# Properties

 Modulus $8820$ Structure $$C_{84}\times C_{6}\times C_{2}\times C_{2}$$ Order $2016$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8820)

pari: g = idealstar(,8820,2)

## Character group

 sage: G.order()  pari: g.no Order = 2016 sage: H.invariants()  pari: g.cyc Structure = $$C_{84}\times C_{6}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8820}(4411,\cdot)$, $\chi_{8820}(7841,\cdot)$, $\chi_{8820}(7057,\cdot)$, $\chi_{8820}(1081,\cdot)$

## First 32 of 2016 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{8820}(1,\cdot)$$ 8820.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8820}(11,\cdot)$$ 8820.hk 42 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$-1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$
$$\chi_{8820}(13,\cdot)$$ 8820.ja 84 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{25}{84}\right)$$
$$\chi_{8820}(17,\cdot)$$ 8820.ig 84 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{8820}(19,\cdot)$$ 8820.cz 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$
$$\chi_{8820}(23,\cdot)$$ 8820.iu 84 yes $$-1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$-1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{43}{84}\right)$$
$$\chi_{8820}(29,\cdot)$$ 8820.ge 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$
$$\chi_{8820}(31,\cdot)$$ 8820.bi 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{8820}(37,\cdot)$$ 8820.iz 84 no $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{8820}(41,\cdot)$$ 8820.gd 42 no $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$
$$\chi_{8820}(43,\cdot)$$ 8820.io 84 yes $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{23}{84}\right)$$
$$\chi_{8820}(47,\cdot)$$ 8820.id 84 yes $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{53}{84}\right)$$
$$\chi_{8820}(53,\cdot)$$ 8820.ik 84 no $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{8820}(59,\cdot)$$ 8820.fw 42 yes $$-1$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{8820}(61,\cdot)$$ 8820.ft 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{8820}(67,\cdot)$$ 8820.dm 12 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{8820}(71,\cdot)$$ 8820.es 14 no $$1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{8820}(73,\cdot)$$ 8820.iv 84 no $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{8820}(79,\cdot)$$ 8820.bj 6 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{8820}(83,\cdot)$$ 8820.ir 84 yes $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$-1$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{59}{84}\right)$$
$$\chi_{8820}(89,\cdot)$$ 8820.ga 42 no $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{8820}(97,\cdot)$$ 8820.ea 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{8820}(101,\cdot)$$ 8820.gi 42 no $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$-1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{8820}(103,\cdot)$$ 8820.il 84 yes $$-1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$1$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{19}{84}\right)$$
$$\chi_{8820}(107,\cdot)$$ 8820.is 84 no $$-1$$ $$1$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{8820}(109,\cdot)$$ 8820.ho 42 no $$1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{8820}(113,\cdot)$$ 8820.if 84 no $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$-1$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{73}{84}\right)$$
$$\chi_{8820}(121,\cdot)$$ 8820.fj 21 no $$1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{8820}(127,\cdot)$$ 8820.fr 28 no $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{8820}(131,\cdot)$$ 8820.he 42 no $$-1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{8820}(137,\cdot)$$ 8820.im 84 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$1$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{23}{84}\right)$$
$$\chi_{8820}(139,\cdot)$$ 8820.gm 42 yes $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$