Properties

Modulus $3724$
Structure \(C_{126}\times C_{6}\times C_{2}\)
Order $1512$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3724)
 
pari: g = idealstar(,3724,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1512
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{126}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3724}(1863,\cdot)$, $\chi_{3724}(3041,\cdot)$, $\chi_{3724}(3137,\cdot)$

First 32 of 1512 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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(23\) \(25\) \(27\)
\(\chi_{3724}(1,\cdot)\) 3724.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3724}(3,\cdot)\) 3724.eg 126 yes \(-1\) \(1\) \(e\left(\frac{115}{126}\right)\) \(e\left(\frac{31}{126}\right)\) \(e\left(\frac{52}{63}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{10}{63}\right)\) \(e\left(\frac{103}{126}\right)\) \(e\left(\frac{107}{126}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{31}{42}\right)\)
\(\chi_{3724}(5,\cdot)\) 3724.ee 126 no \(-1\) \(1\) \(e\left(\frac{31}{126}\right)\) \(e\left(\frac{31}{126}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{19}{126}\right)\) \(e\left(\frac{1}{63}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{31}{42}\right)\)
\(\chi_{3724}(9,\cdot)\) 3724.ec 63 no \(1\) \(1\) \(e\left(\frac{52}{63}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{41}{63}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{50}{63}\right)\) \(e\left(\frac{20}{63}\right)\) \(e\left(\frac{40}{63}\right)\) \(e\left(\frac{44}{63}\right)\) \(e\left(\frac{62}{63}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{3724}(11,\cdot)\) 3724.db 42 yes \(-1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\)
\(\chi_{3724}(13,\cdot)\) 3724.es 126 no \(1\) \(1\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{50}{63}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{20}{63}\right)\) \(e\left(\frac{79}{126}\right)\) \(e\left(\frac{53}{126}\right)\) \(e\left(\frac{26}{63}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{3724}(15,\cdot)\) 3724.el 126 yes \(1\) \(1\) \(e\left(\frac{10}{63}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{20}{63}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{79}{126}\right)\) \(e\left(\frac{41}{63}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{109}{126}\right)\) \(e\left(\frac{62}{63}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{3724}(17,\cdot)\) 3724.ep 126 no \(-1\) \(1\) \(e\left(\frac{103}{126}\right)\) \(e\left(\frac{19}{126}\right)\) \(e\left(\frac{40}{63}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{53}{126}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{55}{126}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{19}{63}\right)\) \(e\left(\frac{19}{42}\right)\)
\(\chi_{3724}(23,\cdot)\) 3724.eh 126 yes \(-1\) \(1\) \(e\left(\frac{107}{126}\right)\) \(e\left(\frac{1}{63}\right)\) \(e\left(\frac{44}{63}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{26}{63}\right)\) \(e\left(\frac{109}{126}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{13}{126}\right)\) \(e\left(\frac{2}{63}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{3724}(25,\cdot)\) 3724.ea 63 no \(1\) \(1\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{62}{63}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{62}{63}\right)\) \(e\left(\frac{19}{63}\right)\) \(e\left(\frac{2}{63}\right)\) \(e\left(\frac{62}{63}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{3724}(27,\cdot)\) 3724.dg 42 yes \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{3724}(29,\cdot)\) 3724.er 126 no \(-1\) \(1\) \(e\left(\frac{89}{126}\right)\) \(e\left(\frac{34}{63}\right)\) \(e\left(\frac{26}{63}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{109}{126}\right)\) \(e\left(\frac{31}{126}\right)\) \(e\left(\frac{10}{63}\right)\) \(e\left(\frac{11}{63}\right)\) \(e\left(\frac{5}{63}\right)\) \(e\left(\frac{5}{42}\right)\)
\(\chi_{3724}(31,\cdot)\) 3724.p 6 no \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)
