# Properties

 Modulus $3332$ Structure $$C_{2}\times C_{2}\times C_{336}$$ Order $1344$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3332)

pari: g = idealstar(,3332,2)

## Character group

 sage: G.order()  pari: g.no Order = 1344 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{336}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3332}(1667,\cdot)$, $\chi_{3332}(885,\cdot)$, $\chi_{3332}(785,\cdot)$

## First 32 of 1344 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$19$$ $$23$$ $$25$$ $$27$$
$$\chi_{3332}(1,\cdot)$$ 3332.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3332}(3,\cdot)$$ 3332.da 336 yes $$-1$$ $$1$$ $$e\left(\frac{197}{336}\right)$$ $$e\left(\frac{1}{336}\right)$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{115}{336}\right)$$ $$e\left(\frac{1}{168}\right)$$ $$e\left(\frac{85}{112}\right)$$
$$\chi_{3332}(5,\cdot)$$ 3332.db 336 no $$1$$ $$1$$ $$e\left(\frac{1}{336}\right)$$ $$e\left(\frac{197}{336}\right)$$ $$e\left(\frac{1}{168}\right)$$ $$e\left(\frac{271}{336}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{311}{336}\right)$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{1}{112}\right)$$
$$\chi_{3332}(9,\cdot)$$ 3332.cw 168 no $$1$$ $$1$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{1}{168}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{131}{168}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{115}{168}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{29}{56}\right)$$
$$\chi_{3332}(11,\cdot)$$ 3332.cy 336 yes $$1$$ $$1$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{271}{336}\right)$$ $$e\left(\frac{131}{168}\right)$$ $$e\left(\frac{221}{336}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{39}{56}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{85}{336}\right)$$ $$e\left(\frac{103}{168}\right)$$ $$e\left(\frac{75}{112}\right)$$
$$\chi_{3332}(13,\cdot)$$ 3332.bw 28 no $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$
$$\chi_{3332}(15,\cdot)$$ 3332.ck 56 yes $$-1$$ $$1$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{39}{56}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$-i$$ $$e\left(\frac{15}{56}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{43}{56}\right)$$
$$\chi_{3332}(19,\cdot)$$ 3332.bs 24 no $$1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{8}\right)$$
$$\chi_{3332}(23,\cdot)$$ 3332.cy 336 yes $$1$$ $$1$$ $$e\left(\frac{115}{336}\right)$$ $$e\left(\frac{311}{336}\right)$$ $$e\left(\frac{115}{168}\right)$$ $$e\left(\frac{85}{336}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{15}{56}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{317}{336}\right)$$ $$e\left(\frac{143}{168}\right)$$ $$e\left(\frac{3}{112}\right)$$
$$\chi_{3332}(25,\cdot)$$ 3332.cw 168 no $$1$$ $$1$$ $$e\left(\frac{1}{168}\right)$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{103}{168}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{143}{168}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{1}{56}\right)$$
$$\chi_{3332}(27,\cdot)$$ 3332.cr 112 yes $$-1$$ $$1$$ $$e\left(\frac{85}{112}\right)$$ $$e\left(\frac{1}{112}\right)$$ $$e\left(\frac{29}{56}\right)$$ $$e\left(\frac{75}{112}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{112}\right)$$ $$e\left(\frac{1}{56}\right)$$ $$e\left(\frac{31}{112}\right)$$
$$\chi_{3332}(29,\cdot)$$ 3332.cs 112 no $$-1$$ $$1$$ $$e\left(\frac{27}{112}\right)$$ $$e\left(\frac{55}{112}\right)$$ $$e\left(\frac{27}{56}\right)$$ $$e\left(\frac{93}{112}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{41}{56}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{53}{112}\right)$$ $$e\left(\frac{55}{56}\right)$$ $$e\left(\frac{81}{112}\right)$$
$$\chi_{3332}(31,\cdot)$$ 3332.ce 48 no $$-1$$ $$1$$ $$e\left(\frac{11}{48}\right)$$ $$e\left(\frac{31}{48}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{5}{48}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{11}{16}\right)$$
$$\chi_{3332}(33,\cdot)$$ 3332.cd 42 no $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{3332}(37,\cdot)$$ 3332.cz 336 no $$-1$$ $$1$$ $$e\left(\frac{277}{336}\right)$$ $$e\left(\frac{137}{336}\right)$$ $$e\left(\frac{109}{168}\right)$$ $$e\left(\frac{307}{336}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{56}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{299}{336}\right)$$ $$e\left(\frac{137}{168}\right)$$ $$e\left(\frac{53}{112}\right)$$
$$\chi_{3332}(39,\cdot)$$ 3332.cy 336 yes $$1$$ $$1$$ $$e\left(\frac{209}{336}\right)$$ $$e\left(\frac{13}{336}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{23}{336}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{319}{336}\right)$$ $$e\left(\frac{13}{168}\right)$$ $$e\left(\frac{97}{112}\right)$$
