sage: H = DirichletGroup(1149)
pari: g = idealstar(,1149,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 764 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{382}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{1149}(767,\cdot)$, $\chi_{1149}(388,\cdot)$ |
First 32 of 764 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{1149}(1,\cdot)\) | 1149.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{1149}(2,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{193}{382}\right)\) | \(e\left(\frac{2}{191}\right)\) | \(e\left(\frac{325}{382}\right)\) | \(e\left(\frac{87}{191}\right)\) | \(e\left(\frac{197}{382}\right)\) | \(e\left(\frac{68}{191}\right)\) | \(e\left(\frac{267}{382}\right)\) | \(e\left(\frac{26}{191}\right)\) | \(e\left(\frac{367}{382}\right)\) | \(e\left(\frac{4}{191}\right)\) |
| \(\chi_{1149}(4,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{2}{191}\right)\) | \(e\left(\frac{4}{191}\right)\) | \(e\left(\frac{134}{191}\right)\) | \(e\left(\frac{174}{191}\right)\) | \(e\left(\frac{6}{191}\right)\) | \(e\left(\frac{136}{191}\right)\) | \(e\left(\frac{76}{191}\right)\) | \(e\left(\frac{52}{191}\right)\) | \(e\left(\frac{176}{191}\right)\) | \(e\left(\frac{8}{191}\right)\) |
| \(\chi_{1149}(5,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{325}{382}\right)\) | \(e\left(\frac{134}{191}\right)\) | \(e\left(\frac{96}{191}\right)\) | \(e\left(\frac{99}{191}\right)\) | \(e\left(\frac{211}{382}\right)\) | \(e\left(\frac{135}{382}\right)\) | \(e\left(\frac{63}{191}\right)\) | \(e\left(\frac{237}{382}\right)\) | \(e\left(\frac{141}{382}\right)\) | \(e\left(\frac{77}{191}\right)\) |
| \(\chi_{1149}(7,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{87}{191}\right)\) | \(e\left(\frac{174}{191}\right)\) | \(e\left(\frac{99}{191}\right)\) | \(e\left(\frac{120}{191}\right)\) | \(e\left(\frac{70}{191}\right)\) | \(e\left(\frac{186}{191}\right)\) | \(e\left(\frac{59}{191}\right)\) | \(e\left(\frac{161}{191}\right)\) | \(e\left(\frac{16}{191}\right)\) | \(e\left(\frac{157}{191}\right)\) |
| \(\chi_{1149}(8,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{197}{382}\right)\) | \(e\left(\frac{6}{191}\right)\) | \(e\left(\frac{211}{382}\right)\) | \(e\left(\frac{70}{191}\right)\) | \(e\left(\frac{209}{382}\right)\) | \(e\left(\frac{13}{191}\right)\) | \(e\left(\frac{37}{382}\right)\) | \(e\left(\frac{78}{191}\right)\) | \(e\left(\frac{337}{382}\right)\) | \(e\left(\frac{12}{191}\right)\) |
| \(\chi_{1149}(10,\cdot)\) | 1149.f | 382 | no | \(-1\) | \(1\) | \(e\left(\frac{68}{191}\right)\) | \(e\left(\frac{136}{191}\right)\) | \(e\left(\frac{135}{382}\right)\) | \(e\left(\frac{186}{191}\right)\) | \(e\left(\frac{13}{191}\right)\) | \(e\left(\frac{271}{382}\right)\) | \(e\left(\frac{11}{382}\right)\) | \(e\left(\frac{289}{382}\right)\) | \(e\left(\frac{63}{191}\right)\) | \(e\left(\frac{81}{191}\right)\) |
| \(\chi_{1149}(11,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{267}{382}\right)\) | \(e\left(\frac{76}{191}\right)\) | \(e\left(\frac{63}{191}\right)\) | \(e\left(\frac{59}{191}\right)\) | \(e\left(\frac{37}{382}\right)\) | \(e\left(\frac{11}{382}\right)\) | \(e\left(\frac{107}{191}\right)\) | \(e\left(\frac{257}{382}\right)\) | \(e\left(\frac{3}{382}\right)\) | \(e\left(\frac{152}{191}\right)\) |
