# Properties

 Modulus $2240$ Structure $$C_{48}\times C_{4}\times C_{2}\times C_{2}$$ Order $768$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2240)

pari: g = idealstar(,2240,2)

## Character group

 sage: G.order()  pari: g.no Order = 768 sage: H.invariants()  pari: g.cyc Structure = $$C_{48}\times C_{4}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2240}(1471,\cdot)$, $\chi_{2240}(1541,\cdot)$, $\chi_{2240}(897,\cdot)$, $\chi_{2240}(1921,\cdot)$

## 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 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{2240}(1,\cdot)$$ 2240.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2240}(3,\cdot)$$ 2240.fm 48 yes $$-1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2240}(9,\cdot)$$ 2240.ei 24 no $$1$$ $$1$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(11,\cdot)$$ 2240.fe 48 no $$-1$$ $$1$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(13,\cdot)$$ 2240.du 16 yes $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$1$$
$$\chi_{2240}(17,\cdot)$$ 2240.dp 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2240}(19,\cdot)$$ 2240.fj 48 yes $$1$$ $$1$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2240}(23,\cdot)$$ 2240.eo 24 no $$1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2240}(27,\cdot)$$ 2240.dt 16 yes $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$
$$\chi_{2240}(29,\cdot)$$ 2240.dz 16 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$-i$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$-1$$
$$\chi_{2240}(31,\cdot)$$ 2240.bz 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(33,\cdot)$$ 2240.dn 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2240}(37,\cdot)$$ 2240.fa 48 yes $$-1$$ $$1$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{7}{48}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2240}(39,\cdot)$$ 2240.el 24 no $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2240}(41,\cdot)$$ 2240.cr 8 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$
$$\chi_{2240}(43,\cdot)$$ 2240.dv 16 no $$1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$
$$\chi_{2240}(47,\cdot)$$ 2240.cu 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(51,\cdot)$$ 2240.fe 48 no $$-1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{25}{48}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(53,\cdot)$$ 2240.fn 48 yes $$-1$$ $$1$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2240}(57,\cdot)$$ 2240.ck 8 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$
$$\chi_{2240}(59,\cdot)$$ 2240.fj 48 yes $$1$$ $$1$$ $$e\left(\frac{17}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2240}(61,\cdot)$$ 2240.fd 48 no $$-1$$ $$1$$ $$e\left(\frac{19}{48}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2240}(67,\cdot)$$ 2240.fk 48 yes $$1$$ $$1$$ $$e\left(\frac{23}{48}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(69,\cdot)$$ 2240.ea 16 yes $$-1$$ $$1$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$1$$
$$\chi_{2240}(71,\cdot)$$ 2240.cf 8 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$
$$\chi_{2240}(73,\cdot)$$ 2240.es 24 no $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2240}(79,\cdot)$$ 2240.di 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2240}(81,\cdot)$$ 2240.df 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(83,\cdot)$$ 2240.dt 16 yes $$-1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$-1$$
$$\chi_{2240}(87,\cdot)$$ 2240.er 24 no $$-1$$ $$1$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2240}(89,\cdot)$$ 2240.ex 24 no $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{24}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2240}(93,\cdot)$$ 2240.fa 48 yes $$-1$$ $$1$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{37}{48}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{47}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{6}\right)$$