Properties

 Modulus $2352$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{84}$$ Order $672$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2352)

pari: g = idealstar(,2352,2)

Character group

 sage: G.order()  pari: g.no Order = 672 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{84}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2352}(1471,\cdot)$, $\chi_{2352}(1765,\cdot)$, $\chi_{2352}(785,\cdot)$, $\chi_{2352}(2257,\cdot)$

First 32 of 672 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$
$$\chi_{2352}(1,\cdot)$$ 2352.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2352}(5,\cdot)$$ 2352.dr 84 yes $$1$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{84}\right)$$
$$\chi_{2352}(11,\cdot)$$ 2352.dl 84 yes $$1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{61}{84}\right)$$
$$\chi_{2352}(13,\cdot)$$ 2352.cu 28 no $$-1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-i$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$-1$$ $$e\left(\frac{25}{28}\right)$$
$$\chi_{2352}(17,\cdot)$$ 2352.dg 42 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{2352}(19,\cdot)$$ 2352.bt 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2352}(23,\cdot)$$ 2352.df 42 no $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{42}\right)$$
$$\chi_{2352}(25,\cdot)$$ 2352.cy 42 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{2352}(29,\cdot)$$ 2352.cs 28 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$i$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$1$$ $$e\left(\frac{13}{28}\right)$$
$$\chi_{2352}(31,\cdot)$$ 2352.bl 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2352}(37,\cdot)$$ 2352.dp 84 no $$1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{53}{84}\right)$$
$$\chi_{2352}(41,\cdot)$$ 2352.ce 14 no $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{2352}(43,\cdot)$$ 2352.co 28 no $$-1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$i$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$-1$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{2352}(47,\cdot)$$ 2352.dj 42 no $$-1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{2352}(53,\cdot)$$ 2352.dm 84 yes $$-1$$ $$1$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{73}{84}\right)$$
$$\chi_{2352}(55,\cdot)$$ 2352.bx 14 no $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{2352}(59,\cdot)$$ 2352.do 84 yes $$-1$$ $$1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{84}\right)$$
$$\chi_{2352}(61,\cdot)$$ 2352.dk 84 no $$-1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{84}\right)$$
$$\chi_{2352}(65,\cdot)$$ 2352.cv 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{2352}(67,\cdot)$$ 2352.bq 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2352}(71,\cdot)$$ 2352.cd 14 no $$1$$ $$1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{2352}(73,\cdot)$$ 2352.dd 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{2352}(79,\cdot)$$ 2352.be 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2352}(83,\cdot)$$ 2352.cq 28 yes $$-1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$i$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$1$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{2352}(85,\cdot)$$ 2352.cp 28 no $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-i$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$1$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{2352}(89,\cdot)$$ 2352.da 42 no $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$
$$\chi_{2352}(95,\cdot)$$ 2352.cz 42 no $$1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{2352}(97,\cdot)$$ 2352.f 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{2352}(101,\cdot)$$ 2352.dr 84 yes $$1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{84}\right)$$
$$\chi_{2352}(103,\cdot)$$ 2352.dh 42 no $$1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{25}{42}\right)$$
$$\chi_{2352}(107,\cdot)$$ 2352.dl 84 yes $$1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$
$$\chi_{2352}(109,\cdot)$$ 2352.dp 84 no $$1$$ $$1$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{84}\right)$$