Properties

Modulus $260$
Structure \(C_{2}\times C_{4}\times C_{12}\)
Order $96$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(260)
 
pari: g = idealstar(,260,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 96
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{4}\times C_{12}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{260}(131,\cdot)$, $\chi_{260}(157,\cdot)$, $\chi_{260}(41,\cdot)$

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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{260}(1,\cdot)\) 260.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{260}(3,\cdot)\) 260.bj 12 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(7,\cdot)\) 260.bl 12 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(9,\cdot)\) 260.ba 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(11,\cdot)\) 260.bn 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(17,\cdot)\) 260.bi 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(19,\cdot)\) 260.bc 12 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(21,\cdot)\) 260.t 4 no \(-1\) \(1\) \(1\) \(-i\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\) \(1\) \(1\)
\(\chi_{260}(23,\cdot)\) 260.bg 12 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(27,\cdot)\) 260.o 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(-i\) \(-1\)
\(\chi_{260}(29,\cdot)\) 260.ba 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(31,\cdot)\) 260.j 4 no \(1\) \(1\) \(-1\) \(-i\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(-1\) \(1\)
\(\chi_{260}(33,\cdot)\) 260.bk 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(37,\cdot)\) 260.bf 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(41,\cdot)\) 260.bd 12 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(43,\cdot)\) 260.bg 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{260}(47,\cdot)\) 260.l 4 yes \(-1\) \(1\) \(i\) \(-1\) \(-1\) \(i\) \(-i\) \(i\) \(-i\) \(-i\) \(-i\) \(-1\)
\(\chi_{260}(49,\cdot)\) 260.z 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(51,\cdot)\) 260.e 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{260}(53,\cdot)\) 260.q 4 no \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(-i\) \(-1\) \(1\) \(i\) \(-i\) \(-1\)
\(\chi_{260}(57,\cdot)\) 260.m 4 no \(1\) \(1\) \(-i\) \(-1\) \(-1\) \(i\) \(-i\) \(i\) \(i\) \(i\) \(i\) \(-1\)
\(\chi_{260}(59,\cdot)\) 260.bc 12 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(61,\cdot)\) 260.i 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(63,\cdot)\) 260.be 12 yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(67,\cdot)\) 260.be 12 yes \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{260}(69,\cdot)\) 260.z 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(71,\cdot)\) 260.bn 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{260}(73,\cdot)\) 260.m 4 no \(1\) \(1\) \(i\) \(-1\) \(-1\) \(-i\) \(i\) \(-i\) \(-i\) \(-i\) \(-i\) \(-1\)
\(\chi_{260}(77,\cdot)\) 260.n 4 no \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(-1\) \(-i\) \(i\) \(-1\)
\(\chi_{260}(79,\cdot)\) 260.h 2 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{260}(81,\cdot)\) 260.i 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{260}(83,\cdot)\) 260.l 4 yes \(-1\) \(1\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(-i\) \(i\) \(i\) \(i\) \(-1\)
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