Properties

Modulus $1170$
Structure \(C_{12}\times C_{12}\times C_{2}\)
Order $288$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1170)
 
pari: g = idealstar(,1170,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 288
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{12}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1170}(911,\cdot)$, $\chi_{1170}(937,\cdot)$, $\chi_{1170}(1081,\cdot)$

First 32 of 288 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 \(-1\) \(1\) \(7\) \(11\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1170}(1,\cdot)\) 1170.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1170}(7,\cdot)\) 1170.dv 12 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(i\)
\(\chi_{1170}(11,\cdot)\) 1170.cs 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(17,\cdot)\) 1170.cl 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1170}(19,\cdot)\) 1170.ct 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1170}(23,\cdot)\) 1170.cm 12 no \(1\) \(1\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(i\)
\(\chi_{1170}(29,\cdot)\) 1170.bl 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(31,\cdot)\) 1170.cq 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(37,\cdot)\) 1170.cf 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1170}(41,\cdot)\) 1170.cx 12 no \(1\) \(1\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\)
\(\chi_{1170}(43,\cdot)\) 1170.di 12 no \(-1\) \(1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(i\)
\(\chi_{1170}(47,\cdot)\) 1170.ce 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1170}(49,\cdot)\) 1170.bz 6 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\)
\(\chi_{1170}(53,\cdot)\) 1170.o 4 no \(1\) \(1\) \(-i\) \(-1\) \(i\) \(-1\) \(-i\) \(1\) \(1\) \(-i\) \(-1\) \(i\)
\(\chi_{1170}(59,\cdot)\) 1170.da 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1170}(61,\cdot)\) 1170.l 3 no \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)
\(\chi_{1170}(67,\cdot)\) 1170.cb 12 no \(1\) \(1\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(i\)
\(\chi_{1170}(71,\cdot)\) 1170.cu 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(73,\cdot)\) 1170.m 4 no \(1\) \(1\) \(-1\) \(-i\) \(i\) \(-i\) \(-i\) \(-1\) \(i\) \(-1\) \(i\) \(-i\)
\(\chi_{1170}(77,\cdot)\) 1170.cp 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1170}(79,\cdot)\) 1170.bo 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1170}(83,\cdot)\) 1170.ce 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1170}(89,\cdot)\) 1170.dc 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1170}(97,\cdot)\) 1170.cb 12 no \(1\) \(1\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(i\)
\(\chi_{1170}(101,\cdot)\) 1170.bw 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1170}(103,\cdot)\) 1170.dl 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1170}(107,\cdot)\) 1170.dk 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1170}(109,\cdot)\) 1170.t 4 no \(-1\) \(1\) \(-i\) \(i\) \(1\) \(-i\) \(1\) \(1\) \(-i\) \(-i\) \(-i\) \(1\)
\(\chi_{1170}(113,\cdot)\) 1170.cj 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1170}(119,\cdot)\) 1170.da 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1170}(121,\cdot)\) 1170.bm 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1170}(127,\cdot)\) 1170.dh 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)