sage: H = DirichletGroup(10002)
pari: g = idealstar(,10002,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 3332 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1666}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{10002}(3335,\cdot)$, $\chi_{10002}(1669,\cdot)$ |
First 32 of 3332 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 | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{10002}(1,\cdot)\) | 10002.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{10002}(5,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{599}{833}\right)\) | \(e\left(\frac{1101}{1666}\right)\) | \(e\left(\frac{479}{1666}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{1339}{1666}\right)\) | \(e\left(\frac{673}{833}\right)\) | \(e\left(\frac{1261}{1666}\right)\) | \(e\left(\frac{365}{833}\right)\) | \(e\left(\frac{20}{833}\right)\) | \(e\left(\frac{563}{833}\right)\) |
| \(\chi_{10002}(7,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1101}{1666}\right)\) | \(e\left(\frac{53}{1666}\right)\) | \(e\left(\frac{80}{833}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{681}{833}\right)\) | \(e\left(\frac{590}{833}\right)\) | \(e\left(\frac{148}{833}\right)\) | \(e\left(\frac{268}{833}\right)\) | \(e\left(\frac{269}{1666}\right)\) | \(e\left(\frac{475}{833}\right)\) |
| \(\chi_{10002}(11,\cdot)\) | 10002.v | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{479}{1666}\right)\) | \(e\left(\frac{80}{833}\right)\) | \(e\left(\frac{373}{1666}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{41}{1666}\right)\) | \(e\left(\frac{178}{833}\right)\) | \(e\left(\frac{815}{1666}\right)\) | \(e\left(\frac{479}{833}\right)\) | \(e\left(\frac{1205}{1666}\right)\) | \(e\left(\frac{821}{833}\right)\) |
| \(\chi_{10002}(13,\cdot)\) | 10002.m | 49 | no | \(1\) | \(1\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{43}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{11}{49}\right)\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{31}{49}\right)\) |
| \(\chi_{10002}(17,\cdot)\) | 10002.v | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1339}{1666}\right)\) | \(e\left(\frac{681}{833}\right)\) | \(e\left(\frac{41}{1666}\right)\) | \(e\left(\frac{43}{49}\right)\) | \(e\left(\frac{1005}{1666}\right)\) | \(e\left(\frac{828}{833}\right)\) | \(e\left(\frac{1367}{1666}\right)\) | \(e\left(\frac{506}{833}\right)\) | \(e\left(\frac{1459}{1666}\right)\) | \(e\left(\frac{356}{833}\right)\) |
| \(\chi_{10002}(19,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{673}{833}\right)\) | \(e\left(\frac{590}{833}\right)\) | \(e\left(\frac{178}{833}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{828}{833}\right)\) | \(e\left(\frac{688}{833}\right)\) | \(e\left(\frac{246}{833}\right)\) | \(e\left(\frac{513}{833}\right)\) | \(e\left(\frac{747}{833}\right)\) | \(e\left(\frac{328}{833}\right)\) |
| \(\chi_{10002}(23,\cdot)\) | 10002.v | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1261}{1666}\right)\) | \(e\left(\frac{148}{833}\right)\) | \(e\left(\frac{815}{1666}\right)\) | \(e\left(\frac{11}{49}\right)\) | \(e\left(\frac{1367}{1666}\right)\) | \(e\left(\frac{246}{833}\right)\) | \(e\left(\frac{883}{1666}\right)\) | \(e\left(\frac{428}{833}\right)\) | \(e\left(\frac{355}{1666}\right)\) | \(e\left(\frac{311}{833}\right)\) |
