sage: H = DirichletGroup(987696)
pari: g = idealstar(,987696,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 311904 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{2}\times C_{6}\times C_{12996}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{987696}(617311,\cdot)$, $\chi_{987696}(740773,\cdot)$, $\chi_{987696}(438977,\cdot)$, $\chi_{987696}(857377,\cdot)$ |
First 32 of 311904 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{987696}(1,\cdot)\) | 987696.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{987696}(5,\cdot)\) | 987696.vr | 12996 | yes | \(-1\) | \(1\) | \(e\left(\frac{7727}{12996}\right)\) | \(e\left(\frac{2005}{2166}\right)\) | \(e\left(\frac{667}{1444}\right)\) | \(e\left(\frac{9643}{12996}\right)\) | \(e\left(\frac{5749}{6498}\right)\) | \(e\left(\frac{2515}{3249}\right)\) | \(e\left(\frac{1229}{6498}\right)\) | \(e\left(\frac{9997}{12996}\right)\) | \(e\left(\frac{99}{361}\right)\) | \(e\left(\frac{6761}{12996}\right)\) |
\(\chi_{987696}(7,\cdot)\) | 987696.qy | 2166 | no | \(-1\) | \(1\) | \(e\left(\frac{2005}{2166}\right)\) | \(e\left(\frac{907}{2166}\right)\) | \(e\left(\frac{650}{1083}\right)\) | \(e\left(\frac{119}{722}\right)\) | \(e\left(\frac{235}{1083}\right)\) | \(e\left(\frac{527}{722}\right)\) | \(e\left(\frac{922}{1083}\right)\) | \(e\left(\frac{2009}{2166}\right)\) | \(e\left(\frac{1109}{2166}\right)\) | \(e\left(\frac{373}{1083}\right)\) |
\(\chi_{987696}(11,\cdot)\) | 987696.sq | 4332 | yes | \(1\) | \(1\) | \(e\left(\frac{667}{1444}\right)\) | \(e\left(\frac{650}{1083}\right)\) | \(e\left(\frac{191}{4332}\right)\) | \(e\left(\frac{617}{4332}\right)\) | \(e\left(\frac{1927}{2166}\right)\) | \(e\left(\frac{1753}{2166}\right)\) | \(e\left(\frac{667}{722}\right)\) | \(e\left(\frac{341}{1444}\right)\) | \(e\left(\frac{251}{2166}\right)\) | \(e\left(\frac{269}{4332}\right)\) |
\(\chi_{987696}(13,\cdot)\) | 987696.wb | 12996 | yes | \(-1\) | \(1\) | \(e\left(\frac{9643}{12996}\right)\) | \(e\left(\frac{119}{722}\right)\) | \(e\left(\frac{617}{4332}\right)\) | \(e\left(\frac{623}{12996}\right)\) | \(e\left(\frac{1780}{3249}\right)\) | \(e\left(\frac{1921}{6498}\right)\) | \(e\left(\frac{3145}{6498}\right)\) | \(e\left(\frac{5771}{12996}\right)\) | \(e\left(\frac{17}{2166}\right)\) | \(e\left(\frac{11785}{12996}\right)\) |
\(\chi_{987696}(17,\cdot)\) | 987696.tz | 6498 | no | \(-1\) | \(1\) | \(e\left(\frac{5749}{6498}\right)\) | \(e\left(\frac{235}{1083}\right)\) | \(e\left(\frac{1927}{2166}\right)\) | \(e\left(\frac{1780}{3249}\right)\) | \(e\left(\frac{3709}{6498}\right)\) | \(e\left(\frac{4781}{6498}\right)\) | \(e\left(\frac{2500}{3249}\right)\) | \(e\left(\frac{4355}{6498}\right)\) | \(e\left(\frac{355}{1083}\right)\) | \(e\left(\frac{661}{6498}\right)\) |
