# Properties

 Modulus $4410$ Structure $$C_{84}\times C_{6}\times C_{2}$$ Order $1008$

Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(4410)

pari: g = idealstar(,4410,2)

## 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 = $\chi_{4410}(1963,\cdot)$, $\chi_{4410}(3431,\cdot)$, $\chi_{4410}(3331,\cdot)$

## 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 $$-1$$ $$1$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{4410}(1,\cdot)$$ 4410.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4410}(11,\cdot)$$ 4410.dh 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$
$$\chi_{4410}(13,\cdot)$$ 4410.en 84 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$1$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{25}{84}\right)$$
$$\chi_{4410}(17,\cdot)$$ 4410.ed 84 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{4410}(19,\cdot)$$ 4410.bc 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$-1$$
$$\chi_{4410}(23,\cdot)$$ 4410.eg 84 no $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$1$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{84}\right)$$
$$\chi_{4410}(29,\cdot)$$ 4410.de 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{31}{42}\right)$$
$$\chi_{4410}(31,\cdot)$$ 4410.br 6 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4410}(37,\cdot)$$ 4410.em 84 no $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{4410}(41,\cdot)$$ 4410.dd 42 no $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$
$$\chi_{4410}(43,\cdot)$$ 4410.ei 84 no $$-1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$-1$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{65}{84}\right)$$
$$\chi_{4410}(47,\cdot)$$ 4410.eo 84 no $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{11}{84}\right)$$
$$\chi_{4410}(53,\cdot)$$ 4410.ef 84 no $$1$$ $$1$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{4410}(59,\cdot)$$ 4410.dz 42 no $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{29}{42}\right)$$
$$\chi_{4410}(61,\cdot)$$ 4410.cz 42 no $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{4410}(67,\cdot)$$ 4410.ci 12 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{4410}(71,\cdot)$$ 4410.cn 14 no $$-1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{4410}(73,\cdot)$$ 4410.ek 84 no $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{4410}(79,\cdot)$$ 4410.bq 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4410}(83,\cdot)$$ 4410.eh 84 no $$-1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$1$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{84}\right)$$
$$\chi_{4410}(89,\cdot)$$ 4410.dc 42 no $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{4410}(97,\cdot)$$ 4410.ca 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{4410}(101,\cdot)$$ 4410.dg 42 no $$1$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$-1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{4410}(103,\cdot)$$ 4410.ej 84 no $$1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$-1$$ $$e\left(\frac{71}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{61}{84}\right)$$
$$\chi_{4410}(107,\cdot)$$ 4410.ef 84 no $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$
$$\chi_{4410}(109,\cdot)$$ 4410.du 42 no $$1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{4410}(113,\cdot)$$ 4410.ec 84 no $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{41}{84}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$-1$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{73}{84}\right)$$
$$\chi_{4410}(121,\cdot)$$ 4410.ct 21 no $$1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{4410}(127,\cdot)$$ 4410.cu 28 no $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$-1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{4410}(131,\cdot)$$ 4410.dg 42 no $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$-1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{4410}(137,\cdot)$$ 4410.eg 84 no $$1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$1$$ $$e\left(\frac{13}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{23}{84}\right)$$
$$\chi_{4410}(139,\cdot)$$ 4410.ds 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$