| \(\chi_{10002}(25,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{365}{833}\right)\) | \(e\left(\frac{268}{833}\right)\) | \(e\left(\frac{479}{833}\right)\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{506}{833}\right)\) | \(e\left(\frac{513}{833}\right)\) | \(e\left(\frac{428}{833}\right)\) | \(e\left(\frac{730}{833}\right)\) | \(e\left(\frac{40}{833}\right)\) | \(e\left(\frac{293}{833}\right)\) |
| \(\chi_{10002}(29,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{20}{833}\right)\) | \(e\left(\frac{269}{1666}\right)\) | \(e\left(\frac{1205}{1666}\right)\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{1459}{1666}\right)\) | \(e\left(\frac{747}{833}\right)\) | \(e\left(\frac{355}{1666}\right)\) | \(e\left(\frac{40}{833}\right)\) | \(e\left(\frac{219}{833}\right)\) | \(e\left(\frac{792}{833}\right)\) |
| \(\chi_{10002}(31,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{563}{833}\right)\) | \(e\left(\frac{475}{833}\right)\) | \(e\left(\frac{821}{833}\right)\) | \(e\left(\frac{31}{49}\right)\) | \(e\left(\frac{356}{833}\right)\) | \(e\left(\frac{328}{833}\right)\) | \(e\left(\frac{311}{833}\right)\) | \(e\left(\frac{293}{833}\right)\) | \(e\left(\frac{792}{833}\right)\) | \(e\left(\frac{137}{833}\right)\) |
| \(\chi_{10002}(35,\cdot)\) | 10002.v | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{633}{1666}\right)\) | \(e\left(\frac{577}{833}\right)\) | \(e\left(\frac{639}{1666}\right)\) | \(e\left(\frac{26}{49}\right)\) | \(e\left(\frac{1035}{1666}\right)\) | \(e\left(\frac{430}{833}\right)\) | \(e\left(\frac{1557}{1666}\right)\) | \(e\left(\frac{633}{833}\right)\) | \(e\left(\frac{309}{1666}\right)\) | \(e\left(\frac{205}{833}\right)\) |
| \(\chi_{10002}(37,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1247}{1666}\right)\) | \(e\left(\frac{1493}{1666}\right)\) | \(e\left(\frac{509}{833}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{449}{833}\right)\) | \(e\left(\frac{526}{833}\right)\) | \(e\left(\frac{67}{833}\right)\) | \(e\left(\frac{414}{833}\right)\) | \(e\left(\frac{285}{1666}\right)\) | \(e\left(\frac{367}{833}\right)\) |
| \(\chi_{10002}(41,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{223}{833}\right)\) | \(e\left(\frac{1375}{1666}\right)\) | \(e\left(\frac{1149}{1666}\right)\) | \(e\left(\frac{41}{49}\right)\) | \(e\left(\frac{899}{1666}\right)\) | \(e\left(\frac{124}{833}\right)\) | \(e\left(\frac{1251}{1666}\right)\) | \(e\left(\frac{446}{833}\right)\) | \(e\left(\frac{401}{833}\right)\) | \(e\left(\frac{1}{833}\right)\) |
| \(\chi_{10002}(43,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{257}{833}\right)\) | \(e\left(\frac{458}{833}\right)\) | \(e\left(\frac{141}{833}\right)\) | \(e\left(\frac{40}{49}\right)\) | \(e\left(\frac{815}{833}\right)\) | \(e\left(\frac{311}{833}\right)\) | \(e\left(\frac{719}{833}\right)\) | \(e\left(\frac{514}{833}\right)\) | \(e\left(\frac{690}{833}\right)\) | \(e\left(\frac{681}{833}\right)\) |
| \(\chi_{10002}(47,\cdot)\) | 10002.v | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1303}{1666}\right)\) | \(e\left(\frac{435}{833}\right)\) | \(e\left(\frac{1039}{1666}\right)\) | \(e\left(\frac{32}{49}\right)\) | \(e\left(\frac{275}{1666}\right)\) | \(e\left(\frac{239}{833}\right)\) | \(e\left(\frac{631}{1666}\right)\) | \(e\left(\frac{470}{833}\right)\) | \(e\left(\frac{565}{1666}\right)\) | \(e\left(\frac{143}{833}\right)\) |
