Properties

Modulus $8$
Structure \(C_{2}\times C_{2}\)
Order $4$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(8)
 
pari: g = idealstar(,8,2)
 

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 = $\chi_{8}(7,\cdot)$, $\chi_{8}(5,\cdot)$

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 \(-1\) \(1\) \(3\) \(5\)
\(\chi_{8}(1,\cdot)\) 8.a 1 no \(1\) \(1\) \(1\) \(1\)
\(\chi_{8}(3,\cdot)\) 8.d 2 yes \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{8}(5,\cdot)\) 8.b 2 yes \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{8}(7,\cdot)\) 8.c 2 no \(-1\) \(1\) \(-1\) \(1\)