Properties

Modulus $1480$
Structure \(C_{2}\times C_{2}\times C_{4}\times C_{36}\)
Order $576$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1480)
 
pari: g = idealstar(,1480,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 576
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{4}\times C_{36}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1480}(1111,\cdot)$, $\chi_{1480}(741,\cdot)$, $\chi_{1480}(297,\cdot)$, $\chi_{1480}(1001,\cdot)$

First 32 of 576 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1480}(1,\cdot)\) 1480.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1480}(3,\cdot)\) 1480.dz 36 yes \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1480}(7,\cdot)\) 1480.el 36 no \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1480}(9,\cdot)\) 1480.di 18 no \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1480}(11,\cdot)\) 1480.bu 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)
\(\chi_{1480}(13,\cdot)\) 1480.ed 36 yes \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1480}(17,\cdot)\) 1480.ef 36 no \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1480}(19,\cdot)\) 1480.eg 36 yes \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1480}(21,\cdot)\) 1480.dr 18 no \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1480}(23,\cdot)\) 1480.cx 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-i\)
\(\chi_{1480}(27,\cdot)\) 1480.cu 12 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(i\)
\(\chi_{1480}(29,\cdot)\) 1480.dc 12 yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(-1\)
\(\chi_{1480}(31,\cdot)\) 1480.bm 4 no \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-i\) \(-i\) \(i\) \(-1\) \(i\) \(1\)
\(\chi_{1480}(33,\cdot)\) 1480.dy 36 no \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1480}(39,\cdot)\) 1480.ea 36 no \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1480}(41,\cdot)\) 1480.dg 18 no \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1480}(43,\cdot)\) 1480.bc 4 yes \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(-1\) \(1\) \(1\) \(-i\) \(1\) \(1\) \(i\)
\(\chi_{1480}(47,\cdot)\) 1480.cl 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(-i\)
\(\chi_{1480}(49,\cdot)\) 1480.di 18 no \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1480}(51,\cdot)\) 1480.db 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(-1\)
\(\chi_{1480}(53,\cdot)\) 1480.ej 36 yes \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1480}(57,\cdot)\) 1480.eo 36 no \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1480}(59,\cdot)\) 1480.eg 36 yes \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1480}(61,\cdot)\) 1480.du 36 no \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1480}(63,\cdot)\) 1480.cl 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(i\)
\(\chi_{1480}(67,\cdot)\) 1480.dz 36 yes \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1480}(69,\cdot)\) 1480.eb 36 yes \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1480}(71,\cdot)\) 1480.dq 18 no \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1480}(73,\cdot)\) 1480.bi 4 no \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(1\) \(-i\) \(i\) \(1\) \(1\) \(-i\) \(-i\)
\(\chi_{1480}(77,\cdot)\) 1480.ek 36 yes \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1480}(79,\cdot)\) 1480.ea 36 no \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1480}(81,\cdot)\) 1480.ce 9 no \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
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