# Properties

 Modulus $2863$ Structure $$C_{6}\times C_{408}$$ Order $2448$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2863)

pari: g = idealstar(,2863,2)

## Character group

 sage: G.order()  pari: g.no Order = 2448 sage: H.invariants()  pari: g.cyc Structure = $$C_{6}\times C_{408}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2863}(1228,\cdot)$, $\chi_{2863}(2066,\cdot)$

## First 32 of 2448 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{2863}(1,\cdot)$$ 2863.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2863}(2,\cdot)$$ 2863.ct 204 yes $$1$$ $$1$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{25}{51}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{65}{102}\right)$$ $$e\left(\frac{65}{204}\right)$$ $$e\left(\frac{31}{34}\right)$$
$$\chi_{2863}(3,\cdot)$$ 2863.cs 204 yes $$-1$$ $$1$$ $$e\left(\frac{21}{34}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{91}{102}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{26}{51}\right)$$ $$e\left(\frac{103}{204}\right)$$ $$e\left(\frac{9}{17}\right)$$
$$\chi_{2863}(4,\cdot)$$ 2863.by 102 yes $$1$$ $$1$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{50}{51}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{14}{51}\right)$$ $$e\left(\frac{65}{102}\right)$$ $$e\left(\frac{14}{17}\right)$$
$$\chi_{2863}(5,\cdot)$$ 2863.cc 102 yes $$-1$$ $$1$$ $$e\left(\frac{25}{51}\right)$$ $$e\left(\frac{91}{102}\right)$$ $$e\left(\frac{50}{51}\right)$$ $$e\left(\frac{59}{102}\right)$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{40}{51}\right)$$ $$e\left(\frac{7}{102}\right)$$ $$e\left(\frac{23}{51}\right)$$ $$e\left(\frac{89}{102}\right)$$
$$\chi_{2863}(6,\cdot)$$ 2863.bq 34 yes $$-1$$ $$1$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{15}{34}\right)$$
$$\chi_{2863}(8,\cdot)$$ 2863.bx 68 no $$1$$ $$1$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{65}{68}\right)$$ $$e\left(\frac{25}{34}\right)$$
$$\chi_{2863}(9,\cdot)$$ 2863.by 102 yes $$1$$ $$1$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{40}{51}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{1}{51}\right)$$ $$e\left(\frac{1}{102}\right)$$ $$e\left(\frac{1}{17}\right)$$
$$\chi_{2863}(10,\cdot)$$ 2863.cp 204 yes $$-1$$ $$1$$ $$e\left(\frac{65}{102}\right)$$ $$e\left(\frac{26}{51}\right)$$ $$e\left(\frac{14}{51}\right)$$ $$e\left(\frac{7}{102}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{1}{51}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{157}{204}\right)$$ $$e\left(\frac{40}{51}\right)$$
$$\chi_{2863}(11,\cdot)$$ 2863.cy 408 yes $$-1$$ $$1$$ $$e\left(\frac{65}{204}\right)$$ $$e\left(\frac{103}{204}\right)$$ $$e\left(\frac{65}{102}\right)$$ $$e\left(\frac{23}{51}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{65}{68}\right)$$ $$e\left(\frac{1}{102}\right)$$ $$e\left(\frac{157}{204}\right)$$ $$e\left(\frac{89}{408}\right)$$ $$e\left(\frac{29}{204}\right)$$
$$\chi_{2863}(12,\cdot)$$ 2863.cs 204 yes $$-1$$ $$1$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{89}{102}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{40}{51}\right)$$ $$e\left(\frac{29}{204}\right)$$ $$e\left(\frac{6}{17}\right)$$
$$\chi_{2863}(13,\cdot)$$ 2863.cl 136 yes $$1$$ $$1$$ $$e\left(\frac{35}{68}\right)$$ $$e\left(\frac{11}{68}\right)$$ $$e\left(\frac{1}{34}\right)$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{37}{68}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{61}{68}\right)$$ $$e\left(\frac{95}{136}\right)$$ $$e\left(\frac{13}{68}\right)$$
