sage: H = DirichletGroup(3645)
pari: g = idealstar(,3645,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1944 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{972}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{3645}(731,\cdot)$, $\chi_{3645}(2917,\cdot)$ |
First 32 of 1944 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{3645}(1,\cdot)\) | 3645.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{3645}(2,\cdot)\) | 3645.bj | 972 | yes | \(1\) | \(1\) | \(e\left(\frac{245}{972}\right)\) | \(e\left(\frac{245}{486}\right)\) | \(e\left(\frac{59}{972}\right)\) | \(e\left(\frac{245}{324}\right)\) | \(e\left(\frac{283}{486}\right)\) | \(e\left(\frac{421}{972}\right)\) | \(e\left(\frac{76}{243}\right)\) | \(e\left(\frac{2}{243}\right)\) | \(e\left(\frac{103}{324}\right)\) | \(e\left(\frac{25}{162}\right)\) |
| \(\chi_{3645}(4,\cdot)\) | 3645.bh | 486 | yes | \(1\) | \(1\) | \(e\left(\frac{245}{486}\right)\) | \(e\left(\frac{2}{243}\right)\) | \(e\left(\frac{59}{486}\right)\) | \(e\left(\frac{83}{162}\right)\) | \(e\left(\frac{40}{243}\right)\) | \(e\left(\frac{421}{486}\right)\) | \(e\left(\frac{152}{243}\right)\) | \(e\left(\frac{4}{243}\right)\) | \(e\left(\frac{103}{162}\right)\) | \(e\left(\frac{25}{81}\right)\) |
| \(\chi_{3645}(7,\cdot)\) | 3645.bi | 972 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{972}\right)\) | \(e\left(\frac{59}{486}\right)\) | \(e\left(\frac{647}{972}\right)\) | \(e\left(\frac{59}{324}\right)\) | \(e\left(\frac{104}{243}\right)\) | \(e\left(\frac{877}{972}\right)\) | \(e\left(\frac{353}{486}\right)\) | \(e\left(\frac{59}{243}\right)\) | \(e\left(\frac{1}{324}\right)\) | \(e\left(\frac{49}{162}\right)\) |
| \(\chi_{3645}(8,\cdot)\) | 3645.be | 324 | no | \(1\) | \(1\) | \(e\left(\frac{245}{324}\right)\) | \(e\left(\frac{83}{162}\right)\) | \(e\left(\frac{59}{324}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{121}{162}\right)\) | \(e\left(\frac{97}{324}\right)\) | \(e\left(\frac{76}{81}\right)\) | \(e\left(\frac{2}{81}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{25}{54}\right)\) |
| \(\chi_{3645}(11,\cdot)\) | 3645.bg | 486 | no | \(-1\) | \(1\) | \(e\left(\frac{283}{486}\right)\) | \(e\left(\frac{40}{243}\right)\) | \(e\left(\frac{104}{243}\right)\) | \(e\left(\frac{121}{162}\right)\) | \(e\left(\frac{385}{486}\right)\) | \(e\left(\frac{79}{243}\right)\) | \(e\left(\frac{5}{486}\right)\) | \(e\left(\frac{80}{243}\right)\) | \(e\left(\frac{35}{162}\right)\) | \(e\left(\frac{14}{81}\right)\) |
| \(\chi_{3645}(13,\cdot)\) | 3645.bi | 972 | yes | \(-1\) | \(1\) | \(e\left(\frac{421}{972}\right)\) | \(e\left(\frac{421}{486}\right)\) | \(e\left(\frac{877}{972}\right)\) | \(e\left(\frac{97}{324}\right)\) | \(e\left(\frac{79}{243}\right)\) | \(e\left(\frac{47}{972}\right)\) | \(e\left(\frac{163}{486}\right)\) | \(e\left(\frac{178}{243}\right)\) | \(e\left(\frac{95}{324}\right)\) | \(e\left(\frac{119}{162}\right)\) |
