sage: H = DirichletGroup(4353)
pari: g = idealstar(,4353,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 2900 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{1450}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{4353}(2903,\cdot)$, $\chi_{4353}(1453,\cdot)$ |
First 32 of 2900 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4353}(1,\cdot)\) | 4353.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{4353}(2,\cdot)\) | 4353.w | 1450 | yes | \(1\) | \(1\) | \(e\left(\frac{363}{725}\right)\) | \(e\left(\frac{1}{725}\right)\) | \(e\left(\frac{839}{1450}\right)\) | \(e\left(\frac{583}{1450}\right)\) | \(e\left(\frac{364}{725}\right)\) | \(e\left(\frac{23}{290}\right)\) | \(e\left(\frac{313}{1450}\right)\) | \(e\left(\frac{977}{1450}\right)\) | \(e\left(\frac{1309}{1450}\right)\) | \(e\left(\frac{2}{725}\right)\) |
| \(\chi_{4353}(4,\cdot)\) | 4353.u | 725 | no | \(1\) | \(1\) | \(e\left(\frac{1}{725}\right)\) | \(e\left(\frac{2}{725}\right)\) | \(e\left(\frac{114}{725}\right)\) | \(e\left(\frac{583}{725}\right)\) | \(e\left(\frac{3}{725}\right)\) | \(e\left(\frac{23}{145}\right)\) | \(e\left(\frac{313}{725}\right)\) | \(e\left(\frac{252}{725}\right)\) | \(e\left(\frac{584}{725}\right)\) | \(e\left(\frac{4}{725}\right)\) |
| \(\chi_{4353}(5,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{839}{1450}\right)\) | \(e\left(\frac{114}{725}\right)\) | \(e\left(\frac{671}{1450}\right)\) | \(e\left(\frac{606}{725}\right)\) | \(e\left(\frac{1067}{1450}\right)\) | \(e\left(\frac{6}{145}\right)\) | \(e\left(\frac{157}{1450}\right)\) | \(e\left(\frac{589}{725}\right)\) | \(e\left(\frac{601}{1450}\right)\) | \(e\left(\frac{228}{725}\right)\) |
| \(\chi_{4353}(7,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{583}{1450}\right)\) | \(e\left(\frac{583}{725}\right)\) | \(e\left(\frac{606}{725}\right)\) | \(e\left(\frac{589}{1450}\right)\) | \(e\left(\frac{299}{1450}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{252}{725}\right)\) | \(e\left(\frac{1191}{1450}\right)\) | \(e\left(\frac{586}{725}\right)\) | \(e\left(\frac{441}{725}\right)\) |
| \(\chi_{4353}(8,\cdot)\) | 4353.w | 1450 | yes | \(1\) | \(1\) | \(e\left(\frac{364}{725}\right)\) | \(e\left(\frac{3}{725}\right)\) | \(e\left(\frac{1067}{1450}\right)\) | \(e\left(\frac{299}{1450}\right)\) | \(e\left(\frac{367}{725}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{939}{1450}\right)\) | \(e\left(\frac{31}{1450}\right)\) | \(e\left(\frac{1027}{1450}\right)\) | \(e\left(\frac{6}{725}\right)\) |
| \(\chi_{4353}(10,\cdot)\) | 4353.s | 290 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{290}\right)\) | \(e\left(\frac{23}{145}\right)\) | \(e\left(\frac{6}{145}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{47}{145}\right)\) | \(e\left(\frac{141}{290}\right)\) | \(e\left(\frac{46}{145}\right)\) | \(e\left(\frac{46}{145}\right)\) |
| \(\chi_{4353}(11,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{313}{1450}\right)\) | \(e\left(\frac{313}{725}\right)\) | \(e\left(\frac{157}{1450}\right)\) | \(e\left(\frac{252}{725}\right)\) | \(e\left(\frac{939}{1450}\right)\) | \(e\left(\frac{47}{145}\right)\) | \(e\left(\frac{819}{1450}\right)\) | \(e\left(\frac{288}{725}\right)\) | \(e\left(\frac{817}{1450}\right)\) | \(e\left(\frac{626}{725}\right)\) |
