# Properties

 Modulus $8281$ Structure $$C_{1092}\times C_{6}$$ Order $6552$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8281)

pari: g = idealstar(,8281,2)

## Character group

 sage: G.order()  pari: g.no Order = 6552 sage: H.invariants()  pari: g.cyc Structure = $$C_{1092}\times C_{6}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{8281}(1522,\cdot)$, $\chi_{8281}(3382,\cdot)$

## First 32 of 6552 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{8281}(1,\cdot)$$ 8281.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8281}(2,\cdot)$$ 8281.ej 1092 yes $$-1$$ $$1$$ $$e\left(\frac{37}{364}\right)$$ $$e\left(\frac{113}{273}\right)$$ $$e\left(\frac{37}{182}\right)$$ $$e\left(\frac{11}{1092}\right)$$ $$e\left(\frac{563}{1092}\right)$$ $$e\left(\frac{111}{364}\right)$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{61}{546}\right)$$ $$e\left(\frac{461}{1092}\right)$$ $$e\left(\frac{337}{546}\right)$$
$$\chi_{8281}(3,\cdot)$$ 8281.dy 546 yes $$-1$$ $$1$$ $$e\left(\frac{113}{273}\right)$$ $$e\left(\frac{107}{182}\right)$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{461}{546}\right)$$ $$e\left(\frac{1}{546}\right)$$ $$e\left(\frac{22}{91}\right)$$ $$e\left(\frac{16}{91}\right)$$ $$e\left(\frac{47}{182}\right)$$ $$e\left(\frac{75}{91}\right)$$ $$e\left(\frac{227}{546}\right)$$
$$\chi_{8281}(4,\cdot)$$ 8281.dw 546 yes $$1$$ $$1$$ $$e\left(\frac{37}{182}\right)$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{37}{91}\right)$$ $$e\left(\frac{11}{546}\right)$$ $$e\left(\frac{17}{546}\right)$$ $$e\left(\frac{111}{182}\right)$$ $$e\left(\frac{179}{273}\right)$$ $$e\left(\frac{61}{273}\right)$$ $$e\left(\frac{461}{546}\right)$$ $$e\left(\frac{64}{273}\right)$$
$$\chi_{8281}(5,\cdot)$$ 8281.en 1092 yes $$1$$ $$1$$ $$e\left(\frac{11}{1092}\right)$$ $$e\left(\frac{461}{546}\right)$$ $$e\left(\frac{11}{546}\right)$$ $$e\left(\frac{593}{1092}\right)$$ $$e\left(\frac{311}{364}\right)$$ $$e\left(\frac{11}{364}\right)$$ $$e\left(\frac{188}{273}\right)$$ $$e\left(\frac{151}{273}\right)$$ $$e\left(\frac{613}{1092}\right)$$ $$e\left(\frac{236}{273}\right)$$
$$\chi_{8281}(6,\cdot)$$ 8281.eo 1092 yes $$1$$ $$1$$ $$e\left(\frac{563}{1092}\right)$$ $$e\left(\frac{1}{546}\right)$$ $$e\left(\frac{17}{546}\right)$$ $$e\left(\frac{311}{364}\right)$$ $$e\left(\frac{565}{1092}\right)$$ $$e\left(\frac{199}{364}\right)$$ $$e\left(\frac{1}{273}\right)$$ $$e\left(\frac{101}{273}\right)$$ $$e\left(\frac{269}{1092}\right)$$ $$e\left(\frac{3}{91}\right)$$
$$\chi_{8281}(8,\cdot)$$ 8281.dv 364 yes $$-1$$ $$1$$ $$e\left(\frac{111}{364}\right)$$ $$e\left(\frac{22}{91}\right)$$ $$e\left(\frac{111}{182}\right)$$ $$e\left(\frac{11}{364}\right)$$ $$e\left(\frac{199}{364}\right)$$ $$e\left(\frac{333}{364}\right)$$ $$e\left(\frac{44}{91}\right)$$ $$e\left(\frac{61}{182}\right)$$ $$e\left(\frac{97}{364}\right)$$ $$e\left(\frac{155}{182}\right)$$