\(\chi_{987696}(23,\cdot)\) | 987696.tt | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{2515}{3249}\right)\) | \(e\left(\frac{527}{722}\right)\) | \(e\left(\frac{1753}{2166}\right)\) | \(e\left(\frac{1921}{6498}\right)\) | \(e\left(\frac{4781}{6498}\right)\) | \(e\left(\frac{3248}{3249}\right)\) | \(e\left(\frac{1781}{3249}\right)\) | \(e\left(\frac{3179}{3249}\right)\) | \(e\left(\frac{1313}{2166}\right)\) | \(e\left(\frac{3275}{6498}\right)\) |
\(\chi_{987696}(25,\cdot)\) | 987696.ui | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{1229}{6498}\right)\) | \(e\left(\frac{922}{1083}\right)\) | \(e\left(\frac{667}{722}\right)\) | \(e\left(\frac{3145}{6498}\right)\) | \(e\left(\frac{2500}{3249}\right)\) | \(e\left(\frac{1781}{3249}\right)\) | \(e\left(\frac{1229}{3249}\right)\) | \(e\left(\frac{3499}{6498}\right)\) | \(e\left(\frac{198}{361}\right)\) | \(e\left(\frac{263}{6498}\right)\) |
\(\chi_{987696}(29,\cdot)\) | 987696.vs | 12996 | yes | \(1\) | \(1\) | \(e\left(\frac{9997}{12996}\right)\) | \(e\left(\frac{2009}{2166}\right)\) | \(e\left(\frac{341}{1444}\right)\) | \(e\left(\frac{5771}{12996}\right)\) | \(e\left(\frac{4355}{6498}\right)\) | \(e\left(\frac{3179}{3249}\right)\) | \(e\left(\frac{3499}{6498}\right)\) | \(e\left(\frac{5309}{12996}\right)\) | \(e\left(\frac{433}{722}\right)\) | \(e\left(\frac{9055}{12996}\right)\) |
\(\chi_{987696}(31,\cdot)\) | 987696.ro | 2166 | no | \(1\) | \(1\) | \(e\left(\frac{99}{361}\right)\) | \(e\left(\frac{1109}{2166}\right)\) | \(e\left(\frac{251}{2166}\right)\) | \(e\left(\frac{17}{2166}\right)\) | \(e\left(\frac{355}{1083}\right)\) | \(e\left(\frac{1313}{2166}\right)\) | \(e\left(\frac{198}{361}\right)\) | \(e\left(\frac{433}{722}\right)\) | \(e\left(\frac{35}{1083}\right)\) | \(e\left(\frac{1703}{2166}\right)\) |
\(\chi_{987696}(35,\cdot)\) | 987696.vj | 12996 | no | \(1\) | \(1\) | \(e\left(\frac{6761}{12996}\right)\) | \(e\left(\frac{373}{1083}\right)\) | \(e\left(\frac{269}{4332}\right)\) | \(e\left(\frac{11785}{12996}\right)\) | \(e\left(\frac{661}{6498}\right)\) | \(e\left(\frac{3275}{6498}\right)\) | \(e\left(\frac{263}{6498}\right)\) | \(e\left(\frac{9055}{12996}\right)\) | \(e\left(\frac{1703}{2166}\right)\) | \(e\left(\frac{11237}{12996}\right)\) |
\(\chi_{987696}(37,\cdot)\) | 987696.ps | 1444 | no | \(-1\) | \(1\) | \(e\left(\frac{857}{1444}\right)\) | \(e\left(\frac{85}{722}\right)\) | \(e\left(\frac{697}{1444}\right)\) | \(e\left(\frac{1333}{1444}\right)\) | \(e\left(\frac{147}{361}\right)\) | \(e\left(\frac{141}{722}\right)\) | \(e\left(\frac{135}{722}\right)\) | \(e\left(\frac{1329}{1444}\right)\) | \(e\left(\frac{451}{722}\right)\) | \(e\left(\frac{1027}{1444}\right)\) |
\(\chi_{987696}(41,\cdot)\) | 987696.tx | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{191}{3249}\right)\) | \(e\left(\frac{98}{1083}\right)\) | \(e\left(\frac{158}{361}\right)\) | \(e\left(\frac{1303}{3249}\right)\) | \(e\left(\frac{6421}{6498}\right)\) | \(e\left(\frac{3341}{6498}\right)\) | \(e\left(\frac{382}{3249}\right)\) | \(e\left(\frac{5357}{6498}\right)\) | \(e\left(\frac{685}{722}\right)\) | \(e\left(\frac{485}{3249}\right)\) |
