# Properties

 Modulus $666$ Structure $$C_{6}\times C_{36}$$ Order $216$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(666)

pari: g = idealstar(,666,2)

## Character group

 sage: G.order()  pari: g.no Order = 216 sage: H.invariants()  pari: g.cyc Structure = $$C_{6}\times C_{36}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{666}(371,\cdot)$, $\chi_{666}(631,\cdot)$

## First 32 of 216 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{666}(1,\cdot)$$ 666.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{666}(5,\cdot)$$ 666.bv 36 no $$1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$-i$$ $$e\left(\frac{13}{18}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{666}(7,\cdot)$$ 666.w 9 no $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{666}(11,\cdot)$$ 666.v 6 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{666}(13,\cdot)$$ 666.bq 36 no $$-1$$ $$1$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$-1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$i$$ $$e\left(\frac{7}{18}\right)$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{666}(17,\cdot)$$ 666.bs 36 no $$1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$
$$\chi_{666}(19,\cdot)$$ 666.bt 36 no $$-1$$ $$1$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$
$$\chi_{666}(23,\cdot)$$ 666.ba 12 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{666}(25,\cdot)$$ 666.bp 18 no $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$1$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$-1$$ $$e\left(\frac{4}{9}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{666}(29,\cdot)$$ 666.ba 12 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{666}(31,\cdot)$$ 666.bd 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{666}(35,\cdot)$$ 666.bs 36 no $$1$$ $$1$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$
$$\chi_{666}(41,\cdot)$$ 666.bi 18 no $$-1$$ $$1$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$-1$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$1$$ $$e\left(\frac{8}{9}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{666}(43,\cdot)$$ 666.bd 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{666}(47,\cdot)$$ 666.u 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{666}(49,\cdot)$$ 666.w 9 no $$1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{666}(53,\cdot)$$ 666.bo 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{666}(55,\cdot)$$ 666.bt 36 no $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$
$$\chi_{666}(59,\cdot)$$ 666.br 36 no $$1$$ $$1$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{666}(61,\cdot)$$ 666.bu 36 no $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{7}{36}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{666}(65,\cdot)$$ 666.bi 18 no $$-1$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$-1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$1$$ $$e\left(\frac{1}{9}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{666}(67,\cdot)$$ 666.bp 18 no $$1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$1$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$-1$$ $$e\left(\frac{2}{9}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{666}(71,\cdot)$$ 666.bo 18 no $$-1$$ $$1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$
$$\chi_{666}(73,\cdot)$$ 666.c 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{666}(77,\cdot)$$ 666.bi 18 no $$-1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$-1$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$1$$ $$e\left(\frac{5}{9}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{666}(79,\cdot)$$ 666.bu 36 no $$-1$$ $$1$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{666}(83,\cdot)$$ 666.bh 18 no $$-1$$ $$1$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$-1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$-1$$ $$e\left(\frac{1}{9}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{666}(85,\cdot)$$ 666.t 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{666}(89,\cdot)$$ 666.bs 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{35}{36}\right)$$ $$e\left(\frac{1}{36}\right)$$ $$e\left(\frac{23}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$i$$
$$\chi_{666}(91,\cdot)$$ 666.bt 36 no $$-1$$ $$1$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{36}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$
$$\chi_{666}(95,\cdot)$$ 666.bm 18 no $$-1$$ $$1$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{666}(97,\cdot)$$ 666.bg 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$