$$\chi_{8281}(9,\cdot)$$ 8281.ds 273 yes $$1$$ $$1$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{16}{91}\right)$$ $$e\left(\frac{179}{273}\right)$$ $$e\left(\frac{188}{273}\right)$$ $$e\left(\frac{1}{273}\right)$$ $$e\left(\frac{44}{91}\right)$$ $$e\left(\frac{32}{91}\right)$$ $$e\left(\frac{47}{91}\right)$$ $$e\left(\frac{59}{91}\right)$$ $$e\left(\frac{227}{273}\right)$$
$$\chi_{8281}(10,\cdot)$$ 8281.eb 546 yes $$-1$$ $$1$$ $$e\left(\frac{61}{546}\right)$$ $$e\left(\frac{47}{182}\right)$$ $$e\left(\frac{61}{273}\right)$$ $$e\left(\frac{151}{273}\right)$$ $$e\left(\frac{101}{273}\right)$$ $$e\left(\frac{61}{182}\right)$$ $$e\left(\frac{47}{91}\right)$$ $$e\left(\frac{121}{182}\right)$$ $$e\left(\frac{179}{182}\right)$$ $$e\left(\frac{263}{546}\right)$$
$$\chi_{8281}(11,\cdot)$$ 8281.ep 1092 yes $$-1$$ $$1$$ $$e\left(\frac{461}{1092}\right)$$ $$e\left(\frac{75}{91}\right)$$ $$e\left(\frac{461}{546}\right)$$ $$e\left(\frac{613}{1092}\right)$$ $$e\left(\frac{269}{1092}\right)$$ $$e\left(\frac{97}{364}\right)$$ $$e\left(\frac{59}{91}\right)$$ $$e\left(\frac{179}{182}\right)$$ $$e\left(\frac{37}{364}\right)$$ $$e\left(\frac{365}{546}\right)$$
$$\chi_{8281}(12,\cdot)$$ 8281.ee 546 yes $$-1$$ $$1$$ $$e\left(\frac{337}{546}\right)$$ $$e\left(\frac{227}{546}\right)$$ $$e\left(\frac{64}{273}\right)$$ $$e\left(\frac{236}{273}\right)$$ $$e\left(\frac{3}{91}\right)$$ $$e\left(\frac{155}{182}\right)$$ $$e\left(\frac{227}{273}\right)$$ $$e\left(\frac{263}{546}\right)$$ $$e\left(\frac{365}{546}\right)$$ $$e\left(\frac{355}{546}\right)$$
$$\chi_{8281}(15,\cdot)$$ 8281.ek 1092 yes $$-1$$ $$1$$ $$e\left(\frac{463}{1092}\right)$$ $$e\left(\frac{118}{273}\right)$$ $$e\left(\frac{463}{546}\right)$$ $$e\left(\frac{141}{364}\right)$$ $$e\left(\frac{935}{1092}\right)$$ $$e\left(\frac{99}{364}\right)$$ $$e\left(\frac{236}{273}\right)$$ $$e\left(\frac{443}{546}\right)$$ $$e\left(\frac{421}{1092}\right)$$ $$e\left(\frac{51}{182}\right)$$
$$\chi_{8281}(16,\cdot)$$ 8281.dt 273 yes $$1$$ $$1$$ $$e\left(\frac{37}{91}\right)$$ $$e\left(\frac{179}{273}\right)$$ $$e\left(\frac{74}{91}\right)$$ $$e\left(\frac{11}{273}\right)$$ $$e\left(\frac{17}{273}\right)$$ $$e\left(\frac{20}{91}\right)$$ $$e\left(\frac{85}{273}\right)$$ $$e\left(\frac{122}{273}\right)$$ $$e\left(\frac{188}{273}\right)$$ $$e\left(\frac{128}{273}\right)$$
$$\chi_{8281}(17,\cdot)$$ 8281.dx 546 yes $$-1$$ $$1$$ $$e\left(\frac{75}{182}\right)$$ $$e\left(\frac{353}{546}\right)$$ $$e\left(\frac{75}{91}\right)$$ $$e\left(\frac{187}{273}\right)$$ $$e\left(\frac{16}{273}\right)$$ $$e\left(\frac{43}{182}\right)$$ $$e\left(\frac{80}{273}\right)$$ $$e\left(\frac{53}{546}\right)$$ $$e\left(\frac{113}{546}\right)$$ $$e\left(\frac{257}{546}\right)$$
