sage: H = DirichletGroup(338130)
pari: g = idealstar(,338130,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 78336 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{4}\times C_{12}\times C_{816}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{338130}(262991,\cdot)$, $\chi_{338130}(67627,\cdot)$, $\chi_{338130}(104041,\cdot)$, $\chi_{338130}(145081,\cdot)$ |
First 32 of 78336 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 | \(-1\) | \(1\) | \(7\) | \(11\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{338130}(1,\cdot)\) | 338130.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{338130}(7,\cdot)\) | 338130.bwr | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{272}\right)\) | \(e\left(\frac{155}{816}\right)\) | \(e\left(\frac{25}{408}\right)\) | \(e\left(\frac{89}{272}\right)\) | \(e\left(\frac{53}{816}\right)\) | \(e\left(\frac{581}{816}\right)\) | \(e\left(\frac{145}{816}\right)\) | \(e\left(\frac{189}{272}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{133}{204}\right)\) |
| \(\chi_{338130}(11,\cdot)\) | 338130.bzh | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{155}{816}\right)\) | \(e\left(\frac{53}{272}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{427}{816}\right)\) | \(e\left(\frac{19}{272}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{809}{816}\right)\) | \(e\left(\frac{715}{816}\right)\) | \(e\left(\frac{385}{408}\right)\) | \(e\left(\frac{19}{51}\right)\) |
| \(\chi_{338130}(19,\cdot)\) | 338130.but | 408 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{408}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{59}{408}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{23}{408}\right)\) | \(e\left(\frac{89}{408}\right)\) | \(e\left(\frac{197}{204}\right)\) | \(e\left(\frac{61}{68}\right)\) |
| \(\chi_{338130}(23,\cdot)\) | 338130.bwg | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{89}{272}\right)\) | \(e\left(\frac{427}{816}\right)\) | \(e\left(\frac{59}{408}\right)\) | \(e\left(\frac{157}{272}\right)\) | \(e\left(\frac{121}{816}\right)\) | \(e\left(\frac{445}{816}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{53}{272}\right)\) | \(e\left(\frac{73}{136}\right)\) | \(e\left(\frac{7}{102}\right)\) |
| \(\chi_{338130}(29,\cdot)\) | 338130.byc | 816 | no | \(1\) | \(1\) | \(e\left(\frac{53}{816}\right)\) | \(e\left(\frac{19}{272}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{121}{816}\right)\) | \(e\left(\frac{257}{272}\right)\) | \(e\left(\frac{383}{816}\right)\) | \(e\left(\frac{95}{816}\right)\) | \(e\left(\frac{613}{816}\right)\) | \(e\left(\frac{283}{408}\right)\) | \(e\left(\frac{127}{204}\right)\) |
| \(\chi_{338130}(31,\cdot)\) | 338130.bvt | 816 | no | \(1\) | \(1\) | \(e\left(\frac{581}{816}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{445}{816}\right)\) | \(e\left(\frac{383}{816}\right)\) | \(e\left(\frac{583}{816}\right)\) | \(e\left(\frac{141}{272}\right)\) | \(e\left(\frac{61}{816}\right)\) | \(e\left(\frac{127}{408}\right)\) | \(e\left(\frac{91}{102}\right)\) |
| \(\chi_{338130}(37,\cdot)\) | 338130.byq | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{145}{816}\right)\) | \(e\left(\frac{809}{816}\right)\) | \(e\left(\frac{23}{408}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{95}{816}\right)\) | \(e\left(\frac{141}{272}\right)\) | \(e\left(\frac{419}{816}\right)\) | \(e\left(\frac{557}{816}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{29}{68}\right)\) |
| \(\chi_{338130}(41,\cdot)\) | 338130.bwl | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{189}{272}\right)\) | \(e\left(\frac{715}{816}\right)\) | \(e\left(\frac{89}{408}\right)\) | \(e\left(\frac{53}{272}\right)\) | \(e\left(\frac{613}{816}\right)\) | \(e\left(\frac{61}{816}\right)\) | \(e\left(\frac{557}{816}\right)\) | \(e\left(\frac{205}{272}\right)\) | \(e\left(\frac{79}{136}\right)\) | \(e\left(\frac{97}{102}\right)\) |
| \(\chi_{338130}(43,\cdot)\) | 338130.bua | 408 | no | \(-1\) | \(1\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{385}{408}\right)\) | \(e\left(\frac{197}{204}\right)\) | \(e\left(\frac{73}{136}\right)\) | \(e\left(\frac{283}{408}\right)\) | \(e\left(\frac{127}{408}\right)\) | \(e\left(\frac{41}{408}\right)\) | \(e\left(\frac{79}{136}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{1}{204}\right)\) |
