Properties

Modulus 20
Structure \(C_{4}\times C_{2}\)
Order 8

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(20)
pari: g = idealstar(,20,2)

Character group

sage: G.order()
pari: g.no
Order = 8
sage: H.invariants()
pari: g.cyc
Structure = \(C_{4}\times C_{2}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{20}(17,\cdot)$, $\chi_{20}(11,\cdot)$

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 7 9 11 13 17
\(\chi_{20}(1,\cdot)\) 20.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{20}(3,\cdot)\) 20.e 4 Yes \(1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(i\) \(-i\)
\(\chi_{20}(7,\cdot)\) 20.e 4 Yes \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\)
\(\chi_{20}(9,\cdot)\) 20.c 2 No \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{20}(11,\cdot)\) 20.b 2 No \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(1\)
\(\chi_{20}(13,\cdot)\) 20.f 4 No \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\)
\(\chi_{20}(17,\cdot)\) 20.f 4 No \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(1\) \(-i\) \(i\)
\(\chi_{20}(19,\cdot)\) 20.d 2 Yes \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\)