# Properties

 Modulus $8624$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{420}$$ Order $3360$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8624)

pari: g = idealstar(,8624,2)

## Character group

 sage: G.order()  pari: g.no Order = 3360 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{420}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8624}(5391,\cdot)$, $\chi_{8624}(6469,\cdot)$, $\chi_{8624}(7745,\cdot)$, $\chi_{8624}(3137,\cdot)$

## First 32 of 3360 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$ $$27$$
$$\chi_{8624}(1,\cdot)$$ 8624.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8624}(3,\cdot)$$ 8624.hf 420 yes $$1$$ $$1$$ $$e\left(\frac{73}{420}\right)$$ $$e\left(\frac{269}{420}\right)$$ $$e\left(\frac{73}{210}\right)$$ $$e\left(\frac{117}{140}\right)$$ $$e\left(\frac{57}{70}\right)$$ $$e\left(\frac{167}{210}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{59}{210}\right)$$ $$e\left(\frac{73}{140}\right)$$
$$\chi_{8624}(5,\cdot)$$ 8624.hi 420 yes $$-1$$ $$1$$ $$e\left(\frac{269}{420}\right)$$ $$e\left(\frac{367}{420}\right)$$ $$e\left(\frac{59}{210}\right)$$ $$e\left(\frac{131}{140}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{181}{210}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{157}{210}\right)$$ $$e\left(\frac{129}{140}\right)$$
$$\chi_{8624}(9,\cdot)$$ 8624.gy 210 no $$1$$ $$1$$ $$e\left(\frac{73}{210}\right)$$ $$e\left(\frac{59}{210}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{3}{70}\right)$$
$$\chi_{8624}(13,\cdot)$$ 8624.gm 140 yes $$1$$ $$1$$ $$e\left(\frac{117}{140}\right)$$ $$e\left(\frac{131}{140}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{39}{140}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{71}{140}\right)$$
$$\chi_{8624}(15,\cdot)$$ 8624.fo 70 no $$-1$$ $$1$$ $$e\left(\frac{57}{70}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{31}{70}\right)$$
$$\chi_{8624}(17,\cdot)$$ 8624.ha 210 no $$1$$ $$1$$ $$e\left(\frac{167}{210}\right)$$ $$e\left(\frac{181}{210}\right)$$ $$e\left(\frac{62}{105}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{27}{70}\right)$$
$$\chi_{8624}(19,\cdot)$$ 8624.fg 60 no $$-1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{8624}(23,\cdot)$$ 8624.ev 42 no $$-1$$ $$1$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{8624}(25,\cdot)$$ 8624.gy 210 no $$1$$ $$1$$ $$e\left(\frac{59}{210}\right)$$ $$e\left(\frac{157}{210}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{1}{35}\right)$$ $$e\left(\frac{76}{105}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{59}{70}\right)$$
$$\chi_{8624}(27,\cdot)$$ 8624.gf 140 yes $$1$$ $$1$$ $$e\left(\frac{73}{140}\right)$$ $$e\left(\frac{129}{140}\right)$$ $$e\left(\frac{3}{70}\right)$$ $$e\left(\frac{71}{140}\right)$$ $$e\left(\frac{31}{70}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{79}{140}\right)$$
$$\chi_{8624}(29,\cdot)$$ 8624.gj 140 yes $$-1$$ $$1$$ $$e\left(\frac{39}{140}\right)$$ $$e\left(\frac{137}{140}\right)$$ $$e\left(\frac{39}{70}\right)$$ $$e\left(\frac{13}{140}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{1}{70}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{67}{70}\right)$$ $$e\left(\frac{117}{140}\right)$$
$$\chi_{8624}(31,\cdot)$$ 8624.ee 30 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{8624}(37,\cdot)$$ 8624.hh 420 yes $$1$$ $$1$$ $$e\left(\frac{47}{420}\right)$$ $$e\left(\frac{61}{420}\right)$$ $$e\left(\frac{47}{210}\right)$$ $$e\left(\frac{13}{140}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{61}{210}\right)$$ $$e\left(\frac{47}{140}\right)$$
$$\chi_{8624}(39,\cdot)$$ 8624.gt 210 no $$1$$ $$1$$ $$e\left(\frac{1}{105}\right)$$ $$e\left(\frac{121}{210}\right)$$ $$e\left(\frac{2}{105}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{71}{210}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{16}{105}\right)$$ $$e\left(\frac{1}{35}\right)$$
$$\chi_{8624}(41,\cdot)$$ 8624.fu 70 no $$1$$ $$1$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{22}{35}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{4}{35}\right)$$ $$e\left(\frac{27}{35}\right)$$
