Properties

Modulus $18$
Structure \(C_{6}\)
Order $6$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(18)
 
pari: g = idealstar(,18,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 6
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{18}(11,\cdot)$

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.

Character Orbit Order Primitive \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\)
\(\chi_{18}(1,\cdot)\) 18.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{18}(5,\cdot)\) 18.d 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{18}(7,\cdot)\) 18.c 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{18}(11,\cdot)\) 18.d 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{18}(13,\cdot)\) 18.c 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{18}(17,\cdot)\) 18.b 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)