# Properties

 Modulus $2736$ Structure $$C_{2}\times C_{2}\times C_{6}\times C_{36}$$ Order $864$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2736)

pari: g = idealstar(,2736,2)

## Character group

 sage: G.order()  pari: g.no Order = 864 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{6}\times C_{36}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2736}(1711,\cdot)$, $\chi_{2736}(2053,\cdot)$, $\chi_{2736}(1217,\cdot)$, $\chi_{2736}(1009,\cdot)$

## 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{2736}(1,\cdot)$$ 2736.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2736}(5,\cdot)$$ 2736.he 36 yes $$-1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$1$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{2736}(7,\cdot)$$ 2736.cr 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{2736}(11,\cdot)$$ 2736.ea 12 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{2736}(13,\cdot)$$ 2736.gp 36 yes $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{36}\right)$$
$$\chi_{2736}(17,\cdot)$$ 2736.fj 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{2736}(23,\cdot)$$ 2736.ez 18 no $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{2736}(25,\cdot)$$ 2736.fd 18 no $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$1$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{2736}(29,\cdot)$$ 2736.gz 36 yes $$1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$-1$$ $$e\left(\frac{19}{36}\right)$$
$$\chi_{2736}(31,\cdot)$$ 2736.di 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{2736}(35,\cdot)$$ 2736.gv 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$
$$\chi_{2736}(37,\cdot)$$ 2736.w 4 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$1$$ $$-1$$ $$-1$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{2736}(41,\cdot)$$ 2736.fn 18 no $$1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$-1$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{2736}(43,\cdot)$$ 2736.hi 36 yes $$-1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{29}{36}\right)$$
$$\chi_{2736}(47,\cdot)$$ 2736.gc 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$-1$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{2736}(49,\cdot)$$ 2736.r 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2736}(53,\cdot)$$ 2736.hc 36 no $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{2736}(55,\cdot)$$ 2736.fv 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{2736}(59,\cdot)$$ 2736.gx 36 yes $$-1$$ $$1$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$1$$ $$e\left(\frac{35}{36}\right)$$
$$\chi_{2736}(61,\cdot)$$ 2736.hf 36 yes $$1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$1$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{2736}(65,\cdot)$$ 2736.bf 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{2736}(67,\cdot)$$ 2736.hh 36 yes $$1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$
$$\chi_{2736}(71,\cdot)$$ 2736.fy 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$
$$\chi_{2736}(73,\cdot)$$ 2736.fi 18 no $$1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{2736}(77,\cdot)$$ 2736.ed 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$
$$\chi_{2736}(79,\cdot)$$ 2736.ex 18 no $$1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{2736}(83,\cdot)$$ 2736.dy 12 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{2736}(85,\cdot)$$ 2736.gm 36 yes $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$
$$\chi_{2736}(89,\cdot)$$ 2736.fh 18 no $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{2736}(91,\cdot)$$ 2736.gt 36 no $$1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{36}\right)$$
$$\chi_{2736}(97,\cdot)$$ 2736.gg 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{2736}(101,\cdot)$$ 2736.he 36 yes $$-1$$ $$1$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$1$$ $$e\left(\frac{13}{36}\right)$$