| \(\chi_{3645}(14,\cdot)\) | 3645.bf | 486 | yes | \(-1\) | \(1\) | \(e\left(\frac{76}{243}\right)\) | \(e\left(\frac{152}{243}\right)\) | \(e\left(\frac{353}{486}\right)\) | \(e\left(\frac{76}{81}\right)\) | \(e\left(\frac{5}{486}\right)\) | \(e\left(\frac{163}{486}\right)\) | \(e\left(\frac{19}{486}\right)\) | \(e\left(\frac{61}{243}\right)\) | \(e\left(\frac{26}{81}\right)\) | \(e\left(\frac{37}{81}\right)\) |
| \(\chi_{3645}(16,\cdot)\) | 3645.bc | 243 | no | \(1\) | \(1\) | \(e\left(\frac{2}{243}\right)\) | \(e\left(\frac{4}{243}\right)\) | \(e\left(\frac{59}{243}\right)\) | \(e\left(\frac{2}{81}\right)\) | \(e\left(\frac{80}{243}\right)\) | \(e\left(\frac{178}{243}\right)\) | \(e\left(\frac{61}{243}\right)\) | \(e\left(\frac{8}{243}\right)\) | \(e\left(\frac{22}{81}\right)\) | \(e\left(\frac{50}{81}\right)\) |
| \(\chi_{3645}(17,\cdot)\) | 3645.be | 324 | no | \(1\) | \(1\) | \(e\left(\frac{103}{324}\right)\) | \(e\left(\frac{103}{162}\right)\) | \(e\left(\frac{1}{324}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{35}{162}\right)\) | \(e\left(\frac{95}{324}\right)\) | \(e\left(\frac{26}{81}\right)\) | \(e\left(\frac{22}{81}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{5}{54}\right)\) |
| \(\chi_{3645}(19,\cdot)\) | 3645.ba | 162 | no | \(1\) | \(1\) | \(e\left(\frac{25}{162}\right)\) | \(e\left(\frac{25}{81}\right)\) | \(e\left(\frac{49}{162}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{14}{81}\right)\) | \(e\left(\frac{119}{162}\right)\) | \(e\left(\frac{37}{81}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{2}{27}\right)\) |
| \(\chi_{3645}(22,\cdot)\) | 3645.bi | 972 | yes | \(-1\) | \(1\) | \(e\left(\frac{811}{972}\right)\) | \(e\left(\frac{325}{486}\right)\) | \(e\left(\frac{475}{972}\right)\) | \(e\left(\frac{163}{324}\right)\) | \(e\left(\frac{91}{243}\right)\) | \(e\left(\frac{737}{972}\right)\) | \(e\left(\frac{157}{486}\right)\) | \(e\left(\frac{82}{243}\right)\) | \(e\left(\frac{173}{324}\right)\) | \(e\left(\frac{53}{162}\right)\) |
| \(\chi_{3645}(23,\cdot)\) | 3645.bj | 972 | yes | \(1\) | \(1\) | \(e\left(\frac{535}{972}\right)\) | \(e\left(\frac{49}{486}\right)\) | \(e\left(\frac{109}{972}\right)\) | \(e\left(\frac{211}{324}\right)\) | \(e\left(\frac{251}{486}\right)\) | \(e\left(\frac{959}{972}\right)\) | \(e\left(\frac{161}{243}\right)\) | \(e\left(\frac{49}{243}\right)\) | \(e\left(\frac{53}{324}\right)\) | \(e\left(\frac{5}{162}\right)\) |
| \(\chi_{3645}(26,\cdot)\) | 3645.u | 54 | no | \(-1\) | \(1\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{26}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{8}{9}\right)\) |
| \(\chi_{3645}(28,\cdot)\) | 3645.x | 108 | no | \(-1\) | \(1\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) |
| \(\chi_{3645}(29,\cdot)\) | 3645.bf | 486 | yes | \(-1\) | \(1\) | \(e\left(\frac{221}{243}\right)\) | \(e\left(\frac{199}{243}\right)\) | \(e\left(\frac{403}{486}\right)\) | \(e\left(\frac{59}{81}\right)\) | \(e\left(\frac{427}{486}\right)\) | \(e\left(\frac{215}{486}\right)\) | \(e\left(\frac{359}{486}\right)\) | \(e\left(\frac{155}{243}\right)\) | \(e\left(\frac{1}{81}\right)\) | \(e\left(\frac{17}{81}\right)\) |
