# Properties

 Modulus $3920$ Structure $$C_{84}\times C_{4}\times C_{2}\times C_{2}$$ Order $1344$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3920)

pari: g = idealstar(,3920,2)

## Character group

 sage: G.order()  pari: g.no Order = 1344 sage: H.invariants()  pari: g.cyc Structure = $$C_{84}\times C_{4}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3920}(1471,\cdot)$, $\chi_{3920}(981,\cdot)$, $\chi_{3920}(3137,\cdot)$, $\chi_{3920}(3041,\cdot)$

## First 32 of 1344 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 $$-1$$ $$1$$ $$3$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$27$$ $$29$$ $$31$$
$$\chi_{3920}(1,\cdot)$$ 3920.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3920}(3,\cdot)$$ 3920.fg 84 yes $$-1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(9,\cdot)$$ 3920.fa 42 no $$1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(11,\cdot)$$ 3920.fv 84 no $$-1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3920}(13,\cdot)$$ 3920.dt 28 yes $$1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$i$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$-1$$
$$\chi_{3920}(17,\cdot)$$ 3920.fx 84 no $$1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3920}(19,\cdot)$$ 3920.cp 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$i$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(23,\cdot)$$ 3920.fy 84 no $$1$$ $$1$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3920}(27,\cdot)$$ 3920.eo 28 yes $$-1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$i$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$1$$
$$\chi_{3920}(29,\cdot)$$ 3920.eg 28 yes $$1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$i$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$1$$
$$\chi_{3920}(31,\cdot)$$ 3920.bs 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(33,\cdot)$$ 3920.fx 84 no $$1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3920}(37,\cdot)$$ 3920.fi 84 yes $$-1$$ $$1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(39,\cdot)$$ 3920.ev 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3920}(41,\cdot)$$ 3920.dh 14 no $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$
$$\chi_{3920}(43,\cdot)$$ 3920.en 28 yes $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$-i$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$-1$$
$$\chi_{3920}(47,\cdot)$$ 3920.fn 84 no $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3920}(51,\cdot)$$ 3920.fv 84 no $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3920}(53,\cdot)$$ 3920.ga 84 yes $$-1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(57,\cdot)$$ 3920.el 28 no $$-1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$1$$
$$\chi_{3920}(59,\cdot)$$ 3920.ft 84 yes $$1$$ $$1$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(61,\cdot)$$ 3920.fo 84 no $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3920}(67,\cdot)$$ 3920.dc 12 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3920}(69,\cdot)$$ 3920.ec 28 yes $$-1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$i$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$-1$$
$$\chi_{3920}(71,\cdot)$$ 3920.df 14 no $$-1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$
$$\chi_{3920}(73,\cdot)$$ 3920.fm 84 no $$1$$ $$1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3920}(79,\cdot)$$ 3920.bt 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3920}(81,\cdot)$$ 3920.ds 21 no $$1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(83,\cdot)$$ 3920.eo 28 yes $$-1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$-i$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$1$$
$$\chi_{3920}(87,\cdot)$$ 3920.fw 84 no $$-1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{3920}(89,\cdot)$$ 3920.et 42 no $$-1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3920}(93,\cdot)$$ 3920.fi 84 yes $$-1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{3}\right)$$