| \(\chi_{4353}(13,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{977}{1450}\right)\) | \(e\left(\frac{252}{725}\right)\) | \(e\left(\frac{589}{725}\right)\) | \(e\left(\frac{1191}{1450}\right)\) | \(e\left(\frac{31}{1450}\right)\) | \(e\left(\frac{141}{290}\right)\) | \(e\left(\frac{288}{725}\right)\) | \(e\left(\frac{429}{1450}\right)\) | \(e\left(\frac{359}{725}\right)\) | \(e\left(\frac{504}{725}\right)\) |
| \(\chi_{4353}(14,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{1309}{1450}\right)\) | \(e\left(\frac{584}{725}\right)\) | \(e\left(\frac{601}{1450}\right)\) | \(e\left(\frac{586}{725}\right)\) | \(e\left(\frac{1027}{1450}\right)\) | \(e\left(\frac{46}{145}\right)\) | \(e\left(\frac{817}{1450}\right)\) | \(e\left(\frac{359}{725}\right)\) | \(e\left(\frac{1031}{1450}\right)\) | \(e\left(\frac{443}{725}\right)\) |
| \(\chi_{4353}(16,\cdot)\) | 4353.u | 725 | no | \(1\) | \(1\) | \(e\left(\frac{2}{725}\right)\) | \(e\left(\frac{4}{725}\right)\) | \(e\left(\frac{228}{725}\right)\) | \(e\left(\frac{441}{725}\right)\) | \(e\left(\frac{6}{725}\right)\) | \(e\left(\frac{46}{145}\right)\) | \(e\left(\frac{626}{725}\right)\) | \(e\left(\frac{504}{725}\right)\) | \(e\left(\frac{443}{725}\right)\) | \(e\left(\frac{8}{725}\right)\) |
| \(\chi_{4353}(17,\cdot)\) | 4353.w | 1450 | yes | \(1\) | \(1\) | \(e\left(\frac{721}{725}\right)\) | \(e\left(\frac{717}{725}\right)\) | \(e\left(\frac{1263}{1450}\right)\) | \(e\left(\frac{411}{1450}\right)\) | \(e\left(\frac{713}{725}\right)\) | \(e\left(\frac{251}{290}\right)\) | \(e\left(\frac{1121}{1450}\right)\) | \(e\left(\frac{159}{1450}\right)\) | \(e\left(\frac{403}{1450}\right)\) | \(e\left(\frac{709}{725}\right)\) |
| \(\chi_{4353}(19,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{653}{1450}\right)\) | \(e\left(\frac{653}{725}\right)\) | \(e\left(\frac{246}{725}\right)\) | \(e\left(\frac{799}{1450}\right)\) | \(e\left(\frac{509}{1450}\right)\) | \(e\left(\frac{229}{290}\right)\) | \(e\left(\frac{332}{725}\right)\) | \(e\left(\frac{1431}{1450}\right)\) | \(e\left(\frac{1}{725}\right)\) | \(e\left(\frac{581}{725}\right)\) |
| \(\chi_{4353}(20,\cdot)\) | 4353.k | 50 | yes | \(-1\) | \(1\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{8}{25}\right)\) |
| \(\chi_{4353}(22,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{1039}{1450}\right)\) | \(e\left(\frac{314}{725}\right)\) | \(e\left(\frac{498}{725}\right)\) | \(e\left(\frac{1087}{1450}\right)\) | \(e\left(\frac{217}{1450}\right)\) | \(e\left(\frac{117}{290}\right)\) | \(e\left(\frac{566}{725}\right)\) | \(e\left(\frac{103}{1450}\right)\) | \(e\left(\frac{338}{725}\right)\) | \(e\left(\frac{628}{725}\right)\) |
| \(\chi_{4353}(23,\cdot)\) | 4353.w | 1450 | yes | \(1\) | \(1\) | \(e\left(\frac{337}{725}\right)\) | \(e\left(\frac{674}{725}\right)\) | \(e\left(\frac{711}{1450}\right)\) | \(e\left(\frac{717}{1450}\right)\) | \(e\left(\frac{286}{725}\right)\) | \(e\left(\frac{277}{290}\right)\) | \(e\left(\frac{1437}{1450}\right)\) | \(e\left(\frac{923}{1450}\right)\) | \(e\left(\frac{1391}{1450}\right)\) | \(e\left(\frac{623}{725}\right)\) |