$$\chi_{2863}(15,\cdot)$$ 2863.cm 204 no $$1$$ $$1$$ $$e\left(\frac{11}{102}\right)$$ $$e\left(\frac{19}{102}\right)$$ $$e\left(\frac{11}{51}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{19}{51}\right)$$ $$e\left(\frac{59}{102}\right)$$ $$e\left(\frac{65}{68}\right)$$ $$e\left(\frac{41}{102}\right)$$
$$\chi_{2863}(16,\cdot)$$ 2863.bs 51 yes $$1$$ $$1$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{49}{51}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{28}{51}\right)$$ $$e\left(\frac{14}{51}\right)$$ $$e\left(\frac{11}{17}\right)$$
$$\chi_{2863}(17,\cdot)$$ 2863.ce 102 yes $$-1$$ $$1$$ $$e\left(\frac{31}{51}\right)$$ $$e\left(\frac{19}{102}\right)$$ $$e\left(\frac{11}{51}\right)$$ $$e\left(\frac{31}{102}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{19}{51}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{19}{51}\right)$$ $$e\left(\frac{41}{102}\right)$$
$$\chi_{2863}(18,\cdot)$$ 2863.ct 204 yes $$1$$ $$1$$ $$e\left(\frac{13}{34}\right)$$ $$e\left(\frac{7}{34}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{14}{51}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{7}{17}\right)$$ $$e\left(\frac{67}{102}\right)$$ $$e\left(\frac{67}{204}\right)$$ $$e\left(\frac{33}{34}\right)$$
$$\chi_{2863}(19,\cdot)$$ 2863.cv 408 yes $$1$$ $$1$$ $$e\left(\frac{157}{204}\right)$$ $$e\left(\frac{197}{204}\right)$$ $$e\left(\frac{55}{102}\right)$$ $$e\left(\frac{35}{102}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{21}{68}\right)$$ $$e\left(\frac{95}{102}\right)$$ $$e\left(\frac{23}{204}\right)$$ $$e\left(\frac{193}{408}\right)$$ $$e\left(\frac{103}{204}\right)$$
$$\chi_{2863}(20,\cdot)$$ 2863.cg 102 yes $$-1$$ $$1$$ $$e\left(\frac{40}{51}\right)$$ $$e\left(\frac{13}{102}\right)$$ $$e\left(\frac{29}{51}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{31}{34}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{13}{51}\right)$$ $$e\left(\frac{35}{102}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{71}{102}\right)$$
$$\chi_{2863}(22,\cdot)$$ 2863.cu 408 no $$-1$$ $$1$$ $$e\left(\frac{95}{204}\right)$$ $$e\left(\frac{25}{204}\right)$$ $$e\left(\frac{95}{102}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{27}{68}\right)$$ $$e\left(\frac{25}{102}\right)$$ $$e\left(\frac{83}{204}\right)$$ $$e\left(\frac{73}{136}\right)$$ $$e\left(\frac{11}{204}\right)$$
$$\chi_{2863}(23,\cdot)$$ 2863.ct 204 yes $$1$$ $$1$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{7}{51}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{59}{102}\right)$$ $$e\left(\frac{161}{204}\right)$$ $$e\left(\frac{25}{34}\right)$$
$$\chi_{2863}(24,\cdot)$$ 2863.bz 102 yes $$-1$$ $$1$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{5}{34}\right)$$ $$e\left(\frac{2}{17}\right)$$ $$e\left(\frac{37}{102}\right)$$ $$e\left(\frac{7}{34}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{43}{102}\right)$$ $$e\left(\frac{47}{102}\right)$$ $$e\left(\frac{9}{34}\right)$$
$$\chi_{2863}(25,\cdot)$$ 2863.bv 51 yes $$1$$ $$1$$ $$e\left(\frac{50}{51}\right)$$ $$e\left(\frac{40}{51}\right)$$ $$e\left(\frac{49}{51}\right)$$ $$e\left(\frac{8}{51}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{29}{51}\right)$$ $$e\left(\frac{7}{51}\right)$$ $$e\left(\frac{46}{51}\right)$$ $$e\left(\frac{38}{51}\right)$$