\(\chi_{3724}(33,\cdot)\) 3724.ef 126 no \(1\) \(1\) \(e\left(\frac{2}{63}\right)\) \(e\left(\frac{67}{126}\right)\) \(e\left(\frac{4}{63}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{10}{63}\right)\) \(e\left(\frac{71}{126}\right)\) \(e\left(\frac{37}{126}\right)\) \(e\left(\frac{55}{63}\right)\) \(e\left(\frac{4}{63}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{3724}(37,\cdot)\) 3724.dj 42 no \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{3724}(39,\cdot)\) 3724.di 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{3724}(41,\cdot)\) 3724.es 126 no \(1\) \(1\) \(e\left(\frac{47}{63}\right)\) \(e\left(\frac{115}{126}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{83}{126}\right)\) \(e\left(\frac{19}{126}\right)\) \(e\left(\frac{1}{63}\right)\) \(e\left(\frac{52}{63}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{3724}(43,\cdot)\) 3724.ei 126 yes \(-1\) \(1\) \(e\left(\frac{25}{126}\right)\) \(e\left(\frac{23}{63}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{10}{63}\right)\) \(e\left(\frac{71}{126}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{89}{126}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{3724}(45,\cdot)\) 3724.dx 42 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{3724}(47,\cdot)\) 3724.en 126 yes \(1\) \(1\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{71}{126}\right)\) \(e\left(\frac{50}{63}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{19}{126}\right)\) \(e\left(\frac{121}{126}\right)\) \(e\left(\frac{53}{126}\right)\) \(e\left(\frac{115}{126}\right)\) \(e\left(\frac{8}{63}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{3724}(51,\cdot)\) 3724.em 126 yes \(1\) \(1\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{103}{126}\right)\) \(e\left(\frac{8}{63}\right)\) \(e\left(\frac{16}{63}\right)\) \(e\left(\frac{73}{126}\right)\) \(e\left(\frac{50}{63}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{3724}(53,\cdot)\) 3724.ed 126 no \(-1\) \(1\) \(e\left(\frac{23}{126}\right)\) \(e\left(\frac{43}{63}\right)\) \(e\left(\frac{23}{63}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{115}{126}\right)\) \(e\left(\frac{109}{126}\right)\) \(e\left(\frac{4}{63}\right)\) \(e\left(\frac{17}{63}\right)\) \(e\left(\frac{23}{63}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{3724}(55,\cdot)\) 3724.ek 126 yes \(1\) \(1\) \(e\left(\frac{23}{63}\right)\) \(e\left(\frac{67}{126}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{125}{126}\right)\) \(e\left(\frac{113}{126}\right)\) \(e\left(\frac{79}{126}\right)\) \(e\left(\frac{5}{126}\right)\) \(e\left(\frac{4}{63}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{3724}(59,\cdot)\) 3724.eg 126 yes \(-1\) \(1\) \(e\left(\frac{67}{126}\right)\) \(e\left(\frac{109}{126}\right)\) \(e\left(\frac{4}{63}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{37}{126}\right)\) \(e\left(\frac{47}{126}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{3724}(61,\cdot)\) 3724.ep 126 no \(-1\) \(1\) \(e\left(\frac{89}{126}\right)\) \(e\left(\frac{47}{126}\right)\) \(e\left(\frac{26}{63}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{25}{126}\right)\) \(e\left(\frac{5}{63}\right)\) \(e\left(\frac{83}{126}\right)\) \(e\left(\frac{11}{63}\right)\) \(e\left(\frac{47}{63}\right)\) \(e\left(\frac{5}{42}\right)\)
\(\chi_{3724}(65,\cdot)\) 3724.dz 42 no \(-1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{3724}(67,\cdot)\) 3724.ca 18 no \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(-1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3724}(69,\cdot)\) 3724.do 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{3724}(71,\cdot)\) 3724.el 126 yes \(1\) \(1\) \(e\left(\frac{8}{63}\right)\) \(e\left(\frac{50}{63}\right)\) \(e\left(\frac{16}{63}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{101}{126}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{11}{63}\right)\) \(e\left(\frac{125}{126}\right)\) \(e\left(\frac{37}{63}\right)\) \(e\left(\frac{8}{21}\right)\)
\(\chi_{3724}(73,\cdot)\) 3724.ep 126 no \(-1\) \(1\) \(e\left(\frac{97}{126}\right)\) \(e\left(\frac{13}{126}\right)\) \(e\left(\frac{34}{63}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{23}{126}\right)\) \(e\left(\frac{55}{63}\right)\) \(e\left(\frac{31}{126}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{13}{63}\right)\) \(e\left(\frac{13}{42}\right)\)
\(\chi_{3724}(75,\cdot)\) 3724.de 42 yes \(-1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{3724}(79,\cdot)\) 3724.ca 18 no \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(-1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\)