# Properties

 Modulus $2960$ Structure $$C_{36}\times C_{4}\times C_{4}\times C_{2}$$ Order $1152$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2960)

pari: g = idealstar(,2960,2)

## Character group

 sage: G.order()  pari: g.no Order = 1152 sage: H.invariants()  pari: g.cyc Structure = $$C_{36}\times C_{4}\times C_{4}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2960}(2591,\cdot)$, $\chi_{2960}(741,\cdot)$, $\chi_{2960}(1777,\cdot)$, $\chi_{2960}(2481,\cdot)$

## First 32 of 1152 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{2960}(1,\cdot)$$ 2960.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2960}(3,\cdot)$$ 2960.hb 36 yes $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2960}(7,\cdot)$$ 2960.gi 36 no $$1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2960}(9,\cdot)$$ 2960.gb 18 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2960}(11,\cdot)$$ 2960.eb 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$-i$$
$$\chi_{2960}(13,\cdot)$$ 2960.gq 36 yes $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2960}(17,\cdot)$$ 2960.hx 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2960}(19,\cdot)$$ 2960.hf 36 yes $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2960}(21,\cdot)$$ 2960.gs 36 no $$1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{2960}(23,\cdot)$$ 2960.ef 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$i$$
$$\chi_{2960}(27,\cdot)$$ 2960.do 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$1$$
$$\chi_{2960}(29,\cdot)$$ 2960.ed 12 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$-i$$
$$\chi_{2960}(31,\cdot)$$ 2960.ck 4 no $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$-1$$ $$i$$ $$1$$
$$\chi_{2960}(33,\cdot)$$ 2960.gk 36 no $$-1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2960}(39,\cdot)$$ 2960.hy 36 no $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2960}(41,\cdot)$$ 2960.gd 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(43,\cdot)$$ 2960.cp 4 yes $$-1$$ $$1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$-1$$ $$1$$
$$\chi_{2960}(47,\cdot)$$ 2960.eh 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$-i$$
$$\chi_{2960}(49,\cdot)$$ 2960.fu 18 no $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2960}(51,\cdot)$$ 2960.dx 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$-i$$
$$\chi_{2960}(53,\cdot)$$ 2960.ha 36 yes $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2960}(57,\cdot)$$ 2960.gp 36 no $$1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{2960}(59,\cdot)$$ 2960.hg 36 yes $$1$$ $$1$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2960}(61,\cdot)$$ 2960.hh 36 no $$-1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2960}(63,\cdot)$$ 2960.eh 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$i$$
$$\chi_{2960}(67,\cdot)$$ 2960.hm 36 yes $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(69,\cdot)$$ 2960.hc 36 yes $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2960}(71,\cdot)$$ 2960.ft 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2960}(73,\cdot)$$ 2960.bn 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$
$$\chi_{2960}(77,\cdot)$$ 2960.gz 36 yes $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2960}(79,\cdot)$$ 2960.gm 36 no $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2960}(81,\cdot)$$ 2960.dk 9 no $$1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$