$$\chi_{2863}(26,\cdot)$$ 2863.da 408 yes $$1$$ $$1$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{53}{68}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{89}{102}\right)$$ $$e\left(\frac{15}{34}\right)$$ $$e\left(\frac{67}{68}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{109}{204}\right)$$ $$e\left(\frac{7}{408}\right)$$ $$e\left(\frac{7}{68}\right)$$
$$\chi_{2863}(27,\cdot)$$ 2863.bw 68 yes $$-1$$ $$1$$ $$e\left(\frac{29}{34}\right)$$ $$e\left(\frac{15}{17}\right)$$ $$e\left(\frac{12}{17}\right)$$ $$e\left(\frac{23}{34}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{35}{68}\right)$$ $$e\left(\frac{10}{17}\right)$$
$$\chi_{2863}(29,\cdot)$$ 2863.cu 408 no $$-1$$ $$1$$ $$e\left(\frac{181}{204}\right)$$ $$e\left(\frac{155}{204}\right)$$ $$e\left(\frac{79}{102}\right)$$ $$e\left(\frac{4}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{45}{68}\right)$$ $$e\left(\frac{53}{102}\right)$$ $$e\left(\frac{25}{204}\right)$$ $$e\left(\frac{99}{136}\right)$$ $$e\left(\frac{109}{204}\right)$$
$$\chi_{2863}(30,\cdot)$$ 2863.bv 51 yes $$1$$ $$1$$ $$e\left(\frac{13}{51}\right)$$ $$e\left(\frac{41}{51}\right)$$ $$e\left(\frac{26}{51}\right)$$ $$e\left(\frac{49}{51}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{31}{51}\right)$$ $$e\left(\frac{11}{51}\right)$$ $$e\left(\frac{14}{51}\right)$$ $$e\left(\frac{16}{51}\right)$$
$$\chi_{2863}(31,\cdot)$$ 2863.bn 24 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{2863}(32,\cdot)$$ 2863.ct 204 yes $$1$$ $$1$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{3}{34}\right)$$ $$e\left(\frac{8}{17}\right)$$ $$e\left(\frac{23}{51}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{7}{34}\right)$$ $$e\left(\frac{3}{17}\right)$$ $$e\left(\frac{19}{102}\right)$$ $$e\left(\frac{121}{204}\right)$$ $$e\left(\frac{19}{34}\right)$$
$$\chi_{2863}(33,\cdot)$$ 2863.cw 408 yes $$1$$ $$1$$ $$e\left(\frac{191}{204}\right)$$ $$e\left(\frac{163}{204}\right)$$ $$e\left(\frac{89}{102}\right)$$ $$e\left(\frac{35}{102}\right)$$ $$e\left(\frac{25}{34}\right)$$ $$e\left(\frac{55}{68}\right)$$ $$e\left(\frac{61}{102}\right)$$ $$e\left(\frac{19}{68}\right)$$ $$e\left(\frac{295}{408}\right)$$ $$e\left(\frac{137}{204}\right)$$
$$\chi_{2863}(34,\cdot)$$ 2863.cr 204 yes $$-1$$ $$1$$ $$e\left(\frac{77}{102}\right)$$ $$e\left(\frac{41}{51}\right)$$ $$e\left(\frac{26}{51}\right)$$ $$e\left(\frac{27}{34}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{9}{34}\right)$$ $$e\left(\frac{31}{51}\right)$$ $$e\left(\frac{28}{51}\right)$$ $$e\left(\frac{47}{68}\right)$$ $$e\left(\frac{16}{51}\right)$$
$$\chi_{2863}(36,\cdot)$$ 2863.bg 17 no $$1$$ $$1$$ $$e\left(\frac{9}{17}\right)$$ $$e\left(\frac{14}{17}\right)$$ $$e\left(\frac{1}{17}\right)$$ $$e\left(\frac{13}{17}\right)$$ $$e\left(\frac{6}{17}\right)$$ $$e\left(\frac{10}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{5}{17}\right)$$ $$e\left(\frac{11}{17}\right)$$ $$e\left(\frac{15}{17}\right)$$
$$\chi_{2863}(37,\cdot)$$ 2863.db 408 yes $$-1$$ $$1$$ $$e\left(\frac{11}{68}\right)$$ $$e\left(\frac{53}{68}\right)$$ $$e\left(\frac{11}{34}\right)$$ $$e\left(\frac{19}{51}\right)$$ $$e\left(\frac{16}{17}\right)$$ $$e\left(\frac{33}{68}\right)$$ $$e\left(\frac{19}{34}\right)$$ $$e\left(\frac{109}{204}\right)$$ $$e\left(\frac{109}{408}\right)$$ $$e\left(\frac{7}{68}\right)$$