# Properties

 Modulus $1148$ Structure $$C_{120}\times C_{2}\times C_{2}$$ Order $480$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1148)

pari: g = idealstar(,1148,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{120}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1148}(575,\cdot)$, $\chi_{1148}(493,\cdot)$, $\chi_{1148}(785,\cdot)$

## 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$23$$ $$25$$
$$\chi_{1148}(1,\cdot)$$ 1148.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1148}(3,\cdot)$$ 1148.bq 24 yes $$-1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1148}(5,\cdot)$$ 1148.ch 60 no $$-1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1148}(9,\cdot)$$ 1148.bi 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1148}(11,\cdot)$$ 1148.cl 120 yes $$1$$ $$1$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1148}(13,\cdot)$$ 1148.cc 40 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$i$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1148}(15,\cdot)$$ 1148.ca 40 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-i$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1148}(17,\cdot)$$ 1148.cj 120 no $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$
$$\chi_{1148}(19,\cdot)$$ 1148.ck 120 yes $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{1148}(23,\cdot)$$ 1148.bv 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1148}(25,\cdot)$$ 1148.bz 30 no $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1148}(27,\cdot)$$ 1148.x 8 yes $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$-1$$
$$\chi_{1148}(29,\cdot)$$ 1148.cd 40 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$i$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1148}(31,\cdot)$$ 1148.bw 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{1148}(33,\cdot)$$ 1148.ch 60 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{1148}(37,\cdot)$$ 1148.bk 15 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1148}(39,\cdot)$$ 1148.ce 60 yes $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1148}(43,\cdot)$$ 1148.bo 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1148}(45,\cdot)$$ 1148.bt 30 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1148}(47,\cdot)$$ 1148.ck 120 yes $$-1$$ $$1$$ $$e\left(\frac{17}{24}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{109}{120}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1148}(51,\cdot)$$ 1148.by 30 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{1148}(53,\cdot)$$ 1148.ci 120 no $$-1$$ $$1$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{49}{120}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1148}(55,\cdot)$$ 1148.x 8 yes $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$-1$$
$$\chi_{1148}(57,\cdot)$$ 1148.n 5 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1148}(59,\cdot)$$ 1148.bu 30 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1148}(61,\cdot)$$ 1148.ch 60 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1148}(65,\cdot)$$ 1148.ci 120 no $$-1$$ $$1$$ $$e\left(\frac{5}{24}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{71}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1148}(67,\cdot)$$ 1148.cl 120 yes $$1$$ $$1$$ $$e\left(\frac{13}{24}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1148}(69,\cdot)$$ 1148.cc 40 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$i$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1148}(71,\cdot)$$ 1148.ca 40 no $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1148}(73,\cdot)$$ 1148.bg 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1148}(75,\cdot)$$ 1148.ck 120 yes $$-1$$ $$1$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{61}{120}\right)$$ $$e\left(\frac{113}{120}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$