# Properties

 Modulus $1386$ Structure $$C_{30}\times C_{6}\times C_{2}$$ Order $360$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1386)

pari: g = idealstar(,1386,2)

## Character group

 sage: G.order()  pari: g.no Order = 360 sage: H.invariants()  pari: g.cyc Structure = $$C_{30}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1386}(155,\cdot)$, $\chi_{1386}(199,\cdot)$, $\chi_{1386}(1135,\cdot)$

## First 32 of 360 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 $$-1$$ $$1$$ $$5$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{1386}(1,\cdot)$$ 1386.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1386}(5,\cdot)$$ 1386.cs 30 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1386}(13,\cdot)$$ 1386.cj 30 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{1386}(17,\cdot)$$ 1386.cp 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1386}(19,\cdot)$$ 1386.ce 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1386}(23,\cdot)$$ 1386.be 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1386}(25,\cdot)$$ 1386.bz 15 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1386}(29,\cdot)$$ 1386.cf 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1386}(31,\cdot)$$ 1386.cy 30 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1386}(37,\cdot)$$ 1386.bx 15 no $$1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1386}(41,\cdot)$$ 1386.cv 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1386}(43,\cdot)$$ 1386.v 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1386}(47,\cdot)$$ 1386.cb 30 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1386}(53,\cdot)$$ 1386.cd 30 no $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1386}(59,\cdot)$$ 1386.cb 30 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1386}(61,\cdot)$$ 1386.db 30 no $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1386}(65,\cdot)$$ 1386.p 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1386}(67,\cdot)$$ 1386.l 3 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1386}(71,\cdot)$$ 1386.bt 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1386}(73,\cdot)$$ 1386.ce 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1386}(79,\cdot)$$ 1386.ca 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1386}(83,\cdot)$$ 1386.cv 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1386}(85,\cdot)$$ 1386.ct 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1386}(89,\cdot)$$ 1386.r 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{1386}(95,\cdot)$$ 1386.cz 30 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1386}(97,\cdot)$$ 1386.ci 30 no $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1386}(101,\cdot)$$ 1386.cu 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1386}(103,\cdot)$$ 1386.cg 30 no $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1386}(107,\cdot)$$ 1386.co 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1386}(109,\cdot)$$ 1386.s 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$
$$\chi_{1386}(113,\cdot)$$ 1386.cm 30 no $$-1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$
$$\chi_{1386}(115,\cdot)$$ 1386.cg 30 no $$-1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$