sage: H = DirichletGroup(723)
pari: g = idealstar(,723,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 480 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{240}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{723}(242,\cdot)$, $\chi_{723}(7,\cdot)$ |
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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{723}(1,\cdot)\) | 723.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{723}(2,\cdot)\) | 723.x | 24 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-i\) | \(e\left(\frac{19}{24}\right)\) | \(-i\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{723}(4,\cdot)\) | 723.r | 12 | no | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{7}{12}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{723}(5,\cdot)\) | 723.bc | 40 | yes | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(i\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(1\) |
\(\chi_{723}(7,\cdot)\) | 723.bm | 240 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{1}{240}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{191}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(8,\cdot)\) | 723.m | 8 | yes | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(i\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
\(\chi_{723}(10,\cdot)\) | 723.z | 30 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{723}(11,\cdot)\) | 723.be | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(13,\cdot)\) | 723.bm | 240 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{47}{240}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{49}{240}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{723}(14,\cdot)\) | 723.bn | 240 | yes | \(1\) | \(1\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{191}{240}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{97}{240}\right)\) | \(e\left(\frac{121}{240}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{723}(16,\cdot)\) | 723.i | 6 | no | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{723}(17,\cdot)\) | 723.bj | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(-1\) |
\(\chi_{723}(19,\cdot)\) | 723.bf | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(20,\cdot)\) | 723.bl | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(-i\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{723}(22,\cdot)\) | 723.bf | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{723}(23,\cdot)\) | 723.bj | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{69}{80}\right)\) | \(-1\) |
\(\chi_{723}(25,\cdot)\) | 723.v | 20 | no | \(1\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) | \(-i\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(1\) |
\(\chi_{723}(26,\cdot)\) | 723.bj | 80 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(-1\) |
\(\chi_{723}(28,\cdot)\) | 723.bi | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(i\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(-1\) |
\(\chi_{723}(29,\cdot)\) | 723.bl | 120 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(i\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{2}{3}\right)\) |
\(\chi_{723}(31,\cdot)\) | 723.bm | 240 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{151}{240}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{137}{240}\right)\) | \(e\left(\frac{41}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(32,\cdot)\) | 723.x | 24 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-i\) | \(e\left(\frac{23}{24}\right)\) | \(-i\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{3}\right)\) |
\(\chi_{723}(34,\cdot)\) | 723.bm | 240 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{61}{240}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{227}{240}\right)\) | \(e\left(\frac{131}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(35,\cdot)\) | 723.bn | 240 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{29}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(37,\cdot)\) | 723.bm | 240 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{73}{240}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{71}{240}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(38,\cdot)\) | 723.be | 48 | yes | \(1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{41}{48}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{5}{6}\right)\) |
\(\chi_{723}(40,\cdot)\) | 723.v | 20 | no | \(1\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(-i\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(1\) |
\(\chi_{723}(41,\cdot)\) | 723.bc | 40 | yes | \(-1\) | \(1\) | \(i\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(-i\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(1\) |
\(\chi_{723}(43,\cdot)\) | 723.bi | 80 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(-i\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(-1\) |
\(\chi_{723}(44,\cdot)\) | 723.t | 16 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(-1\) |
\(\chi_{723}(46,\cdot)\) | 723.bm | 240 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{7}{240}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{89}{240}\right)\) | \(e\left(\frac{137}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |
\(\chi_{723}(47,\cdot)\) | 723.bc | 40 | yes | \(-1\) | \(1\) | \(-i\) | \(-1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(i\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(1\) |