# Properties

 Modulus $2205$ Structure $$C_{84}\times C_{6}\times C_{2}$$ Order $1008$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2205)

pari: g = idealstar(,2205,2)

## Character group

 sage: G.order()  pari: g.no Order = 1008 sage: H.invariants()  pari: g.cyc Structure = $$C_{84}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2205}(1226,\cdot)$, $\chi_{2205}(442,\cdot)$, $\chi_{2205}(1081,\cdot)$

## 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$8$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$22$$ $$23$$
$$\chi_{2205}(1,\cdot)$$ 2205.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2205}(2,\cdot)$$ 2205.el 84 yes $$1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$
$$\chi_{2205}(4,\cdot)$$ 2205.db 42 yes $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{2205}(8,\cdot)$$ 2205.cw 28 no $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$-1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{2205}(11,\cdot)$$ 2205.dx 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$
$$\chi_{2205}(13,\cdot)$$ 2205.ej 84 yes $$1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{65}{84}\right)$$
$$\chi_{2205}(16,\cdot)$$ 2205.cr 21 no $$1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{2205}(17,\cdot)$$ 2205.ed 84 no $$-1$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{73}{84}\right)$$
$$\chi_{2205}(19,\cdot)$$ 2205.bi 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2205}(22,\cdot)$$ 2205.eg 84 yes $$-1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$-1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{11}{84}\right)$$
$$\chi_{2205}(23,\cdot)$$ 2205.en 84 yes $$1$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{67}{84}\right)$$
$$\chi_{2205}(26,\cdot)$$ 2205.dg 42 no $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{37}{42}\right)$$
$$\chi_{2205}(29,\cdot)$$ 2205.dp 42 yes $$-1$$ $$1$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$
$$\chi_{2205}(31,\cdot)$$ 2205.bc 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{2205}(32,\cdot)$$ 2205.el 84 yes $$1$$ $$1$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{2205}(34,\cdot)$$ 2205.dj 42 yes $$-1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$-1$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$
$$\chi_{2205}(37,\cdot)$$ 2205.ei 84 no $$-1$$ $$1$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{59}{84}\right)$$
$$\chi_{2205}(38,\cdot)$$ 2205.em 84 yes $$-1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{23}{84}\right)$$
$$\chi_{2205}(41,\cdot)$$ 2205.de 42 no $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$
$$\chi_{2205}(43,\cdot)$$ 2205.eg 84 yes $$-1$$ $$1$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$-1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$
$$\chi_{2205}(44,\cdot)$$ 2205.dr 42 no $$-1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{2205}(46,\cdot)$$ 2205.cs 21 no $$1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{19}{21}\right)$$
$$\chi_{2205}(47,\cdot)$$ 2205.ek 84 yes $$-1$$ $$1$$ $$e\left(\frac{43}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$
$$\chi_{2205}(52,\cdot)$$ 2205.eo 84 yes $$1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{83}{84}\right)$$
$$\chi_{2205}(53,\cdot)$$ 2205.ee 84 no $$1$$ $$1$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{67}{84}\right)$$
$$\chi_{2205}(58,\cdot)$$ 2205.ep 84 yes $$-1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{61}{84}\right)$$
$$\chi_{2205}(59,\cdot)$$ 2205.dv 42 yes $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{2205}(61,\cdot)$$ 2205.dn 42 no $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{2205}(62,\cdot)$$ 2205.cx 28 no $$-1$$ $$1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$
$$\chi_{2205}(64,\cdot)$$ 2205.cn 14 no $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$
$$\chi_{2205}(67,\cdot)$$ 2205.ci 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$
$$\chi_{2205}(68,\cdot)$$ 2205.bv 12 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$