| \(\chi_{3645}(31,\cdot)\) | 3645.bc | 243 | no | \(1\) | \(1\) | \(e\left(\frac{172}{243}\right)\) | \(e\left(\frac{101}{243}\right)\) | \(e\left(\frac{214}{243}\right)\) | \(e\left(\frac{10}{81}\right)\) | \(e\left(\frac{76}{243}\right)\) | \(e\left(\frac{242}{243}\right)\) | \(e\left(\frac{143}{243}\right)\) | \(e\left(\frac{202}{243}\right)\) | \(e\left(\frac{29}{81}\right)\) | \(e\left(\frac{7}{81}\right)\) |
| \(\chi_{3645}(32,\cdot)\) | 3645.bj | 972 | yes | \(1\) | \(1\) | \(e\left(\frac{253}{972}\right)\) | \(e\left(\frac{253}{486}\right)\) | \(e\left(\frac{295}{972}\right)\) | \(e\left(\frac{253}{324}\right)\) | \(e\left(\frac{443}{486}\right)\) | \(e\left(\frac{161}{972}\right)\) | \(e\left(\frac{137}{243}\right)\) | \(e\left(\frac{10}{243}\right)\) | \(e\left(\frac{191}{324}\right)\) | \(e\left(\frac{125}{162}\right)\) |
| \(\chi_{3645}(34,\cdot)\) | 3645.bh | 486 | yes | \(1\) | \(1\) | \(e\left(\frac{277}{486}\right)\) | \(e\left(\frac{34}{243}\right)\) | \(e\left(\frac{31}{486}\right)\) | \(e\left(\frac{115}{162}\right)\) | \(e\left(\frac{194}{243}\right)\) | \(e\left(\frac{353}{486}\right)\) | \(e\left(\frac{154}{243}\right)\) | \(e\left(\frac{68}{243}\right)\) | \(e\left(\frac{131}{162}\right)\) | \(e\left(\frac{20}{81}\right)\) |
| \(\chi_{3645}(37,\cdot)\) | 3645.bd | 324 | no | \(-1\) | \(1\) | \(e\left(\frac{253}{324}\right)\) | \(e\left(\frac{91}{162}\right)\) | \(e\left(\frac{133}{324}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{19}{81}\right)\) | \(e\left(\frac{323}{324}\right)\) | \(e\left(\frac{31}{162}\right)\) | \(e\left(\frac{10}{81}\right)\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{17}{54}\right)\) |
| \(\chi_{3645}(38,\cdot)\) | 3645.bj | 972 | yes | \(1\) | \(1\) | \(e\left(\frac{395}{972}\right)\) | \(e\left(\frac{395}{486}\right)\) | \(e\left(\frac{353}{972}\right)\) | \(e\left(\frac{71}{324}\right)\) | \(e\left(\frac{367}{486}\right)\) | \(e\left(\frac{163}{972}\right)\) | \(e\left(\frac{187}{243}\right)\) | \(e\left(\frac{152}{243}\right)\) | \(e\left(\frac{133}{324}\right)\) | \(e\left(\frac{37}{162}\right)\) |
| \(\chi_{3645}(41,\cdot)\) | 3645.bg | 486 | no | \(-1\) | \(1\) | \(e\left(\frac{215}{486}\right)\) | \(e\left(\frac{215}{243}\right)\) | \(e\left(\frac{73}{243}\right)\) | \(e\left(\frac{53}{162}\right)\) | \(e\left(\frac{95}{486}\right)\) | \(e\left(\frac{212}{243}\right)\) | \(e\left(\frac{361}{486}\right)\) | \(e\left(\frac{187}{243}\right)\) | \(e\left(\frac{97}{162}\right)\) | \(e\left(\frac{55}{81}\right)\) |
| \(\chi_{3645}(43,\cdot)\) | 3645.bi | 972 | yes | \(-1\) | \(1\) | \(e\left(\frac{665}{972}\right)\) | \(e\left(\frac{179}{486}\right)\) | \(e\left(\frac{785}{972}\right)\) | \(e\left(\frac{17}{324}\right)\) | \(e\left(\frac{89}{243}\right)\) | \(e\left(\frac{379}{972}\right)\) | \(e\left(\frac{239}{486}\right)\) | \(e\left(\frac{179}{243}\right)\) | \(e\left(\frac{187}{324}\right)\) | \(e\left(\frac{91}{162}\right)\) |
| \(\chi_{3645}(44,\cdot)\) | 3645.bb | 162 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{81}\right)\) | \(e\left(\frac{14}{81}\right)\) | \(e\left(\frac{89}{162}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{155}{162}\right)\) | \(e\left(\frac{31}{162}\right)\) | \(e\left(\frac{103}{162}\right)\) | \(e\left(\frac{28}{81}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) |