| \(\chi_{1149}(13,\cdot)\) | 1149.f | 382 | no | \(-1\) | \(1\) | \(e\left(\frac{26}{191}\right)\) | \(e\left(\frac{52}{191}\right)\) | \(e\left(\frac{237}{382}\right)\) | \(e\left(\frac{161}{191}\right)\) | \(e\left(\frac{78}{191}\right)\) | \(e\left(\frac{289}{382}\right)\) | \(e\left(\frac{257}{382}\right)\) | \(e\left(\frac{15}{382}\right)\) | \(e\left(\frac{187}{191}\right)\) | \(e\left(\frac{104}{191}\right)\) |
| \(\chi_{1149}(14,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{367}{382}\right)\) | \(e\left(\frac{176}{191}\right)\) | \(e\left(\frac{141}{382}\right)\) | \(e\left(\frac{16}{191}\right)\) | \(e\left(\frac{337}{382}\right)\) | \(e\left(\frac{63}{191}\right)\) | \(e\left(\frac{3}{382}\right)\) | \(e\left(\frac{187}{191}\right)\) | \(e\left(\frac{17}{382}\right)\) | \(e\left(\frac{161}{191}\right)\) |
| \(\chi_{1149}(16,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{4}{191}\right)\) | \(e\left(\frac{8}{191}\right)\) | \(e\left(\frac{77}{191}\right)\) | \(e\left(\frac{157}{191}\right)\) | \(e\left(\frac{12}{191}\right)\) | \(e\left(\frac{81}{191}\right)\) | \(e\left(\frac{152}{191}\right)\) | \(e\left(\frac{104}{191}\right)\) | \(e\left(\frac{161}{191}\right)\) | \(e\left(\frac{16}{191}\right)\) |
| \(\chi_{1149}(17,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{85}{382}\right)\) | \(e\left(\frac{85}{191}\right)\) | \(e\left(\frac{347}{382}\right)\) | \(e\left(\frac{164}{191}\right)\) | \(e\left(\frac{255}{382}\right)\) | \(e\left(\frac{25}{191}\right)\) | \(e\left(\frac{365}{382}\right)\) | \(e\left(\frac{150}{191}\right)\) | \(e\left(\frac{31}{382}\right)\) | \(e\left(\frac{170}{191}\right)\) |
| \(\chi_{1149}(19,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{115}{191}\right)\) | \(e\left(\frac{39}{191}\right)\) | \(e\left(\frac{65}{191}\right)\) | \(e\left(\frac{73}{191}\right)\) | \(e\left(\frac{154}{191}\right)\) | \(e\left(\frac{180}{191}\right)\) | \(e\left(\frac{168}{191}\right)\) | \(e\left(\frac{125}{191}\right)\) | \(e\left(\frac{188}{191}\right)\) | \(e\left(\frac{78}{191}\right)\) |
| \(\chi_{1149}(20,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{329}{382}\right)\) | \(e\left(\frac{138}{191}\right)\) | \(e\left(\frac{39}{191}\right)\) | \(e\left(\frac{82}{191}\right)\) | \(e\left(\frac{223}{382}\right)\) | \(e\left(\frac{25}{382}\right)\) | \(e\left(\frac{139}{191}\right)\) | \(e\left(\frac{341}{382}\right)\) | \(e\left(\frac{111}{382}\right)\) | \(e\left(\frac{85}{191}\right)\) |
| \(\chi_{1149}(22,\cdot)\) | 1149.f | 382 | no | \(-1\) | \(1\) | \(e\left(\frac{39}{191}\right)\) | \(e\left(\frac{78}{191}\right)\) | \(e\left(\frac{69}{382}\right)\) | \(e\left(\frac{146}{191}\right)\) | \(e\left(\frac{117}{191}\right)\) | \(e\left(\frac{147}{382}\right)\) | \(e\left(\frac{99}{382}\right)\) | \(e\left(\frac{309}{382}\right)\) | \(e\left(\frac{185}{191}\right)\) | \(e\left(\frac{156}{191}\right)\) |
| \(\chi_{1149}(23,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{303}{382}\right)\) | \(e\left(\frac{112}{191}\right)\) | \(e\left(\frac{55}{382}\right)\) | \(e\left(\frac{97}{191}\right)\) | \(e\left(\frac{145}{382}\right)\) | \(e\left(\frac{179}{191}\right)\) | \(e\left(\frac{245}{382}\right)\) | \(e\left(\frac{119}{191}\right)\) | \(e\left(\frac{115}{382}\right)\) | \(e\left(\frac{33}{191}\right)\) |
