Calculate Legendre symbol

Question

When i calculate the legendre symbol for (101/1739), i end up with (2/27)*(5/27) in the middle of the calculation.

I understand how to calculate (5/27), but how do i calculate (2/27). This would have been easy if 27 was a prime but what to do when the denominator is not a prime

Answer 1

There is noo need to refer to Jacobi symbols here, because we have $$ \left( \frac{101}{1739}\right)=\left( \frac{1739}{101}\right) =\left( \frac{22}{101}\right)=\left( \frac{2}{101}\right)\cdot \left( \frac{11}{101}\right)=(-1)\cdot (-1)=1. $$