| \(\chi_{338130}(47,\cdot)\) | 338130.bmn | 204 | no | \(-1\) | \(1\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{61}{68}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{127}{204}\right)\) | \(e\left(\frac{91}{102}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{1}{204}\right)\) | \(e\left(\frac{95}{102}\right)\) |
| \(\chi_{338130}(49,\cdot)\) | 338130.bsn | 408 | no | \(1\) | \(1\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{155}{408}\right)\) | \(e\left(\frac{25}{204}\right)\) | \(e\left(\frac{89}{136}\right)\) | \(e\left(\frac{53}{408}\right)\) | \(e\left(\frac{173}{408}\right)\) | \(e\left(\frac{145}{408}\right)\) | \(e\left(\frac{53}{136}\right)\) | \(e\left(\frac{5}{68}\right)\) | \(e\left(\frac{31}{102}\right)\) |
| \(\chi_{338130}(53,\cdot)\) | 338130.bfs | 136 | no | \(1\) | \(1\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{87}{136}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{67}{68}\right)\) |
| \(\chi_{338130}(59,\cdot)\) | 338130.buv | 408 | no | \(1\) | \(1\) | \(e\left(\frac{107}{408}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{277}{408}\right)\) | \(e\left(\frac{5}{136}\right)\) | \(e\left(\frac{269}{408}\right)\) | \(e\left(\frac{365}{408}\right)\) | \(e\left(\frac{79}{408}\right)\) | \(e\left(\frac{19}{204}\right)\) | \(e\left(\frac{23}{204}\right)\) |
| \(\chi_{338130}(61,\cdot)\) | 338130.byx | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{161}{272}\right)\) | \(e\left(\frac{191}{816}\right)\) | \(e\left(\frac{271}{408}\right)\) | \(e\left(\frac{93}{272}\right)\) | \(e\left(\frac{293}{816}\right)\) | \(e\left(\frac{737}{816}\right)\) | \(e\left(\frac{409}{816}\right)\) | \(e\left(\frac{225}{272}\right)\) | \(e\left(\frac{27}{136}\right)\) | \(e\left(\frac{181}{204}\right)\) |
| \(\chi_{338130}(67,\cdot)\) | 338130.bgx | 204 | no | \(1\) | \(1\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{97}{204}\right)\) | \(e\left(\frac{79}{204}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{103}{204}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{49}{102}\right)\) |
| \(\chi_{338130}(71,\cdot)\) | 338130.bvk | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{29}{816}\right)\) | \(e\left(\frac{121}{816}\right)\) | \(e\left(\frac{127}{408}\right)\) | \(e\left(\frac{301}{816}\right)\) | \(e\left(\frac{223}{816}\right)\) | \(e\left(\frac{69}{272}\right)\) | \(e\left(\frac{655}{816}\right)\) | \(e\left(\frac{397}{816}\right)\) | \(e\left(\frac{151}{408}\right)\) | \(e\left(\frac{4}{17}\right)\) |
| \(\chi_{338130}(73,\cdot)\) | 338130.bpw | 272 | no | \(-1\) | \(1\) | \(e\left(\frac{143}{272}\right)\) | \(e\left(\frac{191}{272}\right)\) | \(e\left(\frac{33}{136}\right)\) | \(e\left(\frac{7}{272}\right)\) | \(e\left(\frac{89}{272}\right)\) | \(e\left(\frac{193}{272}\right)\) | \(e\left(\frac{205}{272}\right)\) | \(e\left(\frac{267}{272}\right)\) | \(e\left(\frac{115}{136}\right)\) | \(e\left(\frac{11}{68}\right)\) |
| \(\chi_{338130}(77,\cdot)\) | 338130.btq | 408 | no | \(1\) | \(1\) | \(e\left(\frac{211}{408}\right)\) | \(e\left(\frac{157}{408}\right)\) | \(e\left(\frac{11}{68}\right)\) | \(e\left(\frac{347}{408}\right)\) | \(e\left(\frac{55}{408}\right)\) | \(e\left(\frac{23}{408}\right)\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{233}{408}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{5}{204}\right)\) |
| \(\chi_{338130}(79,\cdot)\) | 338130.byf | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{271}{816}\right)\) | \(e\left(\frac{643}{816}\right)\) | \(e\left(\frac{81}{136}\right)\) | \(e\left(\frac{611}{816}\right)\) | \(e\left(\frac{337}{816}\right)\) | \(e\left(\frac{701}{816}\right)\) | \(e\left(\frac{191}{272}\right)\) | \(e\left(\frac{263}{816}\right)\) | \(e\left(\frac{377}{408}\right)\) | \(e\left(\frac{115}{204}\right)\) |
