sage: H = DirichletGroup(354)
pari: g = idealstar(,354,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 116 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{58}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{354}(119,\cdot)$, $\chi_{354}(61,\cdot)$ |
First 32 of 116 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{354}(1,\cdot)\) | 354.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{354}(5,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) |
\(\chi_{354}(7,\cdot)\) | 354.e | 29 | no | \(1\) | \(1\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) |
\(\chi_{354}(11,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{7}{58}\right)\) |
\(\chi_{354}(13,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) |
\(\chi_{354}(17,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) |
\(\chi_{354}(19,\cdot)\) | 354.e | 29 | no | \(1\) | \(1\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) |
\(\chi_{354}(23,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{37}{58}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{39}{58}\right)\) |
\(\chi_{354}(25,\cdot)\) | 354.e | 29 | no | \(1\) | \(1\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) |
\(\chi_{354}(29,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) |
\(\chi_{354}(31,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{23}{58}\right)\) |
\(\chi_{354}(35,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{8}{29}\right)\) |
\(\chi_{354}(37,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{27}{58}\right)\) |
\(\chi_{354}(41,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) |
\(\chi_{354}(43,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) |
\(\chi_{354}(47,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{25}{58}\right)\) |
\(\chi_{354}(49,\cdot)\) | 354.e | 29 | no | \(1\) | \(1\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) |
\(\chi_{354}(53,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{17}{29}\right)\) |
\(\chi_{354}(55,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) |
\(\chi_{354}(61,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) |
\(\chi_{354}(65,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{5}{58}\right)\) |
\(\chi_{354}(67,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{31}{58}\right)\) |
\(\chi_{354}(71,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) |
\(\chi_{354}(73,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{11}{58}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{3}{58}\right)\) |
\(\chi_{354}(77,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{19}{58}\right)\) |
\(\chi_{354}(79,\cdot)\) | 354.e | 29 | no | \(1\) | \(1\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) |
\(\chi_{354}(83,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{45}{58}\right)\) |
\(\chi_{354}(85,\cdot)\) | 354.e | 29 | no | \(1\) | \(1\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) |
\(\chi_{354}(89,\cdot)\) | 354.g | 58 | no | \(1\) | \(1\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) |
\(\chi_{354}(91,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{17}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) |
\(\chi_{354}(95,\cdot)\) | 354.h | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{5}{29}\right)\) |
\(\chi_{354}(97,\cdot)\) | 354.f | 58 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) |