sage: H = DirichletGroup(1122)
pari: g = idealstar(,1122,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 320 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{80}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1122}(749,\cdot)$, $\chi_{1122}(409,\cdot)$, $\chi_{1122}(1057,\cdot)$ |
First 32 of 320 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1122}(1,\cdot)\) | 1122.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1122}(5,\cdot)\) | 1122.bn | 80 | no | \(1\) | \(1\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{80}\right)\) |
\(\chi_{1122}(7,\cdot)\) | 1122.bm | 80 | no | \(1\) | \(1\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{80}\right)\) |
\(\chi_{1122}(13,\cdot)\) | 1122.bf | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{1122}(19,\cdot)\) | 1122.bh | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{40}\right)\) |
\(\chi_{1122}(23,\cdot)\) | 1122.y | 16 | no | \(1\) | \(1\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(-1\) | \(e\left(\frac{15}{16}\right)\) |
\(\chi_{1122}(25,\cdot)\) | 1122.bi | 40 | no | \(1\) | \(1\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) |
\(\chi_{1122}(29,\cdot)\) | 1122.bl | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{17}{80}\right)\) |
\(\chi_{1122}(31,\cdot)\) | 1122.bk | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{61}{80}\right)\) |
\(\chi_{1122}(35,\cdot)\) | 1122.x | 10 | no | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) |
\(\chi_{1122}(37,\cdot)\) | 1122.bk | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{37}{80}\right)\) |
\(\chi_{1122}(41,\cdot)\) | 1122.bl | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{23}{80}\right)\) |
\(\chi_{1122}(43,\cdot)\) | 1122.p | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(i\) | \(e\left(\frac{7}{8}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{1122}(47,\cdot)\) | 1122.bd | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{1122}(49,\cdot)\) | 1122.bi | 40 | no | \(1\) | \(1\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{40}\right)\) |
\(\chi_{1122}(53,\cdot)\) | 1122.bj | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{40}\right)\) |
\(\chi_{1122}(59,\cdot)\) | 1122.bj | 40 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{40}\right)\) |
\(\chi_{1122}(61,\cdot)\) | 1122.bm | 80 | no | \(1\) | \(1\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{79}{80}\right)\) |
\(\chi_{1122}(65,\cdot)\) | 1122.ba | 16 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(1\) | \(e\left(\frac{9}{16}\right)\) |
\(\chi_{1122}(67,\cdot)\) | 1122.c | 2 | no | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
\(\chi_{1122}(71,\cdot)\) | 1122.bn | 80 | no | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{69}{80}\right)\) |
\(\chi_{1122}(73,\cdot)\) | 1122.bm | 80 | no | \(1\) | \(1\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{57}{80}\right)\) |
\(\chi_{1122}(79,\cdot)\) | 1122.bm | 80 | no | \(1\) | \(1\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{51}{80}\right)\) |
\(\chi_{1122}(83,\cdot)\) | 1122.bg | 40 | no | \(1\) | \(1\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{40}\right)\) |
\(\chi_{1122}(89,\cdot)\) | 1122.k | 4 | no | \(-1\) | \(1\) | \(i\) | \(i\) | \(1\) | \(-1\) | \(-i\) | \(-1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) |
\(\chi_{1122}(91,\cdot)\) | 1122.bk | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{43}{80}\right)\) |
\(\chi_{1122}(95,\cdot)\) | 1122.bl | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{47}{80}\right)\) |
\(\chi_{1122}(97,\cdot)\) | 1122.bk | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{80}\right)\) |
\(\chi_{1122}(101,\cdot)\) | 1122.r | 10 | no | \(1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{1122}(103,\cdot)\) | 1122.m | 5 | no | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) |
\(\chi_{1122}(107,\cdot)\) | 1122.bl | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{73}{80}\right)\) |
\(\chi_{1122}(109,\cdot)\) | 1122.z | 16 | no | \(1\) | \(1\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(-1\) | \(e\left(\frac{11}{16}\right)\) |