# Properties

 Modulus $2880$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{48}$$ Order $768$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2880)

pari: g = idealstar(,2880,2)

## Character group

 sage: G.order()  pari: g.no Order = 768 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{48}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2880}(2431,\cdot)$, $\chi_{2880}(901,\cdot)$, $\chi_{2880}(641,\cdot)$, $\chi_{2880}(577,\cdot)$

## First 32 of 768 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{2880}(1,\cdot)$$ 2880.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2880}(7,\cdot)$$ 2880.ej 24 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2880}(11,\cdot)$$ 2880.ff 48 no $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$i$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{24}\right)$$
$$\chi_{2880}(13,\cdot)$$ 2880.fm 48 yes $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{19}{24}\right)$$
$$\chi_{2880}(17,\cdot)$$ 2880.bg 4 no $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$1$$
$$\chi_{2880}(19,\cdot)$$ 2880.ec 16 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{2880}(23,\cdot)$$ 2880.el 24 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2880}(29,\cdot)$$ 2880.fh 48 yes $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{24}\right)$$
$$\chi_{2880}(31,\cdot)$$ 2880.bz 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2880}(37,\cdot)$$ 2880.ee 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{2880}(41,\cdot)$$ 2880.eq 24 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2880}(43,\cdot)$$ 2880.ey 48 yes $$1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{2880}(47,\cdot)$$ 2880.de 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2880}(49,\cdot)$$ 2880.cu 12 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2880}(53,\cdot)$$ 2880.ef 16 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{2880}(59,\cdot)$$ 2880.fd 48 yes $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$
$$\chi_{2880}(61,\cdot)$$ 2880.fi 48 no $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{29}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$i$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{2880}(67,\cdot)$$ 2880.ey 48 yes $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$-1$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{2880}(71,\cdot)$$ 2880.cn 8 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$
$$\chi_{2880}(73,\cdot)$$ 2880.cf 8 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$
$$\chi_{2880}(77,\cdot)$$ 2880.fn 48 yes $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{7}{24}\right)$$
$$\chi_{2880}(79,\cdot)$$ 2880.dp 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2880}(83,\cdot)$$ 2880.ez 48 yes $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{23}{24}\right)$$
$$\chi_{2880}(89,\cdot)$$ 2880.ck 8 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$
$$\chi_{2880}(91,\cdot)$$ 2880.ea 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{2880}(97,\cdot)$$ 2880.dm 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2880}(101,\cdot)$$ 2880.fj 48 no $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{2880}(103,\cdot)$$ 2880.ex 24 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2880}(107,\cdot)$$ 2880.dv 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{2880}(109,\cdot)$$ 2880.dy 16 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{2880}(113,\cdot)$$ 2880.dc 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2880}(119,\cdot)$$ 2880.ep 24 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{12}\right)$$