sage: H = DirichletGroup(3020)
pari: g = idealstar(,3020,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1200 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{300}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{3020}(1511,\cdot)$, $\chi_{3020}(2417,\cdot)$, $\chi_{3020}(761,\cdot)$ |
First 32 of 1200 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 | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{3020}(1,\cdot)\) | 3020.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{3020}(3,\cdot)\) | 3020.cf | 100 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{47}{100}\right)\) |
\(\chi_{3020}(7,\cdot)\) | 3020.cr | 300 | yes | \(-1\) | \(1\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{203}{300}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{73}{150}\right)\) | \(e\left(\frac{19}{300}\right)\) | \(e\left(\frac{47}{300}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{29}{100}\right)\) |
\(\chi_{3020}(9,\cdot)\) | 3020.bv | 50 | no | \(1\) | \(1\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{47}{50}\right)\) |
\(\chi_{3020}(11,\cdot)\) | 3020.cn | 150 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{73}{150}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{61}{150}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{26}{75}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{39}{50}\right)\) |
\(\chi_{3020}(13,\cdot)\) | 3020.cs | 300 | no | \(1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{19}{300}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{52}{75}\right)\) | \(e\left(\frac{137}{300}\right)\) | \(e\left(\frac{181}{300}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{34}{75}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{17}{100}\right)\) |
\(\chi_{3020}(17,\cdot)\) | 3020.ct | 300 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{47}{300}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{26}{75}\right)\) | \(e\left(\frac{181}{300}\right)\) | \(e\left(\frac{203}{300}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{17}{75}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{21}{100}\right)\) |
\(\chi_{3020}(19,\cdot)\) | 3020.x | 10 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
\(\chi_{3020}(21,\cdot)\) | 3020.ce | 75 | no | \(1\) | \(1\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{34}{75}\right)\) | \(e\left(\frac{17}{75}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{19}{25}\right)\) |
\(\chi_{3020}(23,\cdot)\) | 3020.cb | 60 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(1\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{11}{20}\right)\) |
\(\chi_{3020}(27,\cdot)\) | 3020.cf | 100 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{41}{100}\right)\) |
\(\chi_{3020}(29,\cdot)\) | 3020.bv | 50 | no | \(1\) | \(1\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{9}{50}\right)\) |
\(\chi_{3020}(31,\cdot)\) | 3020.cn | 150 | no | \(-1\) | \(1\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{1}{150}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{7}{150}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{43}{50}\right)\) |
\(\chi_{3020}(33,\cdot)\) | 3020.bc | 12 | no | \(1\) | \(1\) | \(-i\) | \(e\left(\frac{11}{12}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) |
\(\chi_{3020}(37,\cdot)\) | 3020.ct | 300 | no | \(-1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{119}{300}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{2}{75}\right)\) | \(e\left(\frac{37}{300}\right)\) | \(e\left(\frac{131}{300}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{59}{75}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{17}{100}\right)\) |
\(\chi_{3020}(39,\cdot)\) | 3020.cp | 150 | yes | \(-1\) | \(1\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{37}{75}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{143}{150}\right)\) | \(e\left(\frac{127}{150}\right)\) | \(e\left(\frac{101}{150}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{28}{75}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{16}{25}\right)\) |
\(\chi_{3020}(41,\cdot)\) | 3020.bu | 50 | no | \(-1\) | \(1\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{31}{50}\right)\) |
\(\chi_{3020}(43,\cdot)\) | 3020.cq | 300 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{247}{300}\right)\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{77}{150}\right)\) | \(e\left(\frac{131}{300}\right)\) | \(e\left(\frac{253}{300}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{21}{100}\right)\) |
\(\chi_{3020}(47,\cdot)\) | 3020.cq | 300 | yes | \(1\) | \(1\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{109}{300}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{119}{150}\right)\) | \(e\left(\frac{257}{300}\right)\) | \(e\left(\frac{91}{300}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{49}{75}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{87}{100}\right)\) |
\(\chi_{3020}(49,\cdot)\) | 3020.cj | 150 | no | \(1\) | \(1\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{53}{150}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{73}{75}\right)\) | \(e\left(\frac{19}{150}\right)\) | \(e\left(\frac{47}{150}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{16}{75}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{29}{50}\right)\) |
\(\chi_{3020}(51,\cdot)\) | 3020.co | 150 | no | \(1\) | \(1\) | \(e\left(\frac{14}{25}\right)\) | \(e\left(\frac{44}{75}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{91}{150}\right)\) | \(e\left(\frac{149}{150}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{11}{75}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{17}{25}\right)\) |
\(\chi_{3020}(53,\cdot)\) | 3020.ci | 100 | no | \(1\) | \(1\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{73}{100}\right)\) |
\(\chi_{3020}(57,\cdot)\) | 3020.ci | 100 | no | \(1\) | \(1\) | \(e\left(\frac{9}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{27}{100}\right)\) |
\(\chi_{3020}(59,\cdot)\) | 3020.x | 10 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
\(\chi_{3020}(61,\cdot)\) | 3020.ck | 150 | no | \(-1\) | \(1\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{23}{150}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{43}{75}\right)\) | \(e\left(\frac{79}{150}\right)\) | \(e\left(\frac{1}{75}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{31}{75}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{39}{50}\right)\) |
\(\chi_{3020}(63,\cdot)\) | 3020.cr | 300 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{161}{300}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{1}{150}\right)\) | \(e\left(\frac{253}{300}\right)\) | \(e\left(\frac{89}{300}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{71}{75}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{100}\right)\) |
\(\chi_{3020}(67,\cdot)\) | 3020.cf | 100 | yes | \(-1\) | \(1\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{81}{100}\right)\) |
\(\chi_{3020}(69,\cdot)\) | 3020.cj | 150 | no | \(1\) | \(1\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{7}{150}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{62}{75}\right)\) | \(e\left(\frac{11}{150}\right)\) | \(e\left(\frac{43}{150}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{29}{75}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{50}\right)\) |
\(\chi_{3020}(71,\cdot)\) | 3020.co | 150 | no | \(1\) | \(1\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{7}{75}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{23}{150}\right)\) | \(e\left(\frac{97}{150}\right)\) | \(e\left(\frac{43}{75}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{58}{75}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{25}\right)\) |
\(\chi_{3020}(73,\cdot)\) | 3020.ci | 100 | no | \(1\) | \(1\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{29}{100}\right)\) |
\(\chi_{3020}(77,\cdot)\) | 3020.cs | 300 | no | \(1\) | \(1\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{49}{300}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{227}{300}\right)\) | \(e\left(\frac{151}{300}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{64}{75}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{7}{100}\right)\) |
\(\chi_{3020}(79,\cdot)\) | 3020.bz | 50 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{19}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{17}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{50}\right)\) |