| \(\chi_{3645}(46,\cdot)\) | 3645.w | 81 | no | \(1\) | \(1\) | \(e\left(\frac{65}{81}\right)\) | \(e\left(\frac{49}{81}\right)\) | \(e\left(\frac{14}{81}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{8}{81}\right)\) | \(e\left(\frac{34}{81}\right)\) | \(e\left(\frac{79}{81}\right)\) | \(e\left(\frac{17}{81}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{5}{27}\right)\) |
| \(\chi_{3645}(47,\cdot)\) | 3645.bj | 972 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{972}\right)\) | \(e\left(\frac{41}{486}\right)\) | \(e\left(\frac{359}{972}\right)\) | \(e\left(\frac{41}{324}\right)\) | \(e\left(\frac{91}{486}\right)\) | \(e\left(\frac{733}{972}\right)\) | \(e\left(\frac{100}{243}\right)\) | \(e\left(\frac{41}{243}\right)\) | \(e\left(\frac{127}{324}\right)\) | \(e\left(\frac{67}{162}\right)\) |
| \(\chi_{3645}(49,\cdot)\) | 3645.bh | 486 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{486}\right)\) | \(e\left(\frac{59}{243}\right)\) | \(e\left(\frac{161}{486}\right)\) | \(e\left(\frac{59}{162}\right)\) | \(e\left(\frac{208}{243}\right)\) | \(e\left(\frac{391}{486}\right)\) | \(e\left(\frac{110}{243}\right)\) | \(e\left(\frac{118}{243}\right)\) | \(e\left(\frac{1}{162}\right)\) | \(e\left(\frac{49}{81}\right)\) |
| \(\chi_{3645}(52,\cdot)\) | 3645.bi | 972 | yes | \(-1\) | \(1\) | \(e\left(\frac{911}{972}\right)\) | \(e\left(\frac{425}{486}\right)\) | \(e\left(\frac{23}{972}\right)\) | \(e\left(\frac{263}{324}\right)\) | \(e\left(\frac{119}{243}\right)\) | \(e\left(\frac{889}{972}\right)\) | \(e\left(\frac{467}{486}\right)\) | \(e\left(\frac{182}{243}\right)\) | \(e\left(\frac{301}{324}\right)\) | \(e\left(\frac{7}{162}\right)\) |
| \(\chi_{3645}(53,\cdot)\) | 3645.y | 108 | no | \(1\) | \(1\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) |
| \(\chi_{3645}(56,\cdot)\) | 3645.bg | 486 | no | \(-1\) | \(1\) | \(e\left(\frac{397}{486}\right)\) | \(e\left(\frac{154}{243}\right)\) | \(e\left(\frac{206}{243}\right)\) | \(e\left(\frac{73}{162}\right)\) | \(e\left(\frac{85}{486}\right)\) | \(e\left(\frac{49}{243}\right)\) | \(e\left(\frac{323}{486}\right)\) | \(e\left(\frac{65}{243}\right)\) | \(e\left(\frac{155}{162}\right)\) | \(e\left(\frac{62}{81}\right)\) |
| \(\chi_{3645}(58,\cdot)\) | 3645.bi | 972 | yes | \(-1\) | \(1\) | \(e\left(\frac{157}{972}\right)\) | \(e\left(\frac{157}{486}\right)\) | \(e\left(\frac{865}{972}\right)\) | \(e\left(\frac{157}{324}\right)\) | \(e\left(\frac{112}{243}\right)\) | \(e\left(\frac{851}{972}\right)\) | \(e\left(\frac{25}{486}\right)\) | \(e\left(\frac{157}{243}\right)\) | \(e\left(\frac{107}{324}\right)\) | \(e\left(\frac{59}{162}\right)\) |
| \(\chi_{3645}(59,\cdot)\) | 3645.bf | 486 | yes | \(-1\) | \(1\) | \(e\left(\frac{115}{243}\right)\) | \(e\left(\frac{230}{243}\right)\) | \(e\left(\frac{467}{486}\right)\) | \(e\left(\frac{34}{81}\right)\) | \(e\left(\frac{209}{486}\right)\) | \(e\left(\frac{301}{486}\right)\) | \(e\left(\frac{211}{486}\right)\) | \(e\left(\frac{217}{243}\right)\) | \(e\left(\frac{50}{81}\right)\) | \(e\left(\frac{40}{81}\right)\) |