Computing Legendre Symbol

Use Gauss' Lemma to compute $\displaystyle \left(\frac{22}{37}\right)$

I know how to start this question but just unsure how to finish it, my working is as follows:

$\displaystyle \left(\frac{22}{37}\right) = (-1)^{\mu}$ where $\displaystyle \mu$ is the number of negative least residues of the integers $\displaystyle \{22, 2 \times 22, 3 \times 22, \cdots, 18 \times 22\} \pmod{37} $

the set of least residues mod 37 is $\displaystyle \{-18, -17, \cdots -1, 1, \cdots, 17, 18\}$

Does that mean I have to check through all of the integers in that set ($\displaystyle \{22, 2 \times 22, 3 \times 22, \cdots, 18 \times 22\}$) to see if they have a negative least residue in the set $\displaystyle \{-18, -17, \cdots -1, 1, \cdots, 17, 18\}$ ? Because that would take a VERY long time, is there a faster way?

Cheers