\\ Pari/GP code for working with Dirichlet character 197.b.196


\\ Define the Dirichlet character: 
[g,chi] = znchar(Mod(196, 197))

\\ Kronecker symbol: 
znchartokronecker(g,chi)

\\ Modulus: 
g[1][1]

\\ Conductor: 
znconreyconductor(g,chi)

\\ Order: 
charorder(g,chi)

\\ Whether the character is real: 
charorder(g,chi) <= 2

\\ If the character is primitive: 
#znconreyconductor(g,chi)==1

\\ Parity: 
zncharisodd(g,chi)

\\ Galois orbit: 
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

\\ Field of values of chi: 
nfinit(polcyclo(charorder(g,chi)))