# Properties

 Modulus $4560$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{36}$$ Order $1152$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4560)

pari: g = idealstar(,4560,2)

## Character group

 sage: G.order()  pari: g.no Order = 1152 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{36}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4560}(1711,\cdot)$, $\chi_{4560}(1141,\cdot)$, $\chi_{4560}(3041,\cdot)$, $\chi_{4560}(2737,\cdot)$, $\chi_{4560}(1921,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{4560}(1,\cdot)$$ 4560.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4560}(7,\cdot)$$ 4560.fq 12 no $$1$$ $$1$$ $$-i$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4560}(11,\cdot)$$ 4560.gd 12 no $$1$$ $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4560}(13,\cdot)$$ 4560.ip 36 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{4560}(17,\cdot)$$ 4560.iq 36 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{4560}(23,\cdot)$$ 4560.iv 36 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$
$$\chi_{4560}(29,\cdot)$$ 4560.hq 36 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{13}{36}\right)$$
$$\chi_{4560}(31,\cdot)$$ 4560.di 6 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4560}(37,\cdot)$$ 4560.ch 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$i$$ $$-i$$ $$-1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4560}(41,\cdot)$$ 4560.gk 18 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{4560}(43,\cdot)$$ 4560.in 36 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{4560}(47,\cdot)$$ 4560.hz 36 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{13}{36}\right)$$
$$\chi_{4560}(49,\cdot)$$ 4560.ds 6 no $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4560}(53,\cdot)$$ 4560.il 36 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{4560}(59,\cdot)$$ 4560.iy 36 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$
$$\chi_{4560}(61,\cdot)$$ 4560.jb 36 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$
$$\chi_{4560}(67,\cdot)$$ 4560.ib 36 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{4560}(71,\cdot)$$ 4560.hf 18 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{4560}(73,\cdot)$$ 4560.ir 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{36}\right)$$
$$\chi_{4560}(77,\cdot)$$ 4560.cm 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{4560}(79,\cdot)$$ 4560.go 18 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{4560}(83,\cdot)$$ 4560.fi 12 yes $$-1$$ $$1$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4560}(89,\cdot)$$ 4560.gz 18 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{4560}(91,\cdot)$$ 4560.hm 36 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{19}{36}\right)$$
$$\chi_{4560}(97,\cdot)$$ 4560.hx 36 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$
$$\chi_{4560}(101,\cdot)$$ 4560.ja 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{4560}(103,\cdot)$$ 4560.fv 12 no $$-1$$ $$1$$ $$i$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{4560}(107,\cdot)$$ 4560.ff 12 yes $$1$$ $$1$$ $$i$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4560}(109,\cdot)$$ 4560.hr 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{36}\right)$$
$$\chi_{4560}(113,\cdot)$$ 4560.br 4 no $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$1$$ $$i$$
$$\chi_{4560}(119,\cdot)$$ 4560.gs 18 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{4560}(121,\cdot)$$ 4560.dx 6 no $$1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
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