mod\ 4}} \frac{p-1}{p}$$

Apart from the trivial one:

$$\prod_{\substack{p\le n \\ p \equiv 1\ mod\ 4}} \frac{p-1}{p} \ge \prod_{p\le n} \frac{p-1}{p}$$

Any advice or bibliographic reference will be highly appreciated.