\(\chi_{987696}(43,\cdot)\) | 987696.vq | 12996 | yes | \(-1\) | \(1\) | \(e\left(\frac{245}{12996}\right)\) | \(e\left(\frac{351}{361}\right)\) | \(e\left(\frac{4201}{4332}\right)\) | \(e\left(\frac{8623}{12996}\right)\) | \(e\left(\frac{1430}{3249}\right)\) | \(e\left(\frac{2314}{3249}\right)\) | \(e\left(\frac{245}{6498}\right)\) | \(e\left(\frac{7867}{12996}\right)\) | \(e\left(\frac{1699}{2166}\right)\) | \(e\left(\frac{12881}{12996}\right)\) |
\(\chi_{987696}(47,\cdot)\) | 987696.uj | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{2555}{6498}\right)\) | \(e\left(\frac{863}{2166}\right)\) | \(e\left(\frac{331}{361}\right)\) | \(e\left(\frac{1256}{3249}\right)\) | \(e\left(\frac{1943}{6498}\right)\) | \(e\left(\frac{2468}{3249}\right)\) | \(e\left(\frac{2555}{3249}\right)\) | \(e\left(\frac{2209}{6498}\right)\) | \(e\left(\frac{71}{722}\right)\) | \(e\left(\frac{2572}{3249}\right)\) |
\(\chi_{987696}(49,\cdot)\) | 987696.pl | 1083 | no | \(1\) | \(1\) | \(e\left(\frac{922}{1083}\right)\) | \(e\left(\frac{907}{1083}\right)\) | \(e\left(\frac{217}{1083}\right)\) | \(e\left(\frac{119}{361}\right)\) | \(e\left(\frac{470}{1083}\right)\) | \(e\left(\frac{166}{361}\right)\) | \(e\left(\frac{761}{1083}\right)\) | \(e\left(\frac{926}{1083}\right)\) | \(e\left(\frac{26}{1083}\right)\) | \(e\left(\frac{746}{1083}\right)\) |
\(\chi_{987696}(53,\cdot)\) | 987696.vw | 12996 | no | \(1\) | \(1\) | \(e\left(\frac{1063}{12996}\right)\) | \(e\left(\frac{1471}{2166}\right)\) | \(e\left(\frac{2965}{4332}\right)\) | \(e\left(\frac{10325}{12996}\right)\) | \(e\left(\frac{5933}{6498}\right)\) | \(e\left(\frac{1955}{3249}\right)\) | \(e\left(\frac{1063}{6498}\right)\) | \(e\left(\frac{2651}{12996}\right)\) | \(e\left(\frac{517}{2166}\right)\) | \(e\left(\frac{9889}{12996}\right)\) |
\(\chi_{987696}(55,\cdot)\) | 987696.ty | 6498 | no | \(-1\) | \(1\) | \(e\left(\frac{367}{6498}\right)\) | \(e\left(\frac{1139}{2166}\right)\) | \(e\left(\frac{548}{1083}\right)\) | \(e\left(\frac{5747}{6498}\right)\) | \(e\left(\frac{2516}{3249}\right)\) | \(e\left(\frac{3791}{6498}\right)\) | \(e\left(\frac{367}{3249}\right)\) | \(e\left(\frac{35}{6498}\right)\) | \(e\left(\frac{845}{2166}\right)\) | \(e\left(\frac{1892}{3249}\right)\) |
\(\chi_{987696}(59,\cdot)\) | 987696.wd | 12996 | yes | \(-1\) | \(1\) | \(e\left(\frac{3215}{12996}\right)\) | \(e\left(\frac{41}{1083}\right)\) | \(e\left(\frac{537}{1444}\right)\) | \(e\left(\frac{6181}{12996}\right)\) | \(e\left(\frac{1747}{6498}\right)\) | \(e\left(\frac{149}{6498}\right)\) | \(e\left(\frac{3215}{6498}\right)\) | \(e\left(\frac{8947}{12996}\right)\) | \(e\left(\frac{333}{361}\right)\) | \(e\left(\frac{3707}{12996}\right)\) |
