sage: H = DirichletGroup(356)
pari: g = idealstar(,356,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 176 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{88}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{356}(179,\cdot)$, $\chi_{356}(181,\cdot)$ |
First 32 of 176 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{356}(1,\cdot)\) | 356.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{356}(3,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) |
\(\chi_{356}(5,\cdot)\) | 356.m | 44 | no | \(1\) | \(1\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) |
\(\chi_{356}(7,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{5}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{21}{44}\right)\) |
\(\chi_{356}(9,\cdot)\) | 356.m | 44 | no | \(1\) | \(1\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) |
\(\chi_{356}(11,\cdot)\) | 356.j | 22 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) |
\(\chi_{356}(13,\cdot)\) | 356.p | 88 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{1}{88}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{19}{44}\right)\) |
\(\chi_{356}(15,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{7}{44}\right)\) |
\(\chi_{356}(17,\cdot)\) | 356.m | 44 | no | \(1\) | \(1\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) |
\(\chi_{356}(19,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{63}{88}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{65}{88}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{27}{44}\right)\) |
\(\chi_{356}(21,\cdot)\) | 356.m | 44 | no | \(1\) | \(1\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{9}{22}\right)\) |
\(\chi_{356}(23,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{15}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) |
\(\chi_{356}(25,\cdot)\) | 356.k | 22 | no | \(1\) | \(1\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) |
\(\chi_{356}(27,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{88}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{23}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{81}{88}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{35}{44}\right)\) |
\(\chi_{356}(29,\cdot)\) | 356.p | 88 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{27}{88}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{37}{88}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{43}{44}\right)\) |
\(\chi_{356}(31,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{75}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{9}{88}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{39}{44}\right)\) |
\(\chi_{356}(33,\cdot)\) | 356.p | 88 | no | \(-1\) | \(1\) | \(e\left(\frac{85}{88}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{71}{88}\right)\) | \(e\left(\frac{9}{44}\right)\) |
\(\chi_{356}(35,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{88}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{13}{44}\right)\) | \(e\left(\frac{49}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) |
\(\chi_{356}(37,\cdot)\) | 356.g | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(-i\) | \(e\left(\frac{1}{8}\right)\) | \(i\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(-i\) | \(e\left(\frac{3}{8}\right)\) | \(i\) |
\(\chi_{356}(39,\cdot)\) | 356.l | 22 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{4}{11}\right)\) |
\(\chi_{356}(41,\cdot)\) | 356.p | 88 | no | \(-1\) | \(1\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{29}{88}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{43}{88}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{31}{88}\right)\) | \(e\left(\frac{25}{44}\right)\) |
\(\chi_{356}(43,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) |
\(\chi_{356}(45,\cdot)\) | 356.i | 11 | no | \(1\) | \(1\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{1}{11}\right)\) |
\(\chi_{356}(47,\cdot)\) | 356.n | 44 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) |
\(\chi_{356}(49,\cdot)\) | 356.m | 44 | no | \(1\) | \(1\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{21}{22}\right)\) |
\(\chi_{356}(51,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{51}{88}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{83}{88}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{73}{88}\right)\) | \(e\left(\frac{13}{88}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{25}{88}\right)\) | \(e\left(\frac{23}{44}\right)\) |
\(\chi_{356}(53,\cdot)\) | 356.m | 44 | no | \(1\) | \(1\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{15}{22}\right)\) |
\(\chi_{356}(55,\cdot)\) | 356.e | 4 | yes | \(-1\) | \(1\) | \(i\) | \(-1\) | \(i\) | \(-1\) | \(-1\) | \(i\) | \(-i\) | \(-1\) | \(-i\) | \(-1\) |
\(\chi_{356}(57,\cdot)\) | 356.k | 22 | no | \(1\) | \(1\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{9}{22}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{5}{11}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{6}{11}\right)\) |
\(\chi_{356}(59,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{87}{88}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{88}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{21}{88}\right)\) | \(e\left(\frac{17}{88}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{53}{88}\right)\) | \(e\left(\frac{3}{44}\right)\) |
\(\chi_{356}(61,\cdot)\) | 356.p | 88 | no | \(-1\) | \(1\) | \(e\left(\frac{69}{88}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{88}\right)\) | \(e\left(\frac{59}{88}\right)\) | \(e\left(\frac{31}{44}\right)\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{13}{44}\right)\) |
\(\chi_{356}(63,\cdot)\) | 356.o | 88 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{88}\right)\) | \(e\left(\frac{1}{44}\right)\) | \(e\left(\frac{79}{88}\right)\) | \(e\left(\frac{39}{44}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{61}{88}\right)\) | \(e\left(\frac{41}{88}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{45}{88}\right)\) | \(e\left(\frac{15}{44}\right)\) |