sage: H = DirichletGroup(328)
pari: g = idealstar(,328,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 160 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{40}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{328}(247,\cdot)$, $\chi_{328}(165,\cdot)$, $\chi_{328}(129,\cdot)$ |
First 32 of 160 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{328}(1,\cdot)\) | 328.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{328}(3,\cdot)\) | 328.p | 8 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) |
\(\chi_{328}(5,\cdot)\) | 328.y | 20 | yes | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(-1\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{328}(7,\cdot)\) | 328.bc | 40 | no | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(i\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{328}(9,\cdot)\) | 328.j | 4 | no | \(1\) | \(1\) | \(i\) | \(-1\) | \(i\) | \(-1\) | \(i\) | \(i\) | \(-i\) | \(-i\) | \(-i\) | \(-1\) |
\(\chi_{328}(11,\cdot)\) | 328.bd | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(i\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{328}(13,\cdot)\) | 328.bf | 40 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(i\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{328}(15,\cdot)\) | 328.bc | 40 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(-i\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{328}(17,\cdot)\) | 328.be | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(-i\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{328}(19,\cdot)\) | 328.bd | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(-i\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) |
\(\chi_{328}(21,\cdot)\) | 328.y | 20 | yes | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(-1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{328}(23,\cdot)\) | 328.v | 10 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{328}(25,\cdot)\) | 328.s | 10 | no | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{328}(27,\cdot)\) | 328.p | 8 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(i\) |
\(\chi_{328}(29,\cdot)\) | 328.bf | 40 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(i\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{328}(31,\cdot)\) | 328.v | 10 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{328}(33,\cdot)\) | 328.ba | 20 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(-1\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{328}(35,\cdot)\) | 328.bd | 40 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(-i\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{328}(37,\cdot)\) | 328.u | 10 | yes | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{328}(39,\cdot)\) | 328.bb | 20 | no | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{328}(43,\cdot)\) | 328.z | 20 | yes | \(-1\) | \(1\) | \(-i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{328}(45,\cdot)\) | 328.w | 10 | yes | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{328}(47,\cdot)\) | 328.bc | 40 | no | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(-i\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) |
\(\chi_{328}(49,\cdot)\) | 328.ba | 20 | no | \(1\) | \(1\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(-1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{328}(51,\cdot)\) | 328.x | 10 | yes | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) |
\(\chi_{328}(53,\cdot)\) | 328.bf | 40 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(i\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{328}(55,\cdot)\) | 328.q | 8 | no | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) |
\(\chi_{328}(57,\cdot)\) | 328.m | 5 | no | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{328}(59,\cdot)\) | 328.x | 10 | yes | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) |
\(\chi_{328}(61,\cdot)\) | 328.y | 20 | yes | \(1\) | \(1\) | \(i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(-1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{328}(63,\cdot)\) | 328.bc | 40 | no | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(-i\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) |
\(\chi_{328}(65,\cdot)\) | 328.be | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(-i\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) |