# Properties

 Modulus $3344$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{180}$$ Order $1440$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3344)

pari: g = idealstar(,3344,2)

## Character group

 sage: G.order()  pari: g.no Order = 1440 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{180}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3344}(2927,\cdot)$, $\chi_{3344}(837,\cdot)$, $\chi_{3344}(2433,\cdot)$, $\chi_{3344}(705,\cdot)$

## First 32 of 1440 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$13$$ $$15$$ $$17$$ $$21$$ $$23$$ $$25$$
$$\chi_{3344}(1,\cdot)$$ 3344.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3344}(3,\cdot)$$ 3344.fn 180 yes $$1$$ $$1$$ $$e\left(\frac{97}{180}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{90}\right)$$
$$\chi_{3344}(5,\cdot)$$ 3344.fi 180 yes $$1$$ $$1$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{13}{180}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{107}{180}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{13}{90}\right)$$
$$\chi_{3344}(7,\cdot)$$ 3344.dt 30 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{3344}(9,\cdot)$$ 3344.fc 90 no $$1$$ $$1$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{45}\right)$$
$$\chi_{3344}(13,\cdot)$$ 3344.fl 180 yes $$1$$ $$1$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{107}{180}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{17}{90}\right)$$
$$\chi_{3344}(15,\cdot)$$ 3344.ey 90 no $$1$$ $$1$$ $$e\left(\frac{2}{45}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{45}\right)$$
$$\chi_{3344}(17,\cdot)$$ 3344.ex 90 no $$-1$$ $$1$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{59}{90}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{44}{45}\right)$$
$$\chi_{3344}(21,\cdot)$$ 3344.ec 36 yes $$1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{3344}(23,\cdot)$$ 3344.cx 18 no $$-1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{3344}(25,\cdot)$$ 3344.fc 90 no $$1$$ $$1$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{45}\right)$$
$$\chi_{3344}(27,\cdot)$$ 3344.em 60 yes $$1$$ $$1$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{3344}(29,\cdot)$$ 3344.fl 180 yes $$1$$ $$1$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{121}{180}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{67}{90}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{29}{90}\right)$$
$$\chi_{3344}(31,\cdot)$$ 3344.dz 30 no $$1$$ $$1$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{3344}(35,\cdot)$$ 3344.fg 180 yes $$1$$ $$1$$ $$e\left(\frac{79}{180}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{79}{90}\right)$$ $$e\left(\frac{83}{180}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{37}{90}\right)$$
$$\chi_{3344}(37,\cdot)$$ 3344.dj 20 yes $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{3344}(39,\cdot)$$ 3344.bu 10 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{3344}(41,\cdot)$$ 3344.ev 90 no $$1$$ $$1$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{23}{45}\right)$$
$$\chi_{3344}(43,\cdot)$$ 3344.eh 36 yes $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{3344}(45,\cdot)$$ 3344.cf 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3344}(47,\cdot)$$ 3344.er 90 no $$-1$$ $$1$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{28}{45}\right)$$
$$\chi_{3344}(49,\cdot)$$ 3344.cn 15 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{3344}(51,\cdot)$$ 3344.fj 180 yes $$-1$$ $$1$$ $$e\left(\frac{173}{180}\right)$$ $$e\left(\frac{179}{180}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{61}{180}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{89}{90}\right)$$
$$\chi_{3344}(53,\cdot)$$ 3344.fh 180 yes $$-1$$ $$1$$ $$e\left(\frac{89}{180}\right)$$ $$e\left(\frac{77}{180}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{73}{180}\right)$$ $$e\left(\frac{83}{90}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{77}{90}\right)$$
$$\chi_{3344}(59,\cdot)$$ 3344.fn 180 yes $$1$$ $$1$$ $$e\left(\frac{103}{180}\right)$$ $$e\left(\frac{169}{180}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{79}{90}\right)$$
$$\chi_{3344}(61,\cdot)$$ 3344.fm 180 yes $$-1$$ $$1$$ $$e\left(\frac{161}{180}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{71}{90}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{23}{90}\right)$$
$$\chi_{3344}(63,\cdot)$$ 3344.ez 90 no $$1$$ $$1$$ $$e\left(\frac{1}{90}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{59}{90}\right)$$ $$e\left(\frac{43}{90}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{45}\right)$$
$$\chi_{3344}(65,\cdot)$$ 3344.bi 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3344}(67,\cdot)$$ 3344.ea 36 no $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{3344}(69,\cdot)$$ 3344.eo 60 yes $$-1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{3344}(71,\cdot)$$ 3344.et 90 no $$1$$ $$1$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{29}{45}\right)$$
$$\chi_{3344}(73,\cdot)$$ 3344.eu 90 no $$-1$$ $$1$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{47}{90}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{32}{45}\right)$$