| \(\chi_{1149}(25,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{134}{191}\right)\) | \(e\left(\frac{77}{191}\right)\) | \(e\left(\frac{1}{191}\right)\) | \(e\left(\frac{7}{191}\right)\) | \(e\left(\frac{20}{191}\right)\) | \(e\left(\frac{135}{191}\right)\) | \(e\left(\frac{126}{191}\right)\) | \(e\left(\frac{46}{191}\right)\) | \(e\left(\frac{141}{191}\right)\) | \(e\left(\frac{154}{191}\right)\) |
| \(\chi_{1149}(26,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{245}{382}\right)\) | \(e\left(\frac{54}{191}\right)\) | \(e\left(\frac{90}{191}\right)\) | \(e\left(\frac{57}{191}\right)\) | \(e\left(\frac{353}{382}\right)\) | \(e\left(\frac{43}{382}\right)\) | \(e\left(\frac{71}{191}\right)\) | \(e\left(\frac{67}{382}\right)\) | \(e\left(\frac{359}{382}\right)\) | \(e\left(\frac{108}{191}\right)\) |
| \(\chi_{1149}(28,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{89}{191}\right)\) | \(e\left(\frac{178}{191}\right)\) | \(e\left(\frac{42}{191}\right)\) | \(e\left(\frac{103}{191}\right)\) | \(e\left(\frac{76}{191}\right)\) | \(e\left(\frac{131}{191}\right)\) | \(e\left(\frac{135}{191}\right)\) | \(e\left(\frac{22}{191}\right)\) | \(e\left(\frac{1}{191}\right)\) | \(e\left(\frac{165}{191}\right)\) |
| \(\chi_{1149}(29,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{127}{382}\right)\) | \(e\left(\frac{127}{191}\right)\) | \(e\left(\frac{105}{382}\right)\) | \(e\left(\frac{81}{191}\right)\) | \(e\left(\frac{381}{382}\right)\) | \(e\left(\frac{116}{191}\right)\) | \(e\left(\frac{51}{382}\right)\) | \(e\left(\frac{123}{191}\right)\) | \(e\left(\frac{289}{382}\right)\) | \(e\left(\frac{63}{191}\right)\) |
| \(\chi_{1149}(31,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{43}{191}\right)\) | \(e\left(\frac{86}{191}\right)\) | \(e\left(\frac{16}{191}\right)\) | \(e\left(\frac{112}{191}\right)\) | \(e\left(\frac{129}{191}\right)\) | \(e\left(\frac{59}{191}\right)\) | \(e\left(\frac{106}{191}\right)\) | \(e\left(\frac{163}{191}\right)\) | \(e\left(\frac{155}{191}\right)\) | \(e\left(\frac{172}{191}\right)\) |
| \(\chi_{1149}(32,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{201}{382}\right)\) | \(e\left(\frac{10}{191}\right)\) | \(e\left(\frac{97}{382}\right)\) | \(e\left(\frac{53}{191}\right)\) | \(e\left(\frac{221}{382}\right)\) | \(e\left(\frac{149}{191}\right)\) | \(e\left(\frac{189}{382}\right)\) | \(e\left(\frac{130}{191}\right)\) | \(e\left(\frac{307}{382}\right)\) | \(e\left(\frac{20}{191}\right)\) |
| \(\chi_{1149}(34,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{139}{191}\right)\) | \(e\left(\frac{87}{191}\right)\) | \(e\left(\frac{145}{191}\right)\) | \(e\left(\frac{60}{191}\right)\) | \(e\left(\frac{35}{191}\right)\) | \(e\left(\frac{93}{191}\right)\) | \(e\left(\frac{125}{191}\right)\) | \(e\left(\frac{176}{191}\right)\) | \(e\left(\frac{8}{191}\right)\) | \(e\left(\frac{174}{191}\right)\) |
| \(\chi_{1149}(35,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{117}{382}\right)\) | \(e\left(\frac{117}{191}\right)\) | \(e\left(\frac{4}{191}\right)\) | \(e\left(\frac{28}{191}\right)\) | \(e\left(\frac{351}{382}\right)\) | \(e\left(\frac{125}{382}\right)\) | \(e\left(\frac{122}{191}\right)\) | \(e\left(\frac{177}{382}\right)\) | \(e\left(\frac{173}{382}\right)\) | \(e\left(\frac{43}{191}\right)\) |
