# Properties

 Modulus $1764$ Structure $$C_{2}\times C_{6}\times C_{42}$$ Order $504$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1764)

pari: g = idealstar(,1764,2)

## Character group

 sage: G.order()  pari: g.no Order = 504 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{6}\times C_{42}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1764}(883,\cdot)$, $\chi_{1764}(785,\cdot)$, $\chi_{1764}(1081,\cdot)$

## First 32 of 504 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$
$$\chi_{1764}(1,\cdot)$$ 1764.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1764}(5,\cdot)$$ 1764.cr 42 no $$1$$ $$1$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$-1$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{1764}(11,\cdot)$$ 1764.cm 42 yes $$1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$-1$$ $$e\left(\frac{10}{21}\right)$$
$$\chi_{1764}(13,\cdot)$$ 1764.cl 42 no $$-1$$ $$1$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{1764}(17,\cdot)$$ 1764.cu 42 no $$1$$ $$1$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{1764}(19,\cdot)$$ 1764.bf 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1764}(23,\cdot)$$ 1764.cm 42 yes $$1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$-1$$ $$e\left(\frac{20}{21}\right)$$
$$\chi_{1764}(25,\cdot)$$ 1764.bz 21 no $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$1$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{1764}(29,\cdot)$$ 1764.ch 42 no $$-1$$ $$1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$1$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{1764}(31,\cdot)$$ 1764.n 6 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1764}(37,\cdot)$$ 1764.bx 21 no $$1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{21}\right)$$
$$\chi_{1764}(41,\cdot)$$ 1764.cq 42 no $$1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$-1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{1764}(43,\cdot)$$ 1764.cs 42 yes $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$-1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{1764}(47,\cdot)$$ 1764.ca 42 yes $$-1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{21}\right)$$
$$\chi_{1764}(53,\cdot)$$ 1764.cd 42 no $$-1$$ $$1$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{21}\right)$$
$$\chi_{1764}(55,\cdot)$$ 1764.bv 14 no $$1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$1$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{1764}(59,\cdot)$$ 1764.ca 42 yes $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{21}\right)$$
$$\chi_{1764}(61,\cdot)$$ 1764.cy 42 no $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{21}\right)$$
$$\chi_{1764}(65,\cdot)$$ 1764.db 42 no $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{1764}(67,\cdot)$$ 1764.bl 6 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1764}(71,\cdot)$$ 1764.bs 14 no $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$-1$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{1764}(73,\cdot)$$ 1764.co 42 no $$-1$$ $$1$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{4}{21}\right)$$
$$\chi_{1764}(79,\cdot)$$ 1764.bl 6 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1764}(83,\cdot)$$ 1764.cv 42 yes $$-1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{1764}(85,\cdot)$$ 1764.by 21 no $$1$$ $$1$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{1764}(89,\cdot)$$ 1764.cu 42 no $$1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{1764}(95,\cdot)$$ 1764.cz 42 yes $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{1764}(97,\cdot)$$ 1764.bc 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{1764}(101,\cdot)$$ 1764.cr 42 no $$1$$ $$1$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$-1$$ $$e\left(\frac{16}{21}\right)$$
$$\chi_{1764}(103,\cdot)$$ 1764.ce 42 yes $$1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$1$$ $$e\left(\frac{2}{21}\right)$$
$$\chi_{1764}(107,\cdot)$$ 1764.cj 42 no $$1$$ $$1$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{21}\right)$$
$$\chi_{1764}(109,\cdot)$$ 1764.bx 21 no $$1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{10}{21}\right)$$
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