$$\chi_{8624}(43,\cdot)$$ 8624.ds 28 yes $$1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$-i$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$
$$\chi_{8624}(45,\cdot)$$ 8624.fx 84 no $$-1$$ $$1$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{27}{28}\right)$$
$$\chi_{8624}(47,\cdot)$$ 8624.gr 210 no $$1$$ $$1$$ $$e\left(\frac{2}{105}\right)$$ $$e\left(\frac{137}{210}\right)$$ $$e\left(\frac{4}{105}\right)$$ $$e\left(\frac{51}{70}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{37}{210}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{2}{35}\right)$$
$$\chi_{8624}(51,\cdot)$$ 8624.he 420 yes $$1$$ $$1$$ $$e\left(\frac{407}{420}\right)$$ $$e\left(\frac{211}{420}\right)$$ $$e\left(\frac{197}{210}\right)$$ $$e\left(\frac{53}{140}\right)$$ $$e\left(\frac{33}{70}\right)$$ $$e\left(\frac{163}{210}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{210}\right)$$ $$e\left(\frac{127}{140}\right)$$
$$\chi_{8624}(53,\cdot)$$ 8624.hh 420 yes $$1$$ $$1$$ $$e\left(\frac{331}{420}\right)$$ $$e\left(\frac{233}{420}\right)$$ $$e\left(\frac{121}{210}\right)$$ $$e\left(\frac{29}{140}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{37}{105}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{23}{210}\right)$$ $$e\left(\frac{51}{140}\right)$$
$$\chi_{8624}(57,\cdot)$$ 8624.fj 70 no $$-1$$ $$1$$ $$e\left(\frac{11}{70}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{31}{35}\right)$$ $$e\left(\frac{32}{35}\right)$$ $$e\left(\frac{23}{70}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{33}{70}\right)$$
$$\chi_{8624}(59,\cdot)$$ 8624.hf 420 yes $$1$$ $$1$$ $$e\left(\frac{67}{420}\right)$$ $$e\left(\frac{11}{420}\right)$$ $$e\left(\frac{67}{210}\right)$$ $$e\left(\frac{23}{140}\right)$$ $$e\left(\frac{13}{70}\right)$$ $$e\left(\frac{113}{210}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{210}\right)$$ $$e\left(\frac{67}{140}\right)$$
$$\chi_{8624}(61,\cdot)$$ 8624.hg 420 yes $$1$$ $$1$$ $$e\left(\frac{299}{420}\right)$$ $$e\left(\frac{397}{420}\right)$$ $$e\left(\frac{89}{210}\right)$$ $$e\left(\frac{111}{140}\right)$$ $$e\left(\frac{23}{35}\right)$$ $$e\left(\frac{68}{105}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{187}{210}\right)$$ $$e\left(\frac{19}{140}\right)$$
$$\chi_{8624}(65,\cdot)$$ 8624.ex 42 no $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{8624}(67,\cdot)$$ 8624.cg 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$
$$\chi_{8624}(69,\cdot)$$ 8624.gk 140 yes $$-1$$ $$1$$ $$e\left(\frac{11}{140}\right)$$ $$e\left(\frac{53}{140}\right)$$ $$e\left(\frac{11}{70}\right)$$ $$e\left(\frac{27}{140}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{33}{140}\right)$$
$$\chi_{8624}(71,\cdot)$$ 8624.fq 70 no $$-1$$ $$1$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{19}{35}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{31}{70}\right)$$ $$e\left(\frac{31}{35}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{11}{35}\right)$$
$$\chi_{8624}(73,\cdot)$$ 8624.gn 210 no $$1$$ $$1$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{34}{105}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{33}{35}\right)$$
$$\chi_{8624}(75,\cdot)$$ 8624.hf 420 yes $$1$$ $$1$$ $$e\left(\frac{191}{420}\right)$$ $$e\left(\frac{163}{420}\right)$$ $$e\left(\frac{191}{210}\right)$$ $$e\left(\frac{99}{140}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{109}{210}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{163}{210}\right)$$ $$e\left(\frac{51}{140}\right)$$
$$\chi_{8624}(79,\cdot)$$ 8624.ea 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{8624}(81,\cdot)$$ 8624.ge 105 no $$1$$ $$1$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{59}{105}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{12}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{19}{105}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{13}{105}\right)$$ $$e\left(\frac{3}{35}\right)$$