\(\chi_{987696}(61,\cdot)\) | 987696.vl | 12996 | yes | \(1\) | \(1\) | \(e\left(\frac{679}{12996}\right)\) | \(e\left(\frac{401}{2166}\right)\) | \(e\left(\frac{711}{1444}\right)\) | \(e\left(\frac{9293}{12996}\right)\) | \(e\left(\frac{1333}{3249}\right)\) | \(e\left(\frac{2089}{6498}\right)\) | \(e\left(\frac{679}{6498}\right)\) | \(e\left(\frac{5465}{12996}\right)\) | \(e\left(\frac{92}{361}\right)\) | \(e\left(\frac{3085}{12996}\right)\) |
\(\chi_{987696}(65,\cdot)\) | 987696.ql | 2166 | no | \(1\) | \(1\) | \(e\left(\frac{243}{722}\right)\) | \(e\left(\frac{98}{1083}\right)\) | \(e\left(\frac{1309}{2166}\right)\) | \(e\left(\frac{1711}{2166}\right)\) | \(e\left(\frac{937}{2166}\right)\) | \(e\left(\frac{151}{2166}\right)\) | \(e\left(\frac{243}{361}\right)\) | \(e\left(\frac{77}{361}\right)\) | \(e\left(\frac{611}{2166}\right)\) | \(e\left(\frac{925}{2166}\right)\) |
\(\chi_{987696}(67,\cdot)\) | 987696.vu | 12996 | yes | \(1\) | \(1\) | \(e\left(\frac{3007}{12996}\right)\) | \(e\left(\frac{253}{361}\right)\) | \(e\left(\frac{2123}{4332}\right)\) | \(e\left(\frac{11759}{12996}\right)\) | \(e\left(\frac{643}{3249}\right)\) | \(e\left(\frac{1454}{3249}\right)\) | \(e\left(\frac{3007}{6498}\right)\) | \(e\left(\frac{995}{12996}\right)\) | \(e\left(\frac{655}{1083}\right)\) | \(e\left(\frac{12115}{12996}\right)\) |
\(\chi_{987696}(71,\cdot)\) | 987696.ud | 6498 | no | \(-1\) | \(1\) | \(e\left(\frac{614}{3249}\right)\) | \(e\left(\frac{1955}{2166}\right)\) | \(e\left(\frac{2059}{2166}\right)\) | \(e\left(\frac{1966}{3249}\right)\) | \(e\left(\frac{3319}{6498}\right)\) | \(e\left(\frac{2518}{3249}\right)\) | \(e\left(\frac{1228}{3249}\right)\) | \(e\left(\frac{2711}{6498}\right)\) | \(e\left(\frac{313}{1083}\right)\) | \(e\left(\frac{595}{6498}\right)\) |
\(\chi_{987696}(73,\cdot)\) | 987696.ub | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{3583}{6498}\right)\) | \(e\left(\frac{235}{1083}\right)\) | \(e\left(\frac{1927}{2166}\right)\) | \(e\left(\frac{2477}{6498}\right)\) | \(e\left(\frac{2396}{3249}\right)\) | \(e\left(\frac{1849}{3249}\right)\) | \(e\left(\frac{334}{3249}\right)\) | \(e\left(\frac{23}{6498}\right)\) | \(e\left(\frac{355}{1083}\right)\) | \(e\left(\frac{4993}{6498}\right)\) |
\(\chi_{987696}(77,\cdot)\) | 987696.si | 4332 | yes | \(-1\) | \(1\) | \(e\left(\frac{1679}{4332}\right)\) | \(e\left(\frac{41}{2166}\right)\) | \(e\left(\frac{2791}{4332}\right)\) | \(e\left(\frac{1331}{4332}\right)\) | \(e\left(\frac{77}{722}\right)\) | \(e\left(\frac{584}{1083}\right)\) | \(e\left(\frac{1679}{2166}\right)\) | \(e\left(\frac{709}{4332}\right)\) | \(e\left(\frac{680}{1083}\right)\) | \(e\left(\frac{587}{1444}\right)\) |
\(\chi_{987696}(79,\cdot)\) | 987696.vf | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{2042}{3249}\right)\) | \(e\left(\frac{151}{722}\right)\) | \(e\left(\frac{305}{2166}\right)\) | \(e\left(\frac{5651}{6498}\right)\) | \(e\left(\frac{1658}{3249}\right)\) | \(e\left(\frac{581}{6498}\right)\) | \(e\left(\frac{835}{3249}\right)\) | \(e\left(\frac{4931}{6498}\right)\) | \(e\left(\frac{707}{1083}\right)\) | \(e\left(\frac{5443}{6498}\right)\) |
