# Properties

 Modulus $2160$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{36}$$ Order $576$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2160)

pari: g = idealstar(,2160,2)

## 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 = $\chi_{2160}(271,\cdot)$, $\chi_{2160}(1621,\cdot)$, $\chi_{2160}(2081,\cdot)$, $\chi_{2160}(1297,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{2160}(1,\cdot)$$ 2160.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2160}(7,\cdot)$$ 2160.el 36 no $$1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{2160}(11,\cdot)$$ 2160.ep 36 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{2160}(13,\cdot)$$ 2160.eh 36 yes $$-1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{2160}(17,\cdot)$$ 2160.cv 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2160}(19,\cdot)$$ 2160.da 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2160}(23,\cdot)$$ 2160.ei 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{2160}(29,\cdot)$$ 2160.ds 36 yes $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{2160}(31,\cdot)$$ 2160.dh 18 no $$-1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{2160}(37,\cdot)$$ 2160.cs 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2160}(41,\cdot)$$ 2160.dr 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{2160}(43,\cdot)$$ 2160.ea 36 yes $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{2160}(47,\cdot)$$ 2160.dw 36 no $$-1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{2160}(49,\cdot)$$ 2160.dm 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{2160}(53,\cdot)$$ 2160.bg 4 no $$1$$ $$1$$ $$i$$ $$-i$$ $$1$$ $$i$$ $$i$$ $$i$$ $$-i$$ $$1$$ $$1$$ $$1$$
$$\chi_{2160}(59,\cdot)$$ 2160.du 36 yes $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{2160}(61,\cdot)$$ 2160.dv 36 no $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{2160}(67,\cdot)$$ 2160.ea 36 yes $$1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{2160}(71,\cdot)$$ 2160.cc 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2160}(73,\cdot)$$ 2160.cx 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2160}(77,\cdot)$$ 2160.ec 36 yes $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{2160}(79,\cdot)$$ 2160.dq 18 no $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{2160}(83,\cdot)$$ 2160.ef 36 yes $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{2160}(89,\cdot)$$ 2160.bx 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2160}(91,\cdot)$$ 2160.ch 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2160}(97,\cdot)$$ 2160.ej 36 no $$-1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{2160}(101,\cdot)$$ 2160.en 36 no $$-1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{2160}(103,\cdot)$$ 2160.el 36 no $$1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{2160}(107,\cdot)$$ 2160.ba 4 no $$-1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{2160}(109,\cdot)$$ 2160.bm 4 no $$1$$ $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$1$$ $$i$$ $$1$$ $$i$$ $$-1$$
$$\chi_{2160}(113,\cdot)$$ 2160.ek 36 no $$1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{2160}(119,\cdot)$$ 2160.dd 18 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{18}\right)$$