Properties

Modulus $3549$
Structure \(C_{156}\times C_{6}\times C_{2}\)
Order $1872$

Learn more

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3549)
 
pari: g = idealstar(,3549,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1872
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{156}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3549}(1184,\cdot)$, $\chi_{3549}(1522,\cdot)$, $\chi_{3549}(3382,\cdot)$

First 32 of 1872 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{3549}(1,\cdot)\) 3549.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3549}(2,\cdot)\) 3549.em 156 yes \(1\) \(1\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{35}{156}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{77}{156}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{89}{156}\right)\)
\(\chi_{3549}(4,\cdot)\) 3549.dw 78 no \(1\) \(1\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{78}\right)\)
\(\chi_{3549}(5,\cdot)\) 3549.eh 156 yes \(-1\) \(1\) \(e\left(\frac{35}{156}\right)\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{29}{156}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{121}{156}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{33}{52}\right)\)
\(\chi_{3549}(8,\cdot)\) 3549.cw 52 no \(1\) \(1\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{35}{52}\right)\) \(e\left(\frac{29}{52}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(i\) \(e\left(\frac{37}{52}\right)\)
\(\chi_{3549}(10,\cdot)\) 3549.dj 78 no \(-1\) \(1\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{41}{78}\right)\) \(1\) \(e\left(\frac{8}{39}\right)\)
\(\chi_{3549}(11,\cdot)\) 3549.el 156 yes \(1\) \(1\) \(e\left(\frac{77}{156}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{121}{156}\right)\) \(e\left(\frac{25}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(i\) \(e\left(\frac{119}{156}\right)\)
\(\chi_{3549}(16,\cdot)\) 3549.cq 39 no \(1\) \(1\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{23}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{39}\right)\)
\(\chi_{3549}(17,\cdot)\) 3549.cy 78 yes \(1\) \(1\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{41}{78}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{78}\right)\)
\(\chi_{3549}(19,\cdot)\) 3549.cg 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{3549}(20,\cdot)\) 3549.eg 156 yes \(-1\) \(1\) \(e\left(\frac{89}{156}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{119}{156}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{121}{156}\right)\)
\(\chi_{3549}(22,\cdot)\) 3549.k 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3549}(23,\cdot)\) 3549.bp 6 no \(-1\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3549}(25,\cdot)\) 3549.dg 78 no \(1\) \(1\) \(e\left(\frac{35}{78}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{26}\right)\)
\(\chi_{3549}(29,\cdot)\) 3549.dl 78 no \(-1\) \(1\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{78}\right)\)
\(\chi_{3549}(31,\cdot)\) 3549.ej 156 no \(1\) \(1\) \(e\left(\frac{73}{156}\right)\) \(e\left(\frac{73}{78}\right)\) \(e\left(\frac{7}{156}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{83}{156}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{51}{52}\right)\)
\(\chi_{3549}(32,\cdot)\) 3549.em 156 yes \(1\) \(1\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{19}{156}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{73}{156}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{133}{156}\right)\)
\(\chi_{3549}(34,\cdot)\) 3549.cu 52 no \(1\) \(1\) \(e\left(\frac{49}{52}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{51}{52}\right)\) \(e\left(\frac{43}{52}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(-i\) \(e\left(\frac{45}{52}\right)\)
\(\chi_{3549}(37,\cdot)\) 3549.en 156 no \(-1\) \(1\) \(e\left(\frac{33}{52}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{59}{156}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{5}{156}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{101}{156}\right)\)
\(\chi_{3549}(38,\cdot)\) 3549.dp 78 yes \(1\) \(1\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{26}\right)\)
\(\chi_{3549}(40,\cdot)\) 3549.do 78 no \(-1\) \(1\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{9}{26}\right)\)
\(\chi_{3549}(41,\cdot)\) 3549.eg 156 yes \(-1\) \(1\) \(e\left(\frac{7}{156}\right)\) \(e\left(\frac{7}{78}\right)\) \(e\left(\frac{47}{52}\right)\) \(e\left(\frac{7}{52}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{97}{156}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{155}{156}\right)\)
\(\chi_{3549}(43,\cdot)\) 3549.dm 78 no \(1\) \(1\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{7}{39}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{47}{78}\right)\)
\(\chi_{3549}(44,\cdot)\) 3549.ef 156 yes \(1\) \(1\) \(e\left(\frac{131}{156}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{35}{156}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{25}{156}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{47}{52}\right)\)
\(\chi_{3549}(46,\cdot)\) 3549.en 156 no \(-1\) \(1\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{139}{156}\right)\) \(e\left(\frac{27}{52}\right)\) \(e\left(\frac{5}{78}\right)\) \(e\left(\frac{25}{156}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{37}{156}\right)\)
\(\chi_{3549}(47,\cdot)\) 3549.eh 156 yes \(-1\) \(1\) \(e\left(\frac{89}{156}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{47}{156}\right)\) \(e\left(\frac{37}{52}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{67}{156}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{23}{52}\right)\)
\(\chi_{3549}(50,\cdot)\) 3549.ee 156 no \(1\) \(1\) \(e\left(\frac{97}{156}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{31}{52}\right)\) \(e\left(\frac{45}{52}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{7}{156}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{131}{156}\right)\)
\(\chi_{3549}(53,\cdot)\) 3549.df 78 yes \(-1\) \(1\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{26}\right)\)
\(\chi_{3549}(55,\cdot)\) 3549.du 78 no \(-1\) \(1\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{34}{39}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{78}\right)\)
\(\chi_{3549}(58,\cdot)\) 3549.ek 156 no \(-1\) \(1\) \(e\left(\frac{145}{156}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{5}{156}\right)\) \(e\left(\frac{41}{52}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{21}{52}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{55}{78}\right)\) \(-i\) \(e\left(\frac{139}{156}\right)\)
\(\chi_{3549}(59,\cdot)\) 3549.ep 156 yes \(-1\) \(1\) \(e\left(\frac{3}{52}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{55}{156}\right)\) \(e\left(\frac{9}{52}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{43}{156}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{73}{156}\right)\)
\(\chi_{3549}(61,\cdot)\) 3549.dq 78 no \(-1\) \(1\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{67}{78}\right)\) \(-1\) \(e\left(\frac{29}{78}\right)\)