# Properties

 Modulus $1352$ Structure $$C_{2}\times C_{2}\times C_{156}$$ Order $624$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1352)

pari: g = idealstar(,1352,2)

## Character group

 sage: G.order()  pari: g.no Order = 624 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{156}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1352}(1015,\cdot)$, $\chi_{1352}(677,\cdot)$, $\chi_{1352}(1185,\cdot)$

## First 32 of 624 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$15$$ $$17$$ $$19$$ $$21$$ $$23$$
$$\chi_{1352}(1,\cdot)$$ 1352.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1352}(3,\cdot)$$ 1352.br 78 yes $$-1$$ $$1$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1352}(5,\cdot)$$ 1352.bj 52 yes $$-1$$ $$1$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$i$$ $$e\left(\frac{43}{52}\right)$$ $$-1$$
$$\chi_{1352}(7,\cdot)$$ 1352.bs 156 no $$1$$ $$1$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1352}(9,\cdot)$$ 1352.bg 39 no $$1$$ $$1$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1352}(11,\cdot)$$ 1352.bu 156 yes $$1$$ $$1$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1352}(15,\cdot)$$ 1352.bs 156 no $$1$$ $$1$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1352}(17,\cdot)$$ 1352.bq 78 no $$1$$ $$1$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1352}(19,\cdot)$$ 1352.u 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1352}(21,\cdot)$$ 1352.bj 52 yes $$-1$$ $$1$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$-i$$ $$e\left(\frac{29}{52}\right)$$ $$-1$$
$$\chi_{1352}(23,\cdot)$$ 1352.q 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1352}(25,\cdot)$$ 1352.bb 26 no $$1$$ $$1$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$-1$$ $$e\left(\frac{17}{26}\right)$$ $$1$$
$$\chi_{1352}(27,\cdot)$$ 1352.ba 26 yes $$-1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$-1$$
$$\chi_{1352}(29,\cdot)$$ 1352.bn 78 yes $$1$$ $$1$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1352}(31,\cdot)$$ 1352.bk 52 no $$1$$ $$1$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{17}{26}\right)$$ $$i$$ $$e\left(\frac{5}{52}\right)$$ $$1$$
$$\chi_{1352}(33,\cdot)$$ 1352.bv 156 no $$-1$$ $$1$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{34}{39}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1352}(35,\cdot)$$ 1352.br 78 yes $$-1$$ $$1$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1352}(37,\cdot)$$ 1352.bt 156 yes $$-1$$ $$1$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{31}{156}\right)$$ $$e\left(\frac{115}{156}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1352}(41,\cdot)$$ 1352.bv 156 no $$-1$$ $$1$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{19}{156}\right)$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1352}(43,\cdot)$$ 1352.bp 78 yes $$-1$$ $$1$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1352}(45,\cdot)$$ 1352.bt 156 yes $$-1$$ $$1$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{43}{156}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{29}{156}\right)$$ $$e\left(\frac{17}{156}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1352}(47,\cdot)$$ 1352.bk 52 no $$1$$ $$1$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$-i$$ $$e\left(\frac{15}{52}\right)$$ $$1$$
$$\chi_{1352}(49,\cdot)$$ 1352.bq 78 no $$1$$ $$1$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1352}(51,\cdot)$$ 1352.z 26 yes $$-1$$ $$1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$-1$$ $$e\left(\frac{4}{13}\right)$$ $$-1$$
$$\chi_{1352}(53,\cdot)$$ 1352.bf 26 yes $$1$$ $$1$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$-1$$ $$e\left(\frac{5}{26}\right)$$ $$1$$
$$\chi_{1352}(55,\cdot)$$ 1352.bl 78 no $$-1$$ $$1$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1352}(57,\cdot)$$ 1352.bh 52 no $$-1$$ $$1$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$-i$$ $$e\left(\frac{45}{52}\right)$$ $$-1$$
$$\chi_{1352}(59,\cdot)$$ 1352.bu 156 yes $$1$$ $$1$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{17}{156}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1352}(61,\cdot)$$ 1352.bn 78 yes $$1$$ $$1$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1352}(63,\cdot)$$ 1352.bs 156 no $$1$$ $$1$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{25}{52}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1352}(67,\cdot)$$ 1352.bu 156 yes $$1$$ $$1$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{67}{156}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1352}(69,\cdot)$$ 1352.bm 78 yes $$1$$ $$1$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{2}{3}\right)$$