$$\chi_{8281}(18,\cdot)$$ 8281.dj 156 no $$-1$$ $$1$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{11}{156}\right)$$ $$e\left(\frac{35}{78}\right)$$
$$\chi_{8281}(19,\cdot)$$ 8281.x 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$1$$ $$1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{8281}(20,\cdot)$$ 8281.eo 1092 yes $$1$$ $$1$$ $$e\left(\frac{233}{1092}\right)$$ $$e\left(\frac{367}{546}\right)$$ $$e\left(\frac{233}{546}\right)$$ $$e\left(\frac{205}{364}\right)$$ $$e\left(\frac{967}{1092}\right)$$ $$e\left(\frac{233}{364}\right)$$ $$e\left(\frac{94}{273}\right)$$ $$e\left(\frac{212}{273}\right)$$ $$e\left(\frac{443}{1092}\right)$$ $$e\left(\frac{9}{91}\right)$$
$$\chi_{8281}(22,\cdot)$$ 8281.bl 21 no $$1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{8281}(23,\cdot)$$ 8281.ch 42 no $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$
$$\chi_{8281}(24,\cdot)$$ 8281.ei 1092 yes $$1$$ $$1$$ $$e\left(\frac{785}{1092}\right)$$ $$e\left(\frac{151}{182}\right)$$ $$e\left(\frac{239}{546}\right)$$ $$e\left(\frac{955}{1092}\right)$$ $$e\left(\frac{599}{1092}\right)$$ $$e\left(\frac{57}{364}\right)$$ $$e\left(\frac{60}{91}\right)$$ $$e\left(\frac{54}{91}\right)$$ $$e\left(\frac{33}{364}\right)$$ $$e\left(\frac{73}{273}\right)$$
$$\chi_{8281}(25,\cdot)$$ 8281.ed 546 yes $$1$$ $$1$$ $$e\left(\frac{11}{546}\right)$$ $$e\left(\frac{188}{273}\right)$$ $$e\left(\frac{11}{273}\right)$$ $$e\left(\frac{47}{546}\right)$$ $$e\left(\frac{129}{182}\right)$$ $$e\left(\frac{11}{182}\right)$$ $$e\left(\frac{103}{273}\right)$$ $$e\left(\frac{29}{273}\right)$$ $$e\left(\frac{67}{546}\right)$$ $$e\left(\frac{199}{273}\right)$$
$$\chi_{8281}(27,\cdot)$$ 8281.dp 182 yes $$-1$$ $$1$$ $$e\left(\frac{22}{91}\right)$$ $$e\left(\frac{139}{182}\right)$$ $$e\left(\frac{44}{91}\right)$$ $$e\left(\frac{97}{182}\right)$$ $$e\left(\frac{1}{182}\right)$$ $$e\left(\frac{66}{91}\right)$$ $$e\left(\frac{48}{91}\right)$$ $$e\left(\frac{141}{182}\right)$$ $$e\left(\frac{43}{91}\right)$$ $$e\left(\frac{45}{182}\right)$$
$$\chi_{8281}(29,\cdot)$$ 8281.dr 273 yes $$1$$ $$1$$ $$e\left(\frac{109}{273}\right)$$ $$e\left(\frac{61}{273}\right)$$ $$e\left(\frac{218}{273}\right)$$ $$e\left(\frac{67}{91}\right)$$ $$e\left(\frac{170}{273}\right)$$ $$e\left(\frac{18}{91}\right)$$ $$e\left(\frac{122}{273}\right)$$ $$e\left(\frac{37}{273}\right)$$ $$e\left(\frac{151}{273}\right)$$ $$e\left(\frac{2}{91}\right)$$
$$\chi_{8281}(30,\cdot)$$ 8281.cl 78 no $$1$$ $$1$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{35}{39}\right)$$
$$\chi_{8281}(31,\cdot)$$ 8281.dh 156 no $$1$$ $$1$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{31}{39}\right)$$
