sage: H = DirichletGroup(1096)
pari: g = idealstar(,1096,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 544 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{136}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1096}(823,\cdot)$, $\chi_{1096}(549,\cdot)$, $\chi_{1096}(825,\cdot)$ |
First 32 of 544 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 | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1096}(1,\cdot)\) | 1096.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1096}(3,\cdot)\) | 1096.bc | 136 | yes | \(1\) | \(1\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{111}{136}\right)\) |
\(\chi_{1096}(5,\cdot)\) | 1096.bf | 136 | yes | \(-1\) | \(1\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{29}{136}\right)\) |
\(\chi_{1096}(7,\cdot)\) | 1096.y | 68 | no | \(-1\) | \(1\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{68}\right)\) |
\(\chi_{1096}(9,\cdot)\) | 1096.bb | 68 | no | \(1\) | \(1\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{43}{68}\right)\) |
\(\chi_{1096}(11,\cdot)\) | 1096.z | 68 | yes | \(-1\) | \(1\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{5}{68}\right)\) |
\(\chi_{1096}(13,\cdot)\) | 1096.bf | 136 | yes | \(-1\) | \(1\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{13}{136}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{55}{136}\right)\) |
\(\chi_{1096}(15,\cdot)\) | 1096.t | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{1}{34}\right)\) |
\(\chi_{1096}(17,\cdot)\) | 1096.bb | 68 | no | \(1\) | \(1\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{1}{68}\right)\) |
\(\chi_{1096}(19,\cdot)\) | 1096.z | 68 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{23}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{3}{68}\right)\) |
\(\chi_{1096}(21,\cdot)\) | 1096.bf | 136 | yes | \(-1\) | \(1\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{55}{136}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{13}{136}\right)\) |
\(\chi_{1096}(23,\cdot)\) | 1096.bd | 136 | no | \(1\) | \(1\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{127}{136}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{133}{136}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{71}{136}\right)\) |
\(\chi_{1096}(25,\cdot)\) | 1096.bb | 68 | no | \(1\) | \(1\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{31}{34}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{29}{68}\right)\) |
\(\chi_{1096}(27,\cdot)\) | 1096.bc | 136 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{136}\right)\) | \(e\left(\frac{21}{136}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{61}{136}\right)\) |
\(\chi_{1096}(29,\cdot)\) | 1096.bf | 136 | yes | \(-1\) | \(1\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{31}{136}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{37}{136}\right)\) |
\(\chi_{1096}(31,\cdot)\) | 1096.bd | 136 | no | \(1\) | \(1\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{35}{136}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{11}{136}\right)\) |
\(\chi_{1096}(33,\cdot)\) | 1096.be | 136 | no | \(-1\) | \(1\) | \(e\left(\frac{123}{136}\right)\) | \(e\left(\frac{113}{136}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{83}{136}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{121}{136}\right)\) |
\(\chi_{1096}(35,\cdot)\) | 1096.bc | 136 | yes | \(1\) | \(1\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{3}{136}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{67}{136}\right)\) |
\(\chi_{1096}(37,\cdot)\) | 1096.j | 4 | yes | \(1\) | \(1\) | \(i\) | \(-i\) | \(-1\) | \(-1\) | \(1\) | \(i\) | \(1\) | \(-1\) | \(1\) | \(-i\) |
\(\chi_{1096}(39,\cdot)\) | 1096.y | 68 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{15}{68}\right)\) |
\(\chi_{1096}(41,\cdot)\) | 1096.n | 8 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(-i\) | \(-i\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) | \(i\) | \(i\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{1096}(43,\cdot)\) | 1096.bc | 136 | yes | \(1\) | \(1\) | \(e\left(\frac{97}{136}\right)\) | \(e\left(\frac{135}{136}\right)\) | \(e\left(\frac{31}{68}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{45}{136}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{23}{136}\right)\) |
\(\chi_{1096}(45,\cdot)\) | 1096.bf | 136 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{136}\right)\) | \(e\left(\frac{131}{136}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{35}{68}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{115}{136}\right)\) |
\(\chi_{1096}(47,\cdot)\) | 1096.bd | 136 | no | \(1\) | \(1\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{67}{136}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{1}{136}\right)\) |
\(\chi_{1096}(49,\cdot)\) | 1096.w | 34 | no | \(1\) | \(1\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) |
\(\chi_{1096}(51,\cdot)\) | 1096.bc | 136 | yes | \(1\) | \(1\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{37}{68}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{113}{136}\right)\) |
\(\chi_{1096}(53,\cdot)\) | 1096.bf | 136 | yes | \(-1\) | \(1\) | \(e\left(\frac{63}{136}\right)\) | \(e\left(\frac{101}{136}\right)\) | \(e\left(\frac{31}{68}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{79}{136}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{125}{136}\right)\) |
\(\chi_{1096}(55,\cdot)\) | 1096.bd | 136 | no | \(1\) | \(1\) | \(e\left(\frac{129}{136}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{39}{136}\right)\) |
\(\chi_{1096}(57,\cdot)\) | 1096.be | 136 | no | \(-1\) | \(1\) | \(e\left(\frac{47}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{35}{68}\right)\) | \(e\left(\frac{47}{68}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{117}{136}\right)\) |
\(\chi_{1096}(59,\cdot)\) | 1096.s | 34 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) |
\(\chi_{1096}(61,\cdot)\) | 1096.ba | 68 | yes | \(1\) | \(1\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{59}{68}\right)\) |
\(\chi_{1096}(63,\cdot)\) | 1096.t | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{31}{34}\right)\) |