| \(\chi_{10002}(49,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{268}{833}\right)\) | \(e\left(\frac{53}{833}\right)\) | \(e\left(\frac{160}{833}\right)\) | \(e\left(\frac{44}{49}\right)\) | \(e\left(\frac{529}{833}\right)\) | \(e\left(\frac{347}{833}\right)\) | \(e\left(\frac{296}{833}\right)\) | \(e\left(\frac{536}{833}\right)\) | \(e\left(\frac{269}{833}\right)\) | \(e\left(\frac{117}{833}\right)\) |
| \(\chi_{10002}(53,\cdot)\) | 10002.s | 238 | no | \(-1\) | \(1\) | \(e\left(\frac{155}{238}\right)\) | \(e\left(\frac{8}{119}\right)\) | \(e\left(\frac{73}{238}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{135}{238}\right)\) | \(e\left(\frac{113}{119}\right)\) | \(e\left(\frac{141}{238}\right)\) | \(e\left(\frac{36}{119}\right)\) | \(e\left(\frac{61}{238}\right)\) | \(e\left(\frac{94}{119}\right)\) |
| \(\chi_{10002}(55,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{1666}\right)\) | \(e\left(\frac{1261}{1666}\right)\) | \(e\left(\frac{426}{833}\right)\) | \(e\left(\frac{2}{49}\right)\) | \(e\left(\frac{690}{833}\right)\) | \(e\left(\frac{18}{833}\right)\) | \(e\left(\frac{205}{833}\right)\) | \(e\left(\frac{11}{833}\right)\) | \(e\left(\frac{1245}{1666}\right)\) | \(e\left(\frac{551}{833}\right)\) |
| \(\chi_{10002}(59,\cdot)\) | 10002.t | 238 | no | \(1\) | \(1\) | \(e\left(\frac{61}{119}\right)\) | \(e\left(\frac{41}{238}\right)\) | \(e\left(\frac{135}{238}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{41}{238}\right)\) | \(e\left(\frac{59}{119}\right)\) | \(e\left(\frac{101}{238}\right)\) | \(e\left(\frac{3}{119}\right)\) | \(e\left(\frac{67}{119}\right)\) | \(e\left(\frac{107}{119}\right)\) |
| \(\chi_{10002}(61,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{298}{833}\right)\) | \(e\left(\frac{463}{833}\right)\) | \(e\left(\frac{439}{833}\right)\) | \(e\left(\frac{46}{49}\right)\) | \(e\left(\frac{582}{833}\right)\) | \(e\left(\frac{218}{833}\right)\) | \(e\left(\frac{354}{833}\right)\) | \(e\left(\frac{596}{833}\right)\) | \(e\left(\frac{181}{833}\right)\) | \(e\left(\frac{472}{833}\right)\) |
| \(\chi_{10002}(65,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{667}{833}\right)\) | \(e\left(\frac{183}{1666}\right)\) | \(e\left(\frac{411}{1666}\right)\) | \(e\left(\frac{2}{49}\right)\) | \(e\left(\frac{1135}{1666}\right)\) | \(e\left(\frac{214}{833}\right)\) | \(e\left(\frac{1635}{1666}\right)\) | \(e\left(\frac{501}{833}\right)\) | \(e\left(\frac{598}{833}\right)\) | \(e\left(\frac{257}{833}\right)\) |
| \(\chi_{10002}(67,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{309}{1666}\right)\) | \(e\left(\frac{891}{1666}\right)\) | \(e\left(\frac{229}{833}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{148}{833}\right)\) | \(e\left(\frac{127}{833}\right)\) | \(e\left(\frac{382}{833}\right)\) | \(e\left(\frac{309}{833}\right)\) | \(e\left(\frac{593}{1666}\right)\) | \(e\left(\frac{787}{833}\right)\) |
| \(\chi_{10002}(71,\cdot)\) | 10002.v | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1535}{1666}\right)\) | \(e\left(\frac{632}{833}\right)\) | \(e\left(\frac{531}{1666}\right)\) | \(e\left(\frac{43}{49}\right)\) | \(e\left(\frac{907}{1666}\right)\) | \(e\left(\frac{240}{833}\right)\) | \(e\left(\frac{191}{1666}\right)\) | \(e\left(\frac{702}{833}\right)\) | \(e\left(\frac{773}{1666}\right)\) | \(e\left(\frac{405}{833}\right)\) |
