Properties

Modulus $1560$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\)
Order $384$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1560)
 
pari: g = idealstar(,1560,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 384
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{12}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1560}(391,\cdot)$, $\chi_{1560}(781,\cdot)$, $\chi_{1560}(521,\cdot)$, $\chi_{1560}(937,\cdot)$, $\chi_{1560}(1081,\cdot)$

First 32 of 384 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 \(-1\) \(1\) \(7\) \(11\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1560}(1,\cdot)\) 1560.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1560}(7,\cdot)\) 1560.ga 12 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1560}(11,\cdot)\) 1560.fd 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1560}(17,\cdot)\) 1560.eq 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1560}(19,\cdot)\) 1560.ff 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1560}(23,\cdot)\) 1560.fs 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1560}(29,\cdot)\) 1560.du 6 yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1560}(31,\cdot)\) 1560.ce 4 no \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(i\) \(-i\) \(1\)
\(\chi_{1560}(37,\cdot)\) 1560.el 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1560}(41,\cdot)\) 1560.fa 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1560}(43,\cdot)\) 1560.fp 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1560}(47,\cdot)\) 1560.bo 4 no \(1\) \(1\) \(-1\) \(-i\) \(i\) \(i\) \(i\) \(1\) \(-i\) \(1\) \(-i\) \(-i\)
\(\chi_{1560}(49,\cdot)\) 1560.dr 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1560}(53,\cdot)\) 1560.cr 4 no \(1\) \(1\) \(-i\) \(1\) \(i\) \(1\) \(-i\) \(-1\) \(1\) \(i\) \(-1\) \(-i\)
\(\chi_{1560}(59,\cdot)\) 1560.fg 12 yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1560}(61,\cdot)\) 1560.dm 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1560}(67,\cdot)\) 1560.ej 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1560}(71,\cdot)\) 1560.fe 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1560}(73,\cdot)\) 1560.bh 4 no \(1\) \(1\) \(-1\) \(-i\) \(i\) \(-i\) \(-i\) \(-1\) \(i\) \(-1\) \(i\) \(-i\)
\(\chi_{1560}(77,\cdot)\) 1560.bq 4 yes \(1\) \(1\) \(-i\) \(-1\) \(-i\) \(-1\) \(i\) \(-1\) \(-1\) \(i\) \(1\) \(i\)
\(\chi_{1560}(79,\cdot)\) 1560.s 2 no \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\)
\(\chi_{1560}(83,\cdot)\) 1560.bi 4 yes \(1\) \(1\) \(-1\) \(-i\) \(-i\) \(i\) \(-i\) \(-1\) \(i\) \(-1\) \(i\) \(-i\)
\(\chi_{1560}(89,\cdot)\) 1560.fn 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1560}(97,\cdot)\) 1560.gc 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1560}(101,\cdot)\) 1560.ef 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1560}(103,\cdot)\) 1560.cn 4 no \(1\) \(1\) \(-i\) \(1\) \(-i\) \(-1\) \(-i\) \(-1\) \(1\) \(i\) \(-1\) \(-i\)
\(\chi_{1560}(107,\cdot)\) 1560.fv 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1560}(109,\cdot)\) 1560.ck 4 no \(-1\) \(1\) \(-i\) \(-i\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(i\) \(-i\) \(-1\)
\(\chi_{1560}(113,\cdot)\) 1560.ft 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1560}(119,\cdot)\) 1560.fj 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1560}(121,\cdot)\) 1560.ec 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1560}(127,\cdot)\) 1560.ex 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
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