| \(\chi_{4353}(25,\cdot)\) | 4353.u | 725 | no | \(1\) | \(1\) | \(e\left(\frac{114}{725}\right)\) | \(e\left(\frac{228}{725}\right)\) | \(e\left(\frac{671}{725}\right)\) | \(e\left(\frac{487}{725}\right)\) | \(e\left(\frac{342}{725}\right)\) | \(e\left(\frac{12}{145}\right)\) | \(e\left(\frac{157}{725}\right)\) | \(e\left(\frac{453}{725}\right)\) | \(e\left(\frac{601}{725}\right)\) | \(e\left(\frac{456}{725}\right)\) |
| \(\chi_{4353}(26,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{253}{1450}\right)\) | \(e\left(\frac{253}{725}\right)\) | \(e\left(\frac{567}{1450}\right)\) | \(e\left(\frac{162}{725}\right)\) | \(e\left(\frac{759}{1450}\right)\) | \(e\left(\frac{82}{145}\right)\) | \(e\left(\frac{889}{1450}\right)\) | \(e\left(\frac{703}{725}\right)\) | \(e\left(\frac{577}{1450}\right)\) | \(e\left(\frac{506}{725}\right)\) |
| \(\chi_{4353}(28,\cdot)\) | 4353.s | 290 | no | \(-1\) | \(1\) | \(e\left(\frac{117}{290}\right)\) | \(e\left(\frac{117}{145}\right)\) | \(e\left(\frac{144}{145}\right)\) | \(e\left(\frac{61}{290}\right)\) | \(e\left(\frac{61}{290}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{113}{145}\right)\) | \(e\left(\frac{49}{290}\right)\) | \(e\left(\frac{89}{145}\right)\) | \(e\left(\frac{89}{145}\right)\) |
| \(\chi_{4353}(29,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{1221}{1450}\right)\) | \(e\left(\frac{496}{725}\right)\) | \(e\left(\frac{719}{1450}\right)\) | \(e\left(\frac{309}{725}\right)\) | \(e\left(\frac{763}{1450}\right)\) | \(e\left(\frac{49}{145}\right)\) | \(e\left(\frac{823}{1450}\right)\) | \(e\left(\frac{146}{725}\right)\) | \(e\left(\frac{389}{1450}\right)\) | \(e\left(\frac{267}{725}\right)\) |
| \(\chi_{4353}(31,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{1003}{1450}\right)\) | \(e\left(\frac{278}{725}\right)\) | \(e\left(\frac{621}{725}\right)\) | \(e\left(\frac{399}{1450}\right)\) | \(e\left(\frac{109}{1450}\right)\) | \(e\left(\frac{159}{290}\right)\) | \(e\left(\frac{7}{725}\right)\) | \(e\left(\frac{1181}{1450}\right)\) | \(e\left(\frac{701}{725}\right)\) | \(e\left(\frac{556}{725}\right)\) |
| \(\chi_{4353}(32,\cdot)\) | 4353.t | 290 | yes | \(1\) | \(1\) | \(e\left(\frac{73}{145}\right)\) | \(e\left(\frac{1}{145}\right)\) | \(e\left(\frac{259}{290}\right)\) | \(e\left(\frac{3}{290}\right)\) | \(e\left(\frac{74}{145}\right)\) | \(e\left(\frac{23}{58}\right)\) | \(e\left(\frac{23}{290}\right)\) | \(e\left(\frac{107}{290}\right)\) | \(e\left(\frac{149}{290}\right)\) | \(e\left(\frac{2}{145}\right)\) |
| \(\chi_{4353}(34,\cdot)\) | 4353.u | 725 | no | \(1\) | \(1\) | \(e\left(\frac{359}{725}\right)\) | \(e\left(\frac{718}{725}\right)\) | \(e\left(\frac{326}{725}\right)\) | \(e\left(\frac{497}{725}\right)\) | \(e\left(\frac{352}{725}\right)\) | \(e\left(\frac{137}{145}\right)\) | \(e\left(\frac{717}{725}\right)\) | \(e\left(\frac{568}{725}\right)\) | \(e\left(\frac{131}{725}\right)\) | \(e\left(\frac{711}{725}\right)\) |
| \(\chi_{4353}(35,\cdot)\) | 4353.w | 1450 | yes | \(1\) | \(1\) | \(e\left(\frac{711}{725}\right)\) | \(e\left(\frac{697}{725}\right)\) | \(e\left(\frac{433}{1450}\right)\) | \(e\left(\frac{351}{1450}\right)\) | \(e\left(\frac{683}{725}\right)\) | \(e\left(\frac{81}{290}\right)\) | \(e\left(\frac{661}{1450}\right)\) | \(e\left(\frac{919}{1450}\right)\) | \(e\left(\frac{323}{1450}\right)\) | \(e\left(\frac{669}{725}\right)\) |
