Properties

Modulus $5$
Structure \(C_{4}\)
Order $4$

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5)
 
pari: g = idealstar(,5,2)
 

Character group

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

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 \(-1\) \(1\) \(2\) \(3\)
\(\chi_{5}(1,\cdot)\) 5.a 1 no \(1\) \(1\) \(1\) \(1\)
\(\chi_{5}(2,\cdot)\) 5.c 4 yes \(-1\) \(1\) \(i\) \(-i\)
\(\chi_{5}(3,\cdot)\) 5.c 4 yes \(-1\) \(1\) \(-i\) \(i\)
\(\chi_{5}(4,\cdot)\) 5.b 2 yes \(1\) \(1\) \(-1\) \(-1\)