# Properties

 Modulus $2898$ Structure $$C_{2}\times C_{6}\times C_{66}$$ Order $792$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2898)

pari: g = idealstar(,2898,2)

## Character group

 sage: G.order()  pari: g.no Order = 792 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{6}\times C_{66}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2898}(1289,\cdot)$, $\chi_{2898}(829,\cdot)$, $\chi_{2898}(1891,\cdot)$

## First 32 of 792 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{2898}(1,\cdot)$$ 2898.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2898}(5,\cdot)$$ 2898.ck 66 no $$-1$$ $$1$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{2898}(11,\cdot)$$ 2898.cx 66 no $$1$$ $$1$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$
$$\chi_{2898}(13,\cdot)$$ 2898.cm 66 no $$-1$$ $$1$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$
$$\chi_{2898}(17,\cdot)$$ 2898.co 66 no $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{2898}(19,\cdot)$$ 2898.cu 66 no $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{2898}(25,\cdot)$$ 2898.bz 33 no $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{2898}(29,\cdot)$$ 2898.ch 66 no $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{43}{66}\right)$$
$$\chi_{2898}(31,\cdot)$$ 2898.cy 66 no $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$
$$\chi_{2898}(37,\cdot)$$ 2898.cd 66 no $$-1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{2898}(41,\cdot)$$ 2898.cq 66 no $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{2898}(43,\cdot)$$ 2898.ci 66 no $$-1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{2898}(47,\cdot)$$ 2898.bm 6 no $$1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2898}(53,\cdot)$$ 2898.cv 66 no $$1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{2898}(55,\cdot)$$ 2898.bt 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{2898}(59,\cdot)$$ 2898.cb 66 no $$1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{2898}(61,\cdot)$$ 2898.cc 66 no $$1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{2898}(65,\cdot)$$ 2898.ca 66 no $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$
$$\chi_{2898}(67,\cdot)$$ 2898.da 66 no $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$
$$\chi_{2898}(71,\cdot)$$ 2898.bu 22 no $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{2898}(73,\cdot)$$ 2898.cn 66 no $$-1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{2898}(79,\cdot)$$ 2898.da 66 no $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$
$$\chi_{2898}(83,\cdot)$$ 2898.cl 66 no $$-1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{2898}(85,\cdot)$$ 2898.by 33 no $$1$$ $$1$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{2898}(89,\cdot)$$ 2898.co 66 no $$-1$$ $$1$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{2898}(95,\cdot)$$ 2898.db 66 no $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$
$$\chi_{2898}(97,\cdot)$$ 2898.cp 66 no $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{25}{66}\right)$$
$$\chi_{2898}(101,\cdot)$$ 2898.cr 66 no $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{2898}(103,\cdot)$$ 2898.cs 66 no $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$
$$\chi_{2898}(107,\cdot)$$ 2898.cv 66 no $$1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{2898}(109,\cdot)$$ 2898.cd 66 no $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{2898}(113,\cdot)$$ 2898.cw 66 no $$1$$ $$1$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$