| \(\chi_{4353}(37,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{379}{1450}\right)\) | \(e\left(\frac{379}{725}\right)\) | \(e\left(\frac{578}{725}\right)\) | \(e\left(\frac{557}{1450}\right)\) | \(e\left(\frac{1137}{1450}\right)\) | \(e\left(\frac{17}{290}\right)\) | \(e\left(\frac{226}{725}\right)\) | \(e\left(\frac{533}{1450}\right)\) | \(e\left(\frac{468}{725}\right)\) | \(e\left(\frac{33}{725}\right)\) |
| \(\chi_{4353}(38,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{1379}{1450}\right)\) | \(e\left(\frac{654}{725}\right)\) | \(e\left(\frac{1331}{1450}\right)\) | \(e\left(\frac{691}{725}\right)\) | \(e\left(\frac{1237}{1450}\right)\) | \(e\left(\frac{126}{145}\right)\) | \(e\left(\frac{977}{1450}\right)\) | \(e\left(\frac{479}{725}\right)\) | \(e\left(\frac{1311}{1450}\right)\) | \(e\left(\frac{583}{725}\right)\) |
| \(\chi_{4353}(40,\cdot)\) | 4353.v | 1450 | no | \(-1\) | \(1\) | \(e\left(\frac{117}{1450}\right)\) | \(e\left(\frac{117}{725}\right)\) | \(e\left(\frac{144}{725}\right)\) | \(e\left(\frac{61}{1450}\right)\) | \(e\left(\frac{351}{1450}\right)\) | \(e\left(\frac{81}{290}\right)\) | \(e\left(\frac{548}{725}\right)\) | \(e\left(\frac{1209}{1450}\right)\) | \(e\left(\frac{89}{725}\right)\) | \(e\left(\frac{234}{725}\right)\) |
| \(\chi_{4353}(41,\cdot)\) | 4353.x | 1450 | yes | \(-1\) | \(1\) | \(e\left(\frac{757}{1450}\right)\) | \(e\left(\frac{32}{725}\right)\) | \(e\left(\frac{23}{1450}\right)\) | \(e\left(\frac{628}{725}\right)\) | \(e\left(\frac{821}{1450}\right)\) | \(e\left(\frac{78}{145}\right)\) | \(e\left(\frac{591}{1450}\right)\) | \(e\left(\frac{407}{725}\right)\) | \(e\left(\frac{563}{1450}\right)\) | \(e\left(\frac{64}{725}\right)\) |
| \(\chi_{4353}(43,\cdot)\) | 4353.q | 145 | no | \(1\) | \(1\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{23}{145}\right)\) | \(e\left(\frac{96}{145}\right)\) | \(e\left(\frac{96}{145}\right)\) | \(e\left(\frac{11}{29}\right)\) | \(e\left(\frac{11}{145}\right)\) | \(e\left(\frac{89}{145}\right)\) | \(e\left(\frac{128}{145}\right)\) | \(e\left(\frac{128}{145}\right)\) |
| \(\chi_{4353}(44,\cdot)\) | 4353.r | 290 | yes | \(-1\) | \(1\) | \(e\left(\frac{63}{290}\right)\) | \(e\left(\frac{63}{145}\right)\) | \(e\left(\frac{77}{290}\right)\) | \(e\left(\frac{22}{145}\right)\) | \(e\left(\frac{189}{290}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{289}{290}\right)\) | \(e\left(\frac{108}{145}\right)\) | \(e\left(\frac{107}{290}\right)\) | \(e\left(\frac{126}{145}\right)\) |
| \(\chi_{4353}(46,\cdot)\) | 4353.j | 29 | no | \(1\) | \(1\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) |
| \(\chi_{4353}(47,\cdot)\) | 4353.r | 290 | yes | \(-1\) | \(1\) | \(e\left(\frac{109}{290}\right)\) | \(e\left(\frac{109}{145}\right)\) | \(e\left(\frac{101}{290}\right)\) | \(e\left(\frac{91}{145}\right)\) | \(e\left(\frac{37}{290}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{187}{290}\right)\) | \(e\left(\frac{104}{145}\right)\) | \(e\left(\frac{1}{290}\right)\) | \(e\left(\frac{73}{145}\right)\) |