| \(\chi_{1149}(37,\cdot)\) | 1149.f | 382 | no | \(-1\) | \(1\) | \(e\left(\frac{149}{191}\right)\) | \(e\left(\frac{107}{191}\right)\) | \(e\left(\frac{293}{382}\right)\) | \(e\left(\frac{166}{191}\right)\) | \(e\left(\frac{65}{191}\right)\) | \(e\left(\frac{209}{382}\right)\) | \(e\left(\frac{55}{382}\right)\) | \(e\left(\frac{299}{382}\right)\) | \(e\left(\frac{124}{191}\right)\) | \(e\left(\frac{23}{191}\right)\) |
| \(\chi_{1149}(38,\cdot)\) | 1149.h | 382 | yes | \(-1\) | \(1\) | \(e\left(\frac{41}{382}\right)\) | \(e\left(\frac{41}{191}\right)\) | \(e\left(\frac{73}{382}\right)\) | \(e\left(\frac{160}{191}\right)\) | \(e\left(\frac{123}{382}\right)\) | \(e\left(\frac{57}{191}\right)\) | \(e\left(\frac{221}{382}\right)\) | \(e\left(\frac{151}{191}\right)\) | \(e\left(\frac{361}{382}\right)\) | \(e\left(\frac{82}{191}\right)\) |
| \(\chi_{1149}(40,\cdot)\) | 1149.f | 382 | no | \(-1\) | \(1\) | \(e\left(\frac{70}{191}\right)\) | \(e\left(\frac{140}{191}\right)\) | \(e\left(\frac{21}{382}\right)\) | \(e\left(\frac{169}{191}\right)\) | \(e\left(\frac{19}{191}\right)\) | \(e\left(\frac{161}{382}\right)\) | \(e\left(\frac{163}{382}\right)\) | \(e\left(\frac{11}{382}\right)\) | \(e\left(\frac{48}{191}\right)\) | \(e\left(\frac{89}{191}\right)\) |
| \(\chi_{1149}(41,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{13}{382}\right)\) | \(e\left(\frac{13}{191}\right)\) | \(e\left(\frac{149}{191}\right)\) | \(e\left(\frac{88}{191}\right)\) | \(e\left(\frac{39}{382}\right)\) | \(e\left(\frac{311}{382}\right)\) | \(e\left(\frac{56}{191}\right)\) | \(e\left(\frac{147}{382}\right)\) | \(e\left(\frac{189}{382}\right)\) | \(e\left(\frac{26}{191}\right)\) |
| \(\chi_{1149}(43,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{16}{191}\right)\) | \(e\left(\frac{32}{191}\right)\) | \(e\left(\frac{117}{191}\right)\) | \(e\left(\frac{55}{191}\right)\) | \(e\left(\frac{48}{191}\right)\) | \(e\left(\frac{133}{191}\right)\) | \(e\left(\frac{35}{191}\right)\) | \(e\left(\frac{34}{191}\right)\) | \(e\left(\frac{71}{191}\right)\) | \(e\left(\frac{64}{191}\right)\) |
| \(\chi_{1149}(44,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{271}{382}\right)\) | \(e\left(\frac{80}{191}\right)\) | \(e\left(\frac{6}{191}\right)\) | \(e\left(\frac{42}{191}\right)\) | \(e\left(\frac{49}{382}\right)\) | \(e\left(\frac{283}{382}\right)\) | \(e\left(\frac{183}{191}\right)\) | \(e\left(\frac{361}{382}\right)\) | \(e\left(\frac{355}{382}\right)\) | \(e\left(\frac{160}{191}\right)\) |
| \(\chi_{1149}(46,\cdot)\) | 1149.e | 191 | no | \(1\) | \(1\) | \(e\left(\frac{57}{191}\right)\) | \(e\left(\frac{114}{191}\right)\) | \(e\left(\frac{190}{191}\right)\) | \(e\left(\frac{184}{191}\right)\) | \(e\left(\frac{171}{191}\right)\) | \(e\left(\frac{56}{191}\right)\) | \(e\left(\frac{65}{191}\right)\) | \(e\left(\frac{145}{191}\right)\) | \(e\left(\frac{50}{191}\right)\) | \(e\left(\frac{37}{191}\right)\) |
| \(\chi_{1149}(47,\cdot)\) | 1149.g | 382 | yes | \(1\) | \(1\) | \(e\left(\frac{359}{382}\right)\) | \(e\left(\frac{168}{191}\right)\) | \(e\left(\frac{89}{191}\right)\) | \(e\left(\frac{50}{191}\right)\) | \(e\left(\frac{313}{382}\right)\) | \(e\left(\frac{155}{382}\right)\) | \(e\left(\frac{136}{191}\right)\) | \(e\left(\frac{357}{382}\right)\) | \(e\left(\frac{77}{382}\right)\) | \(e\left(\frac{145}{191}\right)\) |