# Properties

 Modulus $1476$ Structure $$C_{2}\times C_{2}\times C_{120}$$ Order $480$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1476)

pari: g = idealstar(,1476,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{120}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1476}(739,\cdot)$, $\chi_{1476}(821,\cdot)$, $\chi_{1476}(1441,\cdot)$

## 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{1476}(1,\cdot)$$ 1476.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1476}(5,\cdot)$$ 1476.cg 60 no $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1476}(7,\cdot)$$ 1476.cl 120 yes $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{23}{120}\right)$$ $$e\left(\frac{11}{120}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{1476}(11,\cdot)$$ 1476.cj 120 yes $$-1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{120}\right)$$ $$e\left(\frac{107}{120}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1476}(13,\cdot)$$ 1476.ci 120 no $$-1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{67}{120}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1476}(17,\cdot)$$ 1476.cb 40 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1476}(19,\cdot)$$ 1476.ca 40 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{1476}(23,\cdot)$$ 1476.bv 30 yes $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1476}(25,\cdot)$$ 1476.bx 30 no $$1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{1476}(29,\cdot)$$ 1476.ck 120 no $$1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{59}{120}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{91}{120}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{47}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{1476}(31,\cdot)$$ 1476.bz 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1476}(35,\cdot)$$ 1476.cc 40 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1476}(37,\cdot)$$ 1476.n 5 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1476}(43,\cdot)$$ 1476.ce 60 yes $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{1476}(47,\cdot)$$ 1476.cj 120 yes $$-1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{41}{120}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1476}(49,\cdot)$$ 1476.cf 60 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1476}(53,\cdot)$$ 1476.cb 40 no $$1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1476}(55,\cdot)$$ 1476.y 8 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$1$$
$$\chi_{1476}(59,\cdot)$$ 1476.bu 30 yes $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1476}(61,\cdot)$$ 1476.cf 60 no $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{1476}(65,\cdot)$$ 1476.ck 120 no $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{41}{120}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{49}{120}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1476}(67,\cdot)$$ 1476.cl 120 yes $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{49}{120}\right)$$ $$e\left(\frac{13}{120}\right)$$ $$e\left(\frac{101}{120}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{37}{120}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1476}(71,\cdot)$$ 1476.cc 40 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1476}(73,\cdot)$$ 1476.k 4 no $$1$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$-i$$ $$i$$ $$i$$ $$1$$ $$1$$ $$-i$$ $$1$$
$$\chi_{1476}(77,\cdot)$$ 1476.cg 60 no $$-1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{1476}(79,\cdot)$$ 1476.bp 24 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{24}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1476}(83,\cdot)$$ 1476.t 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1476}(85,\cdot)$$ 1476.bs 24 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{11}{24}\right)$$ $$e\left(\frac{7}{24}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{23}{24}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1476}(89,\cdot)$$ 1476.cb 40 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1476}(91,\cdot)$$ 1476.j 4 no $$-1$$ $$1$$ $$-1$$ $$-i$$ $$-i$$ $$i$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$i$$ $$-1$$
$$\chi_{1476}(95,\cdot)$$ 1476.cj 120 yes $$-1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{7}{120}\right)$$ $$e\left(\frac{79}{120}\right)$$ $$e\left(\frac{83}{120}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1476}(97,\cdot)$$ 1476.ci 120 no $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{89}{120}\right)$$ $$e\left(\frac{53}{120}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{17}{120}\right)$$ $$e\left(\frac{7}{30}\right)$$