# Properties

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

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 $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$-1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$