Modulus $3$
Structure \(C_{2}\)
Order $2$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(3)
pari: g = idealstar(,3,2)

Character group

sage: G.order()
Order = 2
sage: H.invariants()
pari: g.cyc
Structure = \(C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{3}(2,\cdot)$


Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive \(-1\) \(1\)
\(\chi_{3}(1,\cdot)\) 3.a 1 no \(1\) \(1\)
\(\chi_{3}(2,\cdot)\) 3.b 2 yes \(-1\) \(1\)