Properties

Modulus $585$
Structure \(C_{2}\times C_{12}\times C_{12}\)
Order $288$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(585)
 
pari: g = idealstar(,585,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 288
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{12}\times C_{12}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{585}(326,\cdot)$, $\chi_{585}(352,\cdot)$, $\chi_{585}(496,\cdot)$

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 \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(14\) \(16\) \(17\) \(19\) \(22\)
\(\chi_{585}(1,\cdot)\) 585.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{585}(2,\cdot)\) 585.cb 12 yes \(-1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\)
\(\chi_{585}(4,\cdot)\) 585.bx 6 yes \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)
\(\chi_{585}(7,\cdot)\) 585.dt 12 yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{585}(8,\cdot)\) 585.m 4 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(i\) \(1\) \(1\) \(-i\) \(-i\) \(-i\)
\(\chi_{585}(11,\cdot)\) 585.cm 12 no \(1\) \(1\) \(-i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(i\) \(i\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\)
\(\chi_{585}(14,\cdot)\) 585.bj 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{585}(16,\cdot)\) 585.l 3 no \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{585}(17,\cdot)\) 585.cv 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{585}(19,\cdot)\) 585.dg 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{585}(22,\cdot)\) 585.cp 12 yes \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\)
\(\chi_{585}(23,\cdot)\) 585.cr 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{585}(28,\cdot)\) 585.dp 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{585}(29,\cdot)\) 585.by 6 yes \(-1\) \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\)
\(\chi_{585}(31,\cdot)\) 585.cy 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{585}(32,\cdot)\) 585.cb 12 yes \(-1\) \(1\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\)
\(\chi_{585}(34,\cdot)\) 585.db 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{585}(37,\cdot)\) 585.dp 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{585}(38,\cdot)\) 585.cs 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(1\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{585}(41,\cdot)\) 585.dd 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{585}(43,\cdot)\) 585.dl 12 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{585}(44,\cdot)\) 585.q 4 no \(1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(-i\) \(-1\) \(1\) \(-1\) \(-i\) \(-1\)
\(\chi_{585}(46,\cdot)\) 585.dh 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{585}(47,\cdot)\) 585.cd 12 yes \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(-i\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{585}(49,\cdot)\) 585.bk 6 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{585}(53,\cdot)\) 585.p 4 no \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(-1\) \(1\) \(1\) \(i\) \(-1\) \(-i\)
\(\chi_{585}(56,\cdot)\) 585.bc 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{585}(58,\cdot)\) 585.ca 12 yes \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\)
\(\chi_{585}(59,\cdot)\) 585.cn 12 yes \(1\) \(1\) \(i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(i\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\)
\(\chi_{585}(61,\cdot)\) 585.k 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{585}(62,\cdot)\) 585.cv 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{585}(64,\cdot)\) 585.h 2 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\)
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