Wir berechnen Schritt für Schritt das Legendre-Symbol.

${\displaystyle {}{\begin{aligned}\left({\frac {563}{1231}}\right)&=(-1)\left({\frac {1231}{563}}\right)\\&=(-1)\left({\frac {105}{563}}\right)\\&=(-1)\left({\frac {3}{563}}\right)\left({\frac {5}{563}}\right)\left({\frac {7}{563}}\right)\\&=(-1)(-1)\left({\frac {563}{3}}\right)\left({\frac {563}{5}}\right)(-1)\left({\frac {563}{7}}\right)\\&=(-1)\left({\frac {2}{3}}\right)\left({\frac {3}{5}}\right)\left({\frac {3}{7}}\right)\\&=(-1)(-1)(-1)(-1)\left({\frac {7}{3}}\right)\\&=1.\end{aligned}}}$