Properties

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

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(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.

orbit label 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 \(-1\) \(1\) \(-1\) \(1\)