Properties

Modulus 36
Structure \(C_{6}\times C_{2}\)
Order 12

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(36)
 
pari: g = idealstar(,36,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 12
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{36}(29,\cdot)$, $\chi_{36}(19,\cdot)$

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 5 7 11 13 17 19 23 25 29 31
\(\chi_{36}(1,\cdot)\) 36.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{36}(5,\cdot)\) 36.g 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{36}(7,\cdot)\) 36.f 6 Yes \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{36}(11,\cdot)\) 36.h 6 Yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{36}(13,\cdot)\) 36.e 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{36}(17,\cdot)\) 36.c 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)
\(\chi_{36}(19,\cdot)\) 36.d 2 No \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{36}(23,\cdot)\) 36.h 6 Yes \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{36}(25,\cdot)\) 36.e 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{36}(29,\cdot)\) 36.g 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{36}(31,\cdot)\) 36.f 6 Yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{36}(35,\cdot)\) 36.b 2 No \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)