sage: H = DirichletGroup(6025)
pari: g = idealstar(,6025,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 4800 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{20}\times C_{240}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{6025}(2652,\cdot)$, $\chi_{6025}(2176,\cdot)$ |
First 32 of 4800 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{6025}(1,\cdot)\) | 6025.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{6025}(2,\cdot)\) | 6025.ip | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{19}{120}\right)\) |
\(\chi_{6025}(3,\cdot)\) | 6025.hz | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{24}\right)\) |
\(\chi_{6025}(4,\cdot)\) | 6025.gu | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) |
\(\chi_{6025}(6,\cdot)\) | 6025.dn | 20 | yes | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{20}\right)\) |
\(\chi_{6025}(7,\cdot)\) | 6025.jp | 240 | no | \(1\) | \(1\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{227}{240}\right)\) |
\(\chi_{6025}(8,\cdot)\) | 6025.er | 40 | yes | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{40}\right)\) |
\(\chi_{6025}(9,\cdot)\) | 6025.gt | 60 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) |
\(\chi_{6025}(11,\cdot)\) | 6025.iu | 240 | yes | \(-1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{23}{240}\right)\) |
\(\chi_{6025}(12,\cdot)\) | 6025.hx | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{73}{120}\right)\) |
\(\chi_{6025}(13,\cdot)\) | 6025.jb | 240 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{227}{240}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{61}{240}\right)\) |
\(\chi_{6025}(14,\cdot)\) | 6025.jg | 240 | yes | \(-1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{71}{240}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{167}{240}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{48}\right)\) |
\(\chi_{6025}(16,\cdot)\) | 6025.ei | 30 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) |
\(\chi_{6025}(17,\cdot)\) | 6025.hn | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(i\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) |
\(\chi_{6025}(18,\cdot)\) | 6025.hw | 120 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(1\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{89}{120}\right)\) |
\(\chi_{6025}(19,\cdot)\) | 6025.iv | 240 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{179}{240}\right)\) |
\(\chi_{6025}(21,\cdot)\) | 6025.hj | 80 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) |
\(\chi_{6025}(22,\cdot)\) | 6025.jn | 240 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{61}{240}\right)\) |
\(\chi_{6025}(23,\cdot)\) | 6025.hn | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(-i\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{49}{80}\right)\) |
\(\chi_{6025}(24,\cdot)\) | 6025.ek | 30 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(-1\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) |
\(\chi_{6025}(26,\cdot)\) | 6025.gz | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(i\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{33}{80}\right)\) |
\(\chi_{6025}(27,\cdot)\) | 6025.fh | 40 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(1\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{6025}(28,\cdot)\) | 6025.hr | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(-i\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{21}{80}\right)\) |
\(\chi_{6025}(29,\cdot)\) | 6025.ic | 120 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(-1\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) |
\(\chi_{6025}(31,\cdot)\) | 6025.je | 240 | yes | \(-1\) | \(1\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{37}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(i\) | \(e\left(\frac{151}{240}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{31}{240}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{41}{240}\right)\) |
\(\chi_{6025}(32,\cdot)\) | 6025.dq | 24 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{5}{24}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{24}\right)\) |
\(\chi_{6025}(33,\cdot)\) | 6025.hs | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) |
\(\chi_{6025}(34,\cdot)\) | 6025.jk | 240 | yes | \(-1\) | \(1\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{181}{240}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{133}{240}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{59}{240}\right)\) |
\(\chi_{6025}(36,\cdot)\) | 6025.bb | 10 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) |
\(\chi_{6025}(37,\cdot)\) | 6025.ix | 240 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(-i\) | \(e\left(\frac{133}{240}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{193}{240}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{203}{240}\right)\) |
\(\chi_{6025}(38,\cdot)\) | 6025.jm | 240 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{203}{240}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{217}{240}\right)\) |
\(\chi_{6025}(39,\cdot)\) | 6025.jk | 240 | yes | \(-1\) | \(1\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{109}{240}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{157}{240}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{131}{240}\right)\) |