| \(\chi_{10002}(73,\cdot)\) | 10002.u | 833 | no | \(1\) | \(1\) | \(e\left(\frac{163}{833}\right)\) | \(e\left(\frac{284}{833}\right)\) | \(e\left(\frac{433}{833}\right)\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{760}{833}\right)\) | \(e\left(\frac{382}{833}\right)\) | \(e\left(\frac{93}{833}\right)\) | \(e\left(\frac{326}{833}\right)\) | \(e\left(\frac{577}{833}\right)\) | \(e\left(\frac{124}{833}\right)\) |
| \(\chi_{10002}(77,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{790}{833}\right)\) | \(e\left(\frac{213}{1666}\right)\) | \(e\left(\frac{533}{1666}\right)\) | \(e\left(\frac{20}{49}\right)\) | \(e\left(\frac{1403}{1666}\right)\) | \(e\left(\frac{768}{833}\right)\) | \(e\left(\frac{1111}{1666}\right)\) | \(e\left(\frac{747}{833}\right)\) | \(e\left(\frac{737}{833}\right)\) | \(e\left(\frac{463}{833}\right)\) |
| \(\chi_{10002}(79,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1265}{1666}\right)\) | \(e\left(\frac{73}{1666}\right)\) | \(e\left(\frac{676}{833}\right)\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{215}{833}\right)\) | \(e\left(\frac{404}{833}\right)\) | \(e\left(\frac{251}{833}\right)\) | \(e\left(\frac{432}{833}\right)\) | \(e\left(\frac{1565}{1666}\right)\) | \(e\left(\frac{57}{833}\right)\) |
| \(\chi_{10002}(83,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{577}{833}\right)\) | \(e\left(\frac{1055}{1666}\right)\) | \(e\left(\frac{403}{1666}\right)\) | \(e\left(\frac{45}{49}\right)\) | \(e\left(\frac{817}{1666}\right)\) | \(e\left(\frac{601}{833}\right)\) | \(e\left(\frac{1287}{1666}\right)\) | \(e\left(\frac{321}{833}\right)\) | \(e\left(\frac{29}{833}\right)\) | \(e\left(\frac{25}{833}\right)\) |
| \(\chi_{10002}(85,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{871}{1666}\right)\) | \(e\left(\frac{797}{1666}\right)\) | \(e\left(\frac{260}{833}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{339}{833}\right)\) | \(e\left(\frac{668}{833}\right)\) | \(e\left(\frac{481}{833}\right)\) | \(e\left(\frac{38}{833}\right)\) | \(e\left(\frac{1499}{1666}\right)\) | \(e\left(\frac{86}{833}\right)\) |
| \(\chi_{10002}(89,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{16}{833}\right)\) | \(e\left(\frac{715}{1666}\right)\) | \(e\left(\frac{131}{1666}\right)\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{1}{1666}\right)\) | \(e\left(\frac{431}{833}\right)\) | \(e\left(\frac{1117}{1666}\right)\) | \(e\left(\frac{32}{833}\right)\) | \(e\left(\frac{675}{833}\right)\) | \(e\left(\frac{467}{833}\right)\) |
| \(\chi_{10002}(91,\cdot)\) | 10002.x | 1666 | no | \(-1\) | \(1\) | \(e\left(\frac{1237}{1666}\right)\) | \(e\left(\frac{801}{1666}\right)\) | \(e\left(\frac{46}{833}\right)\) | \(e\left(\frac{20}{49}\right)\) | \(e\left(\frac{579}{833}\right)\) | \(e\left(\frac{131}{833}\right)\) | \(e\left(\frac{335}{833}\right)\) | \(e\left(\frac{404}{833}\right)\) | \(e\left(\frac{1425}{1666}\right)\) | \(e\left(\frac{169}{833}\right)\) |
| \(\chi_{10002}(95,\cdot)\) | 10002.w | 1666 | no | \(1\) | \(1\) | \(e\left(\frac{439}{833}\right)\) | \(e\left(\frac{615}{1666}\right)\) | \(e\left(\frac{835}{1666}\right)\) | \(e\left(\frac{26}{49}\right)\) | \(e\left(\frac{1329}{1666}\right)\) | \(e\left(\frac{528}{833}\right)\) | \(e\left(\frac{87}{1666}\right)\) | \(e\left(\frac{45}{833}\right)\) | \(e\left(\frac{767}{833}\right)\) | \(e\left(\frac{58}{833}\right)\) |