sage: H = DirichletGroup(287)
pari: g = idealstar(,287,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 240 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{120}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{287}(206,\cdot)$, $\chi_{287}(211,\cdot)$ |
First 32 of 240 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{287}(1,\cdot)\) | 287.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{287}(2,\cdot)\) | 287.bc | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) |
\(\chi_{287}(3,\cdot)\) | 287.w | 24 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{23}{24}\right)\) |
\(\chi_{287}(4,\cdot)\) | 287.z | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{13}{30}\right)\) |
\(\chi_{287}(5,\cdot)\) | 287.bd | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) |
\(\chi_{287}(6,\cdot)\) | 287.bb | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(-i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) |
\(\chi_{287}(8,\cdot)\) | 287.u | 20 | no | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{287}(9,\cdot)\) | 287.r | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) |
\(\chi_{287}(10,\cdot)\) | 287.y | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) |
\(\chi_{287}(11,\cdot)\) | 287.bf | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{43}{120}\right)\) |
\(\chi_{287}(12,\cdot)\) | 287.be | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{120}\right)\) | \(e\left(\frac{47}{120}\right)\) |
\(\chi_{287}(13,\cdot)\) | 287.bb | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(i\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) |
\(\chi_{287}(15,\cdot)\) | 287.ba | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(-i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) |
\(\chi_{287}(16,\cdot)\) | 287.s | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) |
\(\chi_{287}(17,\cdot)\) | 287.be | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) |
\(\chi_{287}(18,\cdot)\) | 287.s | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) |
\(\chi_{287}(19,\cdot)\) | 287.be | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) |
\(\chi_{287}(20,\cdot)\) | 287.t | 20 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{287}(22,\cdot)\) | 287.ba | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(-i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) |
\(\chi_{287}(23,\cdot)\) | 287.z | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) |
\(\chi_{287}(24,\cdot)\) | 287.be | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{73}{120}\right)\) |
\(\chi_{287}(25,\cdot)\) | 287.z | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) |
\(\chi_{287}(26,\cdot)\) | 287.be | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) |
\(\chi_{287}(27,\cdot)\) | 287.l | 8 | yes | \(1\) | \(1\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(i\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(-i\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{287}(29,\cdot)\) | 287.ba | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) |
\(\chi_{287}(30,\cdot)\) | 287.bf | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) |
\(\chi_{287}(31,\cdot)\) | 287.x | 30 | yes | \(-1\) | \(1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) |
\(\chi_{287}(32,\cdot)\) | 287.r | 12 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{12}\right)\) |
\(\chi_{287}(33,\cdot)\) | 287.bd | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{287}(34,\cdot)\) | 287.bb | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) |
\(\chi_{287}(36,\cdot)\) | 287.u | 20 | no | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(-i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{287}(37,\cdot)\) | 287.s | 15 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{15}\right)\) |