Properties

Modulus $336$
Structure \(C_{12}\times C_{2}\times C_{2}\times C_{2}\)
Order $96$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(336)
 
pari: g = idealstar(,336,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{336}(127,\cdot)$, $\chi_{336}(85,\cdot)$, $\chi_{336}(113,\cdot)$, $\chi_{336}(241,\cdot)$

First 32 of 96 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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{336}(1,\cdot)\) 336.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{336}(5,\cdot)\) 336.bo 12 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{336}(11,\cdot)\) 336.bu 12 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{336}(13,\cdot)\) 336.r 4 no \(-1\) \(1\) \(i\) \(-i\) \(-i\) \(-1\) \(-i\) \(-1\) \(-1\) \(i\) \(-1\) \(-i\)
\(\chi_{336}(17,\cdot)\) 336.bc 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{336}(19,\cdot)\) 336.bs 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{336}(23,\cdot)\) 336.bd 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{336}(25,\cdot)\) 336.bk 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{336}(29,\cdot)\) 336.t 4 no \(-1\) \(1\) \(i\) \(i\) \(i\) \(-1\) \(i\) \(1\) \(-1\) \(-i\) \(1\) \(-i\)
\(\chi_{336}(31,\cdot)\) 336.bl 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{336}(37,\cdot)\) 336.bq 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{336}(41,\cdot)\) 336.i 2 no \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{336}(43,\cdot)\) 336.x 4 no \(-1\) \(1\) \(i\) \(-i\) \(-i\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(-1\) \(i\)
\(\chi_{336}(47,\cdot)\) 336.z 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{336}(53,\cdot)\) 336.bt 12 yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{336}(55,\cdot)\) 336.p 2 no \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{336}(59,\cdot)\) 336.br 12 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{336}(61,\cdot)\) 336.bv 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{336}(65,\cdot)\) 336.bn 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{336}(67,\cdot)\) 336.bp 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{336}(71,\cdot)\) 336.j 2 no \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{336}(73,\cdot)\) 336.bf 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{336}(79,\cdot)\) 336.be 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{336}(83,\cdot)\) 336.v 4 yes \(-1\) \(1\) \(-i\) \(-i\) \(-i\) \(1\) \(i\) \(-1\) \(-1\) \(-i\) \(1\) \(-i\)
\(\chi_{336}(85,\cdot)\) 336.w 4 no \(1\) \(1\) \(i\) \(i\) \(-i\) \(1\) \(-i\) \(-1\) \(-1\) \(-i\) \(1\) \(i\)
\(\chi_{336}(89,\cdot)\) 336.bi 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{336}(95,\cdot)\) 336.bj 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{336}(97,\cdot)\) 336.f 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{336}(101,\cdot)\) 336.bo 12 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{336}(103,\cdot)\) 336.bb 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{336}(107,\cdot)\) 336.bu 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{336}(109,\cdot)\) 336.bq 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)