Properties

 Modulus $3822$ Structure $$C_{2}\times C_{6}\times C_{84}$$ Order $1008$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(3822)

pari: g = idealstar(,3822,2)

Character group

 sage: G.order()  pari: g.no Order = 1008 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{6}\times C_{84}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3822}(2549,\cdot)$, $\chi_{3822}(3433,\cdot)$, $\chi_{3822}(1471,\cdot)$

First 32 of 1008 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{3822}(1,\cdot)$$ 3822.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3822}(5,\cdot)$$ 3822.eg 84 no $$-1$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{3822}(11,\cdot)$$ 3822.el 84 no $$1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$i$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$
$$\chi_{3822}(17,\cdot)$$ 3822.dh 42 no $$1$$ $$1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{25}{42}\right)$$
$$\chi_{3822}(19,\cdot)$$ 3822.bz 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3822}(23,\cdot)$$ 3822.dt 42 no $$-1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{19}{21}\right)$$
$$\chi_{3822}(25,\cdot)$$ 3822.df 42 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{3822}(29,\cdot)$$ 3822.dw 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$
$$\chi_{3822}(31,\cdot)$$ 3822.ca 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$
$$\chi_{3822}(37,\cdot)$$ 3822.ep 84 no $$-1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{1}{84}\right)$$
$$\chi_{3822}(41,\cdot)$$ 3822.eh 84 no $$-1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$i$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{79}{84}\right)$$
$$\chi_{3822}(43,\cdot)$$ 3822.dx 42 no $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$-1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$
$$\chi_{3822}(47,\cdot)$$ 3822.eg 84 no $$-1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{3822}(53,\cdot)$$ 3822.de 42 no $$-1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{3822}(55,\cdot)$$ 3822.dy 42 no $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$-1$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{41}{42}\right)$$
$$\chi_{3822}(59,\cdot)$$ 3822.eo 84 no $$-1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{5}{84}\right)$$
$$\chi_{3822}(61,\cdot)$$ 3822.db 42 no $$-1$$ $$1$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$-1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$
$$\chi_{3822}(67,\cdot)$$ 3822.cf 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{3822}(71,\cdot)$$ 3822.en 84 no $$1$$ $$1$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$-i$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{41}{84}\right)$$
$$\chi_{3822}(73,\cdot)$$ 3822.ei 84 no $$1$$ $$1$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{3822}(79,\cdot)$$ 3822.i 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{3822}(83,\cdot)$$ 3822.cw 28 no $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$i$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$i$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{3822}(85,\cdot)$$ 3822.ee 84 no $$-1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$i$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{17}{84}\right)$$
$$\chi_{3822}(89,\cdot)$$ 3822.eo 84 no $$-1$$ $$1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{25}{84}\right)$$
$$\chi_{3822}(95,\cdot)$$ 3822.dt 42 no $$-1$$ $$1$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{3822}(97,\cdot)$$ 3822.by 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3822}(101,\cdot)$$ 3822.dc 42 no $$1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{3822}(103,\cdot)$$ 3822.dp 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{3822}(107,\cdot)$$ 3822.dg 42 no $$-1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{23}{42}\right)$$
$$\chi_{3822}(109,\cdot)$$ 3822.ec 84 no $$-1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$
$$\chi_{3822}(113,\cdot)$$ 3822.dw 42 no $$-1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$
$$\chi_{3822}(115,\cdot)$$ 3822.ej 84 no $$1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$-i$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{43}{84}\right)$$