$$\chi_{3332}(41,\cdot)$$ 3332.cq 112 no $$1$$ $$1$$ $$e\left(\frac{5}{112}\right)$$ $$e\left(\frac{89}{112}\right)$$ $$e\left(\frac{5}{56}\right)$$ $$e\left(\frac{11}{112}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{47}{56}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{99}{112}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{15}{112}\right)$$
$$\chi_{3332}(43,\cdot)$$ 3332.ck 56 yes $$-1$$ $$1$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{56}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$i$$ $$e\left(\frac{45}{56}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{17}{56}\right)$$
$$\chi_{3332}(45,\cdot)$$ 3332.db 336 no $$1$$ $$1$$ $$e\left(\frac{59}{336}\right)$$ $$e\left(\frac{199}{336}\right)$$ $$e\left(\frac{59}{168}\right)$$ $$e\left(\frac{197}{336}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{205}{336}\right)$$ $$e\left(\frac{31}{168}\right)$$ $$e\left(\frac{59}{112}\right)$$
$$\chi_{3332}(47,\cdot)$$ 3332.co 84 yes $$1$$ $$1$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{3332}(53,\cdot)$$ 3332.cw 168 no $$1$$ $$1$$ $$e\left(\frac{19}{168}\right)$$ $$e\left(\frac{47}{168}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{109}{168}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{29}{168}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{19}{56}\right)$$
$$\chi_{3332}(55,\cdot)$$ 3332.bv 28 yes $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{3332}(57,\cdot)$$ 3332.cs 112 no $$-1$$ $$1$$ $$e\left(\frac{89}{112}\right)$$ $$e\left(\frac{61}{112}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{95}{112}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{56}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{71}{112}\right)$$ $$e\left(\frac{5}{56}\right)$$ $$e\left(\frac{43}{112}\right)$$
$$\chi_{3332}(59,\cdot)$$ 3332.cu 168 yes $$1$$ $$1$$ $$e\left(\frac{73}{168}\right)$$ $$e\left(\frac{17}{168}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{43}{168}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{107}{168}\right)$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{17}{56}\right)$$
$$\chi_{3332}(61,\cdot)$$ 3332.db 336 no $$1$$ $$1$$ $$e\left(\frac{151}{336}\right)$$ $$e\left(\frac{179}{336}\right)$$ $$e\left(\frac{151}{168}\right)$$ $$e\left(\frac{265}{336}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{55}{56}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{257}{336}\right)$$ $$e\left(\frac{11}{168}\right)$$ $$e\left(\frac{39}{112}\right)$$
$$\chi_{3332}(65,\cdot)$$ 3332.cz 336 no $$-1$$ $$1$$ $$e\left(\frac{13}{336}\right)$$ $$e\left(\frac{209}{336}\right)$$ $$e\left(\frac{13}{168}\right)$$ $$e\left(\frac{331}{336}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{37}{56}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{179}{336}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{13}{112}\right)$$
$$\chi_{3332}(67,\cdot)$$ 3332.o 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{3332}(69,\cdot)$$ 3332.bi 14 no $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$-1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$
$$\chi_{3332}(71,\cdot)$$ 3332.ct 112 yes $$1$$ $$1$$ $$e\left(\frac{15}{112}\right)$$ $$e\left(\frac{99}{112}\right)$$ $$e\left(\frac{15}{56}\right)$$ $$e\left(\frac{89}{112}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{56}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{17}{112}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{45}{112}\right)$$
$$\chi_{3332}(73,\cdot)$$ 3332.db 336 no $$1$$ $$1$$ $$e\left(\frac{65}{336}\right)$$ $$e\left(\frac{37}{336}\right)$$ $$e\left(\frac{65}{168}\right)$$ $$e\left(\frac{143}{336}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{17}{56}\right)$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{55}{336}\right)$$ $$e\left(\frac{37}{168}\right)$$ $$e\left(\frac{65}{112}\right)$$
$$\chi_{3332}(75,\cdot)$$ 3332.da 336 yes $$-1$$ $$1$$ $$e\left(\frac{199}{336}\right)$$ $$e\left(\frac{59}{336}\right)$$ $$e\left(\frac{31}{168}\right)$$ $$e\left(\frac{169}{336}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{43}{56}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{65}{336}\right)$$ $$e\left(\frac{59}{168}\right)$$ $$e\left(\frac{87}{112}\right)$$
$$\chi_{3332}(79,\cdot)$$ 3332.cg 48 no $$1$$ $$1$$ $$e\left(\frac{13}{48}\right)$$ $$e\left(\frac{41}{48}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{43}{48}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{35}{48}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{13}{16}\right)$$