# Properties

 Modulus $7800$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}$$ Order $1920$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(7800)

pari: g = idealstar(,7800,2)

## Character group

 sage: G.order()  pari: g.no Order = 1920 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7800}(1951,\cdot)$, $\chi_{7800}(3901,\cdot)$, $\chi_{7800}(5201,\cdot)$, $\chi_{7800}(7177,\cdot)$, $\chi_{7800}(4201,\cdot)$

## First 32 of 1920 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{7800}(1,\cdot)$$ 7800.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7800}(7,\cdot)$$ 7800.hg 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{7800}(11,\cdot)$$ 7800.lm 60 yes $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{7800}(17,\cdot)$$ 7800.lz 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{7800}(19,\cdot)$$ 7800.lk 60 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7800}(23,\cdot)$$ 7800.kx 60 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{7800}(29,\cdot)$$ 7800.kj 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7800}(31,\cdot)$$ 7800.ij 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$1$$
$$\chi_{7800}(37,\cdot)$$ 7800.kq 60 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{7800}(41,\cdot)$$ 7800.lp 60 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{7800}(43,\cdot)$$ 7800.gv 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{7800}(47,\cdot)$$ 7800.hl 20 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$-i$$
$$\chi_{7800}(49,\cdot)$$ 7800.ds 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{7800}(53,\cdot)$$ 7800.hw 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{7800}(59,\cdot)$$ 7800.lj 60 yes $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7800}(61,\cdot)$$ 7800.jm 30 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{7800}(67,\cdot)$$ 7800.ks 60 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{7800}(71,\cdot)$$ 7800.ll 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7800}(73,\cdot)$$ 7800.hs 20 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-i$$
$$\chi_{7800}(77,\cdot)$$ 7800.ix 20 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$i$$
$$\chi_{7800}(79,\cdot)$$ 7800.fm 10 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$
$$\chi_{7800}(83,\cdot)$$ 7800.hr 20 yes $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$
$$\chi_{7800}(89,\cdot)$$ 7800.lc 60 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7800}(97,\cdot)$$ 7800.mb 60 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{7800}(101,\cdot)$$ 7800.eg 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{7800}(103,\cdot)$$ 7800.ia 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-i$$
$$\chi_{7800}(107,\cdot)$$ 7800.hb 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{7800}(109,\cdot)$$ 7800.id 20 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-1$$
$$\chi_{7800}(113,\cdot)$$ 7800.kw 60 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{7800}(119,\cdot)$$ 7800.lg 60 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{7800}(121,\cdot)$$ 7800.kb 30 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7800}(127,\cdot)$$ 7800.ls 60 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$