Properties

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

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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 \(1\) \(1\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{2}{3}\right)\)
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