Properties

Modulus $1520$
Structure \(C_{36}\times C_{4}\times C_{2}\times C_{2}\)
Order $576$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1520)
 
pari: g = idealstar(,1520,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 576
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{36}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1520}(191,\cdot)$, $\chi_{1520}(1141,\cdot)$, $\chi_{1520}(1217,\cdot)$, $\chi_{1520}(401,\cdot)$

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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{1520}(1,\cdot)\) 1520.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1520}(3,\cdot)\) 1520.ef 36 yes \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{1520}(7,\cdot)\) 1520.cu 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1520}(9,\cdot)\) 1520.dp 18 no \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{1520}(11,\cdot)\) 1520.cv 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1520}(13,\cdot)\) 1520.ed 36 yes \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{1520}(17,\cdot)\) 1520.dw 36 no \(-1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{1520}(21,\cdot)\) 1520.eo 36 no \(-1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{1520}(23,\cdot)\) 1520.dz 36 no \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{1520}(27,\cdot)\) 1520.da 12 yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1520}(29,\cdot)\) 1520.du 36 yes \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{1520}(31,\cdot)\) 1520.bq 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1520}(33,\cdot)\) 1520.dy 36 no \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{1520}(37,\cdot)\) 1520.bn 4 yes \(1\) \(1\) \(1\) \(-i\) \(1\) \(i\) \(1\) \(i\) \(-i\) \(i\) \(1\) \(-i\)
\(\chi_{1520}(39,\cdot)\) 1520.i 2 no \(-1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\)
\(\chi_{1520}(41,\cdot)\) 1520.dh 18 no \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{1520}(43,\cdot)\) 1520.eh 36 yes \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{1520}(47,\cdot)\) 1520.el 36 no \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{1520}(49,\cdot)\) 1520.bz 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1520}(51,\cdot)\) 1520.dt 36 no \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{1520}(53,\cdot)\) 1520.eg 36 yes \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{1520}(59,\cdot)\) 1520.en 36 yes \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{1520}(61,\cdot)\) 1520.em 36 no \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{1520}(63,\cdot)\) 1520.el 36 no \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{1520}(67,\cdot)\) 1520.ea 36 yes \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{1520}(69,\cdot)\) 1520.cx 12 yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1520}(71,\cdot)\) 1520.dn 18 no \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{1520}(73,\cdot)\) 1520.ei 36 no \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{1520}(77,\cdot)\) 1520.bo 4 no \(-1\) \(1\) \(1\) \(-i\) \(1\) \(-i\) \(1\) \(i\) \(-i\) \(i\) \(1\) \(-i\)
\(\chi_{1520}(79,\cdot)\) 1520.dj 18 no \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{1520}(81,\cdot)\) 1520.ce 9 no \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{1520}(83,\cdot)\) 1520.ch 12 yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\)