322 REPORT — 1861. 



To enable the reader to form with facility the complete character of any 

 given properly primitive class, we add the following Table, taken from 

 Dirichlet (Creile, vol. xix. p. 338), in which S" denotes the greatest square 



dividing D ; P or 2P is the quotient — , according as that quotient is uneven 



o 



or even; p,p' ... are the prime divisors of P; and r, r' the uneven primes 

 dividing S, but not P. 



I. D=PS^ P = l, mod 4. 

 (a) S = l,mod2. 



©• (|>- I (0- (^■- 



(/3) S = 2, mod4. 

 (y) S ^ 0, mod 4. 



II. D=PS^ P = 3, mod4. 

 (a) S = l, mod 2. 



(/3) S = 2, mod4. 

 /-I 



^ 0, mod 4. 



III. D=2PS^ P = l, mod4. 

 (a) S = l, mod 2. 



<->'^' e->(^^>- 1(0- (^)-- 



(jS) S = 0, mod 2. 



IV. D=2PS% P = 3, mod 4. 

 (a) S = l, mod 2. 



(/3) S = 0, mod2. 



It appears from this Table, that if /* be the number of uneven primes which 



