sage: H = DirichletGroup(250)
pari: g = idealstar(,250,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 100 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{100}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{250}(127,\cdot)$ |
First 32 of 100 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{250}(1,\cdot)\) | 250.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{250}(3,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{47}{100}\right)\) |
\(\chi_{250}(7,\cdot)\) | 250.f | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(i\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) |
\(\chi_{250}(9,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{47}{50}\right)\) |
\(\chi_{250}(11,\cdot)\) | 250.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) |
\(\chi_{250}(13,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{19}{100}\right)\) |
\(\chi_{250}(17,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) |
\(\chi_{250}(19,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{39}{50}\right)\) |
\(\chi_{250}(21,\cdot)\) | 250.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) |
\(\chi_{250}(23,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{51}{100}\right)\) |
\(\chi_{250}(27,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{41}{100}\right)\) |
\(\chi_{250}(29,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{1}{50}\right)\) |
\(\chi_{250}(31,\cdot)\) | 250.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) |
\(\chi_{250}(33,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) |
\(\chi_{250}(37,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{9}{100}\right)\) |
\(\chi_{250}(39,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{33}{50}\right)\) |
\(\chi_{250}(41,\cdot)\) | 250.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) |
\(\chi_{250}(43,\cdot)\) | 250.f | 20 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(-i\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) |
\(\chi_{250}(47,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{37}{100}\right)\) |
\(\chi_{250}(49,\cdot)\) | 250.e | 10 | no | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) |
\(\chi_{250}(51,\cdot)\) | 250.d | 5 | no | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{250}(53,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{7}{100}\right)\) |
\(\chi_{250}(57,\cdot)\) | 250.c | 4 | no | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(i\) | \(-1\) | \(1\) | \(-i\) | \(i\) |
\(\chi_{250}(59,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{7}{50}\right)\) |
\(\chi_{250}(61,\cdot)\) | 250.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{19}{25}\right)\) |
\(\chi_{250}(63,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{79}{100}\right)\) |
\(\chi_{250}(67,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{73}{100}\right)\) |
\(\chi_{250}(69,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{49}{50}\right)\) |
\(\chi_{250}(71,\cdot)\) | 250.g | 25 | no | \(1\) | \(1\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) |
\(\chi_{250}(73,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{11}{100}\right)\) |
\(\chi_{250}(77,\cdot)\) | 250.i | 100 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) |
\(\chi_{250}(79,\cdot)\) | 250.h | 50 | no | \(1\) | \(1\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{11}{50}\right)\) |