# Properties

 Modulus $3024$ Structure $$C_{36}\times C_{6}\times C_{2}\times C_{2}$$ Order $864$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3024)

pari: g = idealstar(,3024,2)

## Character group

 sage: G.order()  pari: g.no Order = 864 sage: H.invariants()  pari: g.cyc Structure = $$C_{36}\times C_{6}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3024}(1135,\cdot)$, $\chi_{3024}(757,\cdot)$, $\chi_{3024}(785,\cdot)$, $\chi_{3024}(2593,\cdot)$

## First 32 of 864 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$
$$\chi_{3024}(1,\cdot)$$ 3024.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3024}(5,\cdot)$$ 3024.hi 36 yes $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$1$$ $$i$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{3024}(11,\cdot)$$ 3024.gp 36 yes $$1$$ $$1$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3024}(13,\cdot)$$ 3024.hd 36 yes $$-1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{3024}(17,\cdot)$$ 3024.df 6 no $$1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3024}(19,\cdot)$$ 3024.en 12 no $$1$$ $$1$$ $$i$$ $$i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{3024}(23,\cdot)$$ 3024.ez 18 no $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3024}(25,\cdot)$$ 3024.gi 18 no $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3024}(29,\cdot)$$ 3024.ha 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{3024}(31,\cdot)$$ 3024.fv 18 no $$1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$
$$\chi_{3024}(37,\cdot)$$ 3024.ea 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3024}(41,\cdot)$$ 3024.ff 18 no $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3024}(43,\cdot)$$ 3024.gw 36 no $$-1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{3024}(47,\cdot)$$ 3024.fg 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$1$$
$$\chi_{3024}(53,\cdot)$$ 3024.eg 12 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{3024}(55,\cdot)$$ 3024.p 2 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{3024}(59,\cdot)$$ 3024.gt 36 yes $$-1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$i$$
$$\chi_{3024}(61,\cdot)$$ 3024.hf 36 yes $$-1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$-i$$
$$\chi_{3024}(65,\cdot)$$ 3024.fw 18 no $$-1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$1$$
$$\chi_{3024}(67,\cdot)$$ 3024.gu 36 yes $$-1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$-i$$
$$\chi_{3024}(71,\cdot)$$ 3024.bz 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$
$$\chi_{3024}(73,\cdot)$$ 3024.bx 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3024}(79,\cdot)$$ 3024.fn 18 no $$-1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$1$$
$$\chi_{3024}(83,\cdot)$$ 3024.gr 36 yes $$-1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{3024}(85,\cdot)$$ 3024.gs 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3024}(89,\cdot)$$ 3024.bg 6 no $$1$$ $$1$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{3024}(95,\cdot)$$ 3024.ge 18 no $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$1$$
$$\chi_{3024}(97,\cdot)$$ 3024.ga 18 no $$-1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{3024}(101,\cdot)$$ 3024.hi 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$1$$ $$i$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3024}(103,\cdot)$$ 3024.ew 18 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{3024}(107,\cdot)$$ 3024.el 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{3024}(109,\cdot)$$ 3024.dx 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$