| \(\chi_{338130}(83,\cdot)\) | 338130.bvd | 408 | no | \(-1\) | \(1\) | \(e\left(\frac{371}{408}\right)\) | \(e\left(\frac{161}{408}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{133}{408}\right)\) | \(e\left(\frac{365}{408}\right)\) | \(e\left(\frac{403}{408}\right)\) | \(e\left(\frac{131}{136}\right)\) | \(e\left(\frac{313}{408}\right)\) | \(e\left(\frac{47}{102}\right)\) | \(e\left(\frac{28}{51}\right)\) |
| \(\chi_{338130}(89,\cdot)\) | 338130.bhe | 204 | no | \(1\) | \(1\) | \(e\left(\frac{23}{102}\right)\) | \(e\left(\frac{1}{102}\right)\) | \(e\left(\frac{169}{204}\right)\) | \(e\left(\frac{29}{204}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{47}{68}\right)\) |
| \(\chi_{338130}(97,\cdot)\) | 338130.byv | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{55}{272}\right)\) | \(e\left(\frac{461}{816}\right)\) | \(e\left(\frac{127}{408}\right)\) | \(e\left(\frac{55}{272}\right)\) | \(e\left(\frac{563}{816}\right)\) | \(e\left(\frac{275}{816}\right)\) | \(e\left(\frac{655}{816}\right)\) | \(e\left(\frac{155}{272}\right)\) | \(e\left(\frac{39}{136}\right)\) | \(e\left(\frac{133}{204}\right)\) |
| \(\chi_{338130}(101,\cdot)\) | 338130.bez | 102 | no | \(-1\) | \(1\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{7}{51}\right)\) |
| \(\chi_{338130}(103,\cdot)\) | 338130.biu | 204 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{204}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{5}{17}\right)\) | \(e\left(\frac{79}{204}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{23}{204}\right)\) |
| \(\chi_{338130}(107,\cdot)\) | 338130.bvo | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{577}{816}\right)\) | \(e\left(\frac{65}{816}\right)\) | \(e\left(\frac{5}{408}\right)\) | \(e\left(\frac{509}{816}\right)\) | \(e\left(\frac{371}{816}\right)\) | \(e\left(\frac{109}{272}\right)\) | \(e\left(\frac{539}{816}\right)\) | \(e\left(\frac{365}{816}\right)\) | \(e\left(\frac{377}{408}\right)\) | \(e\left(\frac{11}{17}\right)\) |
| \(\chi_{338130}(109,\cdot)\) | 338130.bqk | 272 | no | \(1\) | \(1\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{113}{272}\right)\) | \(e\left(\frac{27}{136}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{79}{272}\right)\) | \(e\left(\frac{127}{272}\right)\) | \(e\left(\frac{7}{272}\right)\) | \(e\left(\frac{101}{272}\right)\) | \(e\left(\frac{91}{136}\right)\) | \(e\left(\frac{13}{34}\right)\) |
| \(\chi_{338130}(113,\cdot)\) | 338130.bzj | 816 | no | \(-1\) | \(1\) | \(e\left(\frac{91}{816}\right)\) | \(e\left(\frac{57}{272}\right)\) | \(e\left(\frac{55}{408}\right)\) | \(e\left(\frac{431}{816}\right)\) | \(e\left(\frac{91}{272}\right)\) | \(e\left(\frac{61}{816}\right)\) | \(e\left(\frac{217}{816}\right)\) | \(e\left(\frac{479}{816}\right)\) | \(e\left(\frac{203}{408}\right)\) | \(e\left(\frac{23}{51}\right)\) |
| \(\chi_{338130}(121,\cdot)\) | 338130.btc | 408 | no | \(1\) | \(1\) | \(e\left(\frac{155}{408}\right)\) | \(e\left(\frac{53}{136}\right)\) | \(e\left(\frac{41}{204}\right)\) | \(e\left(\frac{19}{408}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{281}{408}\right)\) | \(e\left(\frac{401}{408}\right)\) | \(e\left(\frac{307}{408}\right)\) | \(e\left(\frac{181}{204}\right)\) | \(e\left(\frac{38}{51}\right)\) |
| \(\chi_{338130}(127,\cdot)\) | 338130.bty | 408 | no | \(-1\) | \(1\) | \(e\left(\frac{191}{408}\right)\) | \(e\left(\frac{301}{408}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{259}{408}\right)\) | \(e\left(\frac{199}{408}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{241}{408}\right)\) | \(e\left(\frac{121}{408}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{5}{68}\right)\) |
| \(\chi_{338130}(131,\cdot)\) | 338130.yr | 48 | no | \(1\) | \(1\) | \(e\left(\frac{13}{48}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) |
| \(\chi_{338130}(133,\cdot)\) | 338130.bzs | 816 | no | \(1\) | \(1\) | \(e\left(\frac{317}{816}\right)\) | \(e\left(\frac{79}{272}\right)\) | \(e\left(\frac{353}{408}\right)\) | \(e\left(\frac{385}{816}\right)\) | \(e\left(\frac{45}{272}\right)\) | \(e\left(\frac{755}{816}\right)\) | \(e\left(\frac{191}{816}\right)\) | \(e\left(\frac{745}{816}\right)\) | \(e\left(\frac{1}{408}\right)\) | \(e\left(\frac{28}{51}\right)\) |