Calculate $\left(\frac{37}{97}\right)$.

To translate the text into English, I have kept the format and line breaks as in the original text.
Let's apply quadratic reciprocity:

$$
\begin{array}{rlrl}
\left(\frac{37}{97}\right) & =\left(\frac{97}{37}\right) & & \text{since }\left(\frac{37}{97}\right)\left(\frac{97}{37}\right)=1 \\
& =\left(\frac{23}{37}\right) & & \text{since only the class of } 97 \text{ mod } 37 \text{ matters } \\
& =\left(\frac{37}{23}\right)=\left(\frac{14}{23}\right) & & \text{since }\left(\frac{37}{23}\right)\left(\frac{23}{37}\right)=1 \\
& =\left(\frac{2}{23}\right)\left(\frac{7}{23}\right) \\
& =\left(\frac{2}{23}\right) \cdot-\left(\frac{23}{7}\right) & & \text{since the Legendre symbol is multiplicative } \\
& =-1 & & \text{since }\left(\frac{7}{23}\right)\left(\frac{23}{7}\right)=-1 \\
& =1 \text{ and }\left(\frac{2}{7}\right)=1
\end{array}
$$