# Properties

 Modulus $7440$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}$$ Order $1920$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7440)

pari: g = idealstar(,7440,2)

## 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 = $\chi_{7440}(6511,\cdot)$, $\chi_{7440}(1861,\cdot)$, $\chi_{7440}(4961,\cdot)$, $\chi_{7440}(2977,\cdot)$, $\chi_{7440}(5521,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$37$$ $$41$$ $$43$$
$$\chi_{7440}(1,\cdot)$$ 7440.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7440}(7,\cdot)$$ 7440.lt 60 no $$1$$ $$1$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$
$$\chi_{7440}(11,\cdot)$$ 7440.mf 60 no $$-1$$ $$1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{7440}(13,\cdot)$$ 7440.lk 60 no $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{7440}(17,\cdot)$$ 7440.lu 60 no $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$
$$\chi_{7440}(19,\cdot)$$ 7440.ko 60 no $$-1$$ $$1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$
$$\chi_{7440}(23,\cdot)$$ 7440.hy 20 no $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{7440}(29,\cdot)$$ 7440.hp 20 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-i$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{7440}(37,\cdot)$$ 7440.gk 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{7440}(41,\cdot)$$ 7440.kf 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{7440}(43,\cdot)$$ 7440.lc 60 no $$-1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{7440}(47,\cdot)$$ 7440.hu 20 no $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{7440}(49,\cdot)$$ 7440.jq 30 no $$1$$ $$1$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{7440}(53,\cdot)$$ 7440.lj 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{7440}(59,\cdot)$$ 7440.kr 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{7440}(61,\cdot)$$ 7440.bj 4 no $$-1$$ $$1$$ $$-1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$i$$
$$\chi_{7440}(67,\cdot)$$ 7440.gi 12 no $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7440}(71,\cdot)$$ 7440.ji 30 no $$1$$ $$1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{7440}(73,\cdot)$$ 7440.lz 60 no $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{7440}(77,\cdot)$$ 7440.ij 20 yes $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{7440}(79,\cdot)$$ 7440.kl 30 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{7440}(83,\cdot)$$ 7440.lr 60 yes $$1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{7440}(89,\cdot)$$ 7440.fn 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{7440}(91,\cdot)$$ 7440.hs 20 no $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{7440}(97,\cdot)$$ 7440.hz 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$i$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{7440}(101,\cdot)$$ 7440.jd 20 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{7440}(103,\cdot)$$ 7440.lt 60 no $$1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{7440}(107,\cdot)$$ 7440.lh 60 yes $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{7440}(109,\cdot)$$ 7440.hq 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{7440}(113,\cdot)$$ 7440.ku 60 no $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{7440}(119,\cdot)$$ 7440.dj 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7440}(121,\cdot)$$ 7440.jz 30 no $$1$$ $$1$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$