Properties

Modulus 7
Structure \(C_{6}\)
Order 6

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(7)
pari: g = idealstar(,7,2)

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 = $\chi_{7}(3,\cdot)$

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 2 3 4 5
\(\chi_{7}(1,\cdot)\) 7.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{7}(2,\cdot)\) 7.c 3 Yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{7}(3,\cdot)\) 7.d 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{7}(4,\cdot)\) 7.c 3 Yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{7}(5,\cdot)\) 7.d 6 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{7}(6,\cdot)\) 7.b 2 Yes \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\)