$$\chi_{8281}(32,\cdot)$$ 8281.ej 1092 yes $$-1$$ $$1$$ $$e\left(\frac{185}{364}\right)$$ $$e\left(\frac{19}{273}\right)$$ $$e\left(\frac{3}{182}\right)$$ $$e\left(\frac{55}{1092}\right)$$ $$e\left(\frac{631}{1092}\right)$$ $$e\left(\frac{191}{364}\right)$$ $$e\left(\frac{38}{273}\right)$$ $$e\left(\frac{305}{546}\right)$$ $$e\left(\frac{121}{1092}\right)$$ $$e\left(\frac{47}{546}\right)$$
$$\chi_{8281}(33,\cdot)$$ 8281.ei 1092 yes $$1$$ $$1$$ $$e\left(\frac{913}{1092}\right)$$ $$e\left(\frac{75}{182}\right)$$ $$e\left(\frac{367}{546}\right)$$ $$e\left(\frac{443}{1092}\right)$$ $$e\left(\frac{271}{1092}\right)$$ $$e\left(\frac{185}{364}\right)$$ $$e\left(\frac{75}{91}\right)$$ $$e\left(\frac{22}{91}\right)$$ $$e\left(\frac{337}{364}\right)$$ $$e\left(\frac{23}{273}\right)$$
$$\chi_{8281}(34,\cdot)$$ 8281.du 364 yes $$1$$ $$1$$ $$e\left(\frac{187}{364}\right)$$ $$e\left(\frac{11}{182}\right)$$ $$e\left(\frac{5}{182}\right)$$ $$e\left(\frac{253}{364}\right)$$ $$e\left(\frac{209}{364}\right)$$ $$e\left(\frac{197}{364}\right)$$ $$e\left(\frac{11}{91}\right)$$ $$e\left(\frac{19}{91}\right)$$ $$e\left(\frac{229}{364}\right)$$ $$e\left(\frac{8}{91}\right)$$
$$\chi_{8281}(36,\cdot)$$ 8281.ec 546 yes $$1$$ $$1$$ $$e\left(\frac{17}{546}\right)$$ $$e\left(\frac{1}{273}\right)$$ $$e\left(\frac{17}{273}\right)$$ $$e\left(\frac{129}{182}\right)$$ $$e\left(\frac{19}{546}\right)$$ $$e\left(\frac{17}{182}\right)$$ $$e\left(\frac{2}{273}\right)$$ $$e\left(\frac{202}{273}\right)$$ $$e\left(\frac{269}{546}\right)$$ $$e\left(\frac{6}{91}\right)$$
$$\chi_{8281}(37,\cdot)$$ 8281.ej 1092 yes $$-1$$ $$1$$ $$e\left(\frac{283}{364}\right)$$ $$e\left(\frac{215}{273}\right)$$ $$e\left(\frac{101}{182}\right)$$ $$e\left(\frac{881}{1092}\right)$$ $$e\left(\frac{617}{1092}\right)$$ $$e\left(\frac{121}{364}\right)$$ $$e\left(\frac{157}{273}\right)$$ $$e\left(\frac{319}{546}\right)$$ $$e\left(\frac{191}{1092}\right)$$ $$e\left(\frac{187}{546}\right)$$
$$\chi_{8281}(38,\cdot)$$ 8281.ee 546 yes $$-1$$ $$1$$ $$e\left(\frac{101}{546}\right)$$ $$e\left(\frac{499}{546}\right)$$ $$e\left(\frac{101}{273}\right)$$ $$e\left(\frac{253}{273}\right)$$ $$e\left(\frac{9}{91}\right)$$ $$e\left(\frac{101}{182}\right)$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{61}{546}\right)$$ $$e\left(\frac{367}{546}\right)$$ $$e\left(\frac{155}{546}\right)$$
$$\chi_{8281}(40,\cdot)$$ 8281.ea 546 yes $$-1$$ $$1$$ $$e\left(\frac{86}{273}\right)$$ $$e\left(\frac{47}{546}\right)$$ $$e\left(\frac{172}{273}\right)$$ $$e\left(\frac{313}{546}\right)$$ $$e\left(\frac{73}{182}\right)$$ $$e\left(\frac{86}{91}\right)$$ $$e\left(\frac{47}{273}\right)$$ $$e\left(\frac{485}{546}\right)$$ $$e\left(\frac{226}{273}\right)$$ $$e\left(\frac{391}{546}\right)$$