# Properties

 Modulus $1848$ Structure $$C_{30}\times C_{2}\times C_{2}\times C_{2}\times C_{2}$$ Order $480$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1848)

pari: g = idealstar(,1848,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{30}\times C_{2}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1848}(463,\cdot)$, $\chi_{1848}(925,\cdot)$, $\chi_{1848}(617,\cdot)$, $\chi_{1848}(1585,\cdot)$, $\chi_{1848}(673,\cdot)$

## First 32 of 480 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 $$-1$$ $$1$$ $$5$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{1848}(1,\cdot)$$ 1848.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1848}(5,\cdot)$$ 1848.ea 30 yes $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1848}(13,\cdot)$$ 1848.cx 10 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{1848}(17,\cdot)$$ 1848.em 30 no $$-1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1848}(19,\cdot)$$ 1848.ex 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1848}(23,\cdot)$$ 1848.cl 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$
$$\chi_{1848}(25,\cdot)$$ 1848.ds 15 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1848}(29,\cdot)$$ 1848.cn 10 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1848}(31,\cdot)$$ 1848.ee 30 no $$1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1848}(37,\cdot)$$ 1848.ef 30 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1848}(41,\cdot)$$ 1848.cq 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1848}(43,\cdot)$$ 1848.j 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{1848}(47,\cdot)$$ 1848.ew 30 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1848}(53,\cdot)$$ 1848.er 30 yes $$-1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1848}(59,\cdot)$$ 1848.dx 30 yes $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1848}(61,\cdot)$$ 1848.eu 30 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1848}(65,\cdot)$$ 1848.ca 6 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{1848}(67,\cdot)$$ 1848.by 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$
$$\chi_{1848}(71,\cdot)$$ 1848.dj 10 no $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1848}(73,\cdot)$$ 1848.dz 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1848}(79,\cdot)$$ 1848.et 30 no $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1848}(83,\cdot)$$ 1848.dp 10 yes $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1848}(85,\cdot)$$ 1848.dh 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1848}(89,\cdot)$$ 1848.bl 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{1848}(95,\cdot)$$ 1848.eh 30 no $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1848}(97,\cdot)$$ 1848.dr 10 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1848}(101,\cdot)$$ 1848.ec 30 yes $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1848}(103,\cdot)$$ 1848.ee 30 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1848}(107,\cdot)$$ 1848.en 30 yes $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1848}(109,\cdot)$$ 1848.cj 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$
$$\chi_{1848}(113,\cdot)$$ 1848.dg 10 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1848}(115,\cdot)$$ 1848.ek 30 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$