\(\chi_{987696}(83,\cdot)\) | 987696.sn | 4332 | yes | \(1\) | \(1\) | \(e\left(\frac{3251}{4332}\right)\) | \(e\left(\frac{14}{1083}\right)\) | \(e\left(\frac{1457}{4332}\right)\) | \(e\left(\frac{77}{1444}\right)\) | \(e\left(\frac{959}{2166}\right)\) | \(e\left(\frac{351}{722}\right)\) | \(e\left(\frac{1085}{2166}\right)\) | \(e\left(\frac{493}{4332}\right)\) | \(e\left(\frac{1325}{2166}\right)\) | \(e\left(\frac{3307}{4332}\right)\) |
\(\chi_{987696}(85,\cdot)\) | 987696.vh | 12996 | yes | \(1\) | \(1\) | \(e\left(\frac{6229}{12996}\right)\) | \(e\left(\frac{103}{722}\right)\) | \(e\left(\frac{1523}{4332}\right)\) | \(e\left(\frac{3767}{12996}\right)\) | \(e\left(\frac{1480}{3249}\right)\) | \(e\left(\frac{3313}{6498}\right)\) | \(e\left(\frac{6229}{6498}\right)\) | \(e\left(\frac{5711}{12996}\right)\) | \(e\left(\frac{652}{1083}\right)\) | \(e\left(\frac{8083}{12996}\right)\) |
\(\chi_{987696}(89,\cdot)\) | 987696.ue | 6498 | no | \(1\) | \(1\) | \(e\left(\frac{2227}{3249}\right)\) | \(e\left(\frac{449}{1083}\right)\) | \(e\left(\frac{433}{1083}\right)\) | \(e\left(\frac{728}{3249}\right)\) | \(e\left(\frac{2561}{6498}\right)\) | \(e\left(\frac{5365}{6498}\right)\) | \(e\left(\frac{1205}{3249}\right)\) | \(e\left(\frac{4081}{6498}\right)\) | \(e\left(\frac{1057}{2166}\right)\) | \(e\left(\frac{325}{3249}\right)\) |
\(\chi_{987696}(91,\cdot)\) | 987696.vt | 12996 | no | \(1\) | \(1\) | \(e\left(\frac{8677}{12996}\right)\) | \(e\left(\frac{632}{1083}\right)\) | \(e\left(\frac{3217}{4332}\right)\) | \(e\left(\frac{2765}{12996}\right)\) | \(e\left(\frac{2485}{3249}\right)\) | \(e\left(\frac{83}{3249}\right)\) | \(e\left(\frac{2179}{6498}\right)\) | \(e\left(\frac{4829}{12996}\right)\) | \(e\left(\frac{563}{1083}\right)\) | \(e\left(\frac{3265}{12996}\right)\) |
\(\chi_{987696}(97,\cdot)\) | 987696.vc | 6498 | no | \(-1\) | \(1\) | \(e\left(\frac{2540}{3249}\right)\) | \(e\left(\frac{241}{361}\right)\) | \(e\left(\frac{1051}{1083}\right)\) | \(e\left(\frac{1559}{6498}\right)\) | \(e\left(\frac{554}{3249}\right)\) | \(e\left(\frac{2137}{3249}\right)\) | \(e\left(\frac{1831}{3249}\right)\) | \(e\left(\frac{3521}{6498}\right)\) | \(e\left(\frac{1255}{2166}\right)\) | \(e\left(\frac{1460}{3249}\right)\) |
\(\chi_{987696}(101,\cdot)\) | 987696.vr | 12996 | yes | \(-1\) | \(1\) | \(e\left(\frac{11971}{12996}\right)\) | \(e\left(\frac{1835}{2166}\right)\) | \(e\left(\frac{443}{1444}\right)\) | \(e\left(\frac{5255}{12996}\right)\) | \(e\left(\frac{3263}{6498}\right)\) | \(e\left(\frac{287}{3249}\right)\) | \(e\left(\frac{5473}{6498}\right)\) | \(e\left(\frac{1301}{12996}\right)\) | \(e\left(\frac{69}{361}\right)\) | \(e\left(\frac{9985}{12996}\right)\) |