Properties

Modulus $12$
Structure \(C_{2}\times C_{2}\)
Order $4$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(12)
 
pari: g = idealstar(,12,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 4
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{12}(7,\cdot)$, $\chi_{12}(5,\cdot)$

Characters

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 \(-1\) \(1\) \(5\) \(7\)
\(\chi_{12}(1,\cdot)\) 12.a 1 no \(1\) \(1\) \(1\) \(1\)
\(\chi_{12}(5,\cdot)\) 12.c 2 no \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{12}(7,\cdot)\) 12.d 2 no \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{12}(11,\cdot)\) 12.b 2 yes \(1\) \(1\) \(-1\) \(-1\)