Pagina:Werkecarlf02gausrich.djvu/144

$${\begin{array}{l|c|l}{\text{Modulus.}}&{\text{Character.}}&{\text{Numeri.}}\\\hline +3+10i&1&{\phantom {+}}1+i,-1-2i,1-4i\\&2&-3,3+2i,1+4i,-5-2i\\&3&-1+2i,3-2i\\-7+8i&0&{\phantom {+}}1+i,-7\\&1&{\phantom {+}}3+2i,3-2i,1-4i,-5-2i\\&2&-1-2i,1+4i,-5+2i,-1-6i\\&3&-1+2i,-3,-1+6i\\-11&0&-3\\&1&{\phantom {+}}1+i,3-2i,1+4i,-5+2i,5+4i\\&2&-1+2i,-1-2i\\&3&{\phantom {+}}3+2i,1-4i,-5-2i,5-4i\\-11+4i&0&{\phantom {+}}1+i,-1+2i,3+2i,5+4i\\&1&-1-2i,-1+6i\\&2&-5+2i\\&3&-3,3-2i,1+4i,1-4i,-5-2i\\+7+10i&0&{\phantom {+}}1+4i,1-4i,-1+6i,-1-6i\\&1&-1+2i,3+2i,-5+2i\\&2&{\phantom {+}}1+i,3-2i\\&3&-1-2i,-3,-5-2i\\+11+6i&0&{\phantom {+}}1+i,-1+2i,-3,1+4i,1-4i,-7\\&1&-1-2i,3+2i,3-2i\\&2&-5-2i,-1+6i,-5-4i\\&3&-5+2i,5+4i,7-2i\\\end{array}}$$

63.

Operam nunc dabimus, ut criteria communia modulorum, pro quibus numerus primus datus characterem eundem habet, per inductionem detegamus. Modulos semper supponimus primarios inter associatos, puta tales ${\textstyle a+bi}$, pro quibus vel ${\textstyle a\equiv 1}$, ${\textstyle b\equiv 0}$, vel ${\textstyle a\equiv 3}$, ${\textstyle b\equiv 2{\pmod {4}}}$.

Respectu numeri ${\textstyle 1+i}$, a quo initium facimus, inductionis lex facilius arripitur, si modulos prioris generis (pro quibus ${\textstyle a\equiv 1}$, ${\textstyle b\equiv 0}$) a modulis posterioris generis (pro quibus ${\textstyle a\equiv 3}$, ${\textstyle b\equiv 2}$) separamus. Adiumento tabulae art. praec. invenimus respondere