# Properties

 Modulus $1368$ Structure $$C_{2}\times C_{2}\times C_{6}\times C_{18}$$ Order $432$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1368)

pari: g = idealstar(,1368,2)

## Character group

 sage: G.order()  pari: g.no Order = 432 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{6}\times C_{18}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1368}(343,\cdot)$, $\chi_{1368}(685,\cdot)$, $\chi_{1368}(1217,\cdot)$, $\chi_{1368}(1009,\cdot)$

## First 32 of 432 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{1368}(1,\cdot)$$ 1368.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1368}(5,\cdot)$$ 1368.ea 18 yes $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{1368}(7,\cdot)$$ 1368.bs 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1368}(11,\cdot)$$ 1368.db 6 yes $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1368}(13,\cdot)$$ 1368.ex 18 yes $$-1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{1368}(17,\cdot)$$ 1368.dv 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{1368}(23,\cdot)$$ 1368.di 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{1368}(25,\cdot)$$ 1368.dd 9 no $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$
$$\chi_{1368}(29,\cdot)$$ 1368.dz 18 yes $$1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$-1$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{1368}(31,\cdot)$$ 1368.da 6 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1368}(35,\cdot)$$ 1368.el 18 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{1368}(37,\cdot)$$ 1368.i 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{1368}(41,\cdot)$$ 1368.dn 18 no $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$-1$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{1368}(43,\cdot)$$ 1368.dh 18 yes $$-1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{1368}(47,\cdot)$$ 1368.eo 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$-1$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{1368}(49,\cdot)$$ 1368.r 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1368}(53,\cdot)$$ 1368.dt 18 no $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{1368}(55,\cdot)$$ 1368.em 18 no $$-1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{1368}(59,\cdot)$$ 1368.ee 18 yes $$-1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$1$$ $$e\left(\frac{13}{18}\right)$$
$$\chi_{1368}(61,\cdot)$$ 1368.dp 18 yes $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$1$$ $$e\left(\frac{17}{18}\right)$$
$$\chi_{1368}(65,\cdot)$$ 1368.x 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1368}(67,\cdot)$$ 1368.dg 18 yes $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{9}\right)$$
$$\chi_{1368}(71,\cdot)$$ 1368.ef 18 no $$-1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{1368}(73,\cdot)$$ 1368.dc 9 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{9}\right)$$
$$\chi_{1368}(77,\cdot)$$ 1368.bj 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{1368}(79,\cdot)$$ 1368.dj 18 no $$1$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{18}\right)$$
$$\chi_{1368}(83,\cdot)$$ 1368.bn 6 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1368}(85,\cdot)$$ 1368.eu 18 yes $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{18}\right)$$
$$\chi_{1368}(89,\cdot)$$ 1368.dw 18 no $$1$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{18}\right)$$
$$\chi_{1368}(91,\cdot)$$ 1368.eg 18 no $$1$$ $$1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$
$$\chi_{1368}(97,\cdot)$$ 1368.es 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$
$$\chi_{1368}(101,\cdot)$$ 1368.ea 18 yes $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$