sage: H = DirichletGroup(2025)
pari: g = idealstar(,2025,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1080 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{540}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{2025}(326,\cdot)$, $\chi_{2025}(1702,\cdot)$ |
First 32 of 1080 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2025}(1,\cdot)\) | 2025.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{2025}(2,\cdot)\) | 2025.bv | 540 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{540}\right)\) | \(e\left(\frac{37}{270}\right)\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{11}{270}\right)\) | \(e\left(\frac{53}{540}\right)\) | \(e\left(\frac{83}{135}\right)\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{71}{90}\right)\) |
| \(\chi_{2025}(4,\cdot)\) | 2025.br | 270 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{270}\right)\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{11}{135}\right)\) | \(e\left(\frac{53}{270}\right)\) | \(e\left(\frac{31}{135}\right)\) | \(e\left(\frac{74}{135}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) |
| \(\chi_{2025}(7,\cdot)\) | 2025.bm | 108 | no | \(-1\) | \(1\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{13}{18}\right)\) |
| \(\chi_{2025}(8,\cdot)\) | 2025.bp | 180 | no | \(1\) | \(1\) | \(e\left(\frac{37}{180}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) |
| \(\chi_{2025}(11,\cdot)\) | 2025.bt | 270 | yes | \(-1\) | \(1\) | \(e\left(\frac{11}{270}\right)\) | \(e\left(\frac{11}{135}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{251}{270}\right)\) | \(e\left(\frac{17}{135}\right)\) | \(e\left(\frac{241}{270}\right)\) | \(e\left(\frac{22}{135}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{43}{45}\right)\) |
| \(\chi_{2025}(13,\cdot)\) | 2025.bu | 540 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{540}\right)\) | \(e\left(\frac{53}{270}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{17}{135}\right)\) | \(e\left(\frac{127}{540}\right)\) | \(e\left(\frac{59}{270}\right)\) | \(e\left(\frac{53}{135}\right)\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{19}{90}\right)\) |
| \(\chi_{2025}(14,\cdot)\) | 2025.bs | 270 | yes | \(-1\) | \(1\) | \(e\left(\frac{83}{135}\right)\) | \(e\left(\frac{31}{135}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{241}{270}\right)\) | \(e\left(\frac{59}{270}\right)\) | \(e\left(\frac{41}{270}\right)\) | \(e\left(\frac{62}{135}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) |
| \(\chi_{2025}(16,\cdot)\) | 2025.bo | 135 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{135}\right)\) | \(e\left(\frac{74}{135}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{22}{135}\right)\) | \(e\left(\frac{53}{135}\right)\) | \(e\left(\frac{62}{135}\right)\) | \(e\left(\frac{13}{135}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) |
| \(\chi_{2025}(17,\cdot)\) | 2025.bp | 180 | no | \(1\) | \(1\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) |
| \(\chi_{2025}(19,\cdot)\) | 2025.bk | 90 | no | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) |
| \(\chi_{2025}(22,\cdot)\) | 2025.bu | 540 | yes | \(-1\) | \(1\) | \(e\left(\frac{59}{540}\right)\) | \(e\left(\frac{59}{270}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{131}{135}\right)\) | \(e\left(\frac{121}{540}\right)\) | \(e\left(\frac{137}{270}\right)\) | \(e\left(\frac{59}{135}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{67}{90}\right)\) |
| \(\chi_{2025}(23,\cdot)\) | 2025.bv | 540 | yes | \(1\) | \(1\) | \(e\left(\frac{407}{540}\right)\) | \(e\left(\frac{137}{270}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{121}{270}\right)\) | \(e\left(\frac{43}{540}\right)\) | \(e\left(\frac{103}{135}\right)\) | \(e\left(\frac{2}{135}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{61}{90}\right)\) |
| \(\chi_{2025}(26,\cdot)\) | 2025.j | 6 | no | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
| \(\chi_{2025}(28,\cdot)\) | 2025.bi | 60 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
| \(\chi_{2025}(29,\cdot)\) | 2025.bs | 270 | yes | \(-1\) | \(1\) | \(e\left(\frac{106}{135}\right)\) | \(e\left(\frac{77}{135}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{137}{270}\right)\) | \(e\left(\frac{103}{270}\right)\) | \(e\left(\frac{67}{270}\right)\) | \(e\left(\frac{19}{135}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) |
| \(\chi_{2025}(31,\cdot)\) | 2025.bo | 135 | yes | \(1\) | \(1\) | \(e\left(\frac{104}{135}\right)\) | \(e\left(\frac{73}{135}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{29}{135}\right)\) | \(e\left(\frac{76}{135}\right)\) | \(e\left(\frac{94}{135}\right)\) | \(e\left(\frac{11}{135}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) |
| \(\chi_{2025}(32,\cdot)\) | 2025.bn | 108 | no | \(1\) | \(1\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{17}{18}\right)\) |
| \(\chi_{2025}(34,\cdot)\) | 2025.br | 270 | yes | \(1\) | \(1\) | \(e\left(\frac{89}{270}\right)\) | \(e\left(\frac{89}{135}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{52}{135}\right)\) | \(e\left(\frac{91}{270}\right)\) | \(e\left(\frac{122}{135}\right)\) | \(e\left(\frac{43}{135}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{37}{45}\right)\) |
| \(\chi_{2025}(37,\cdot)\) | 2025.bq | 180 | no | \(-1\) | \(1\) | \(e\left(\frac{41}{180}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{139}{180}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) |
| \(\chi_{2025}(38,\cdot)\) | 2025.bv | 540 | yes | \(1\) | \(1\) | \(e\left(\frac{463}{540}\right)\) | \(e\left(\frac{193}{270}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{269}{270}\right)\) | \(e\left(\frac{167}{540}\right)\) | \(e\left(\frac{17}{135}\right)\) | \(e\left(\frac{58}{135}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{59}{90}\right)\) |
| \(\chi_{2025}(41,\cdot)\) | 2025.bt | 270 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{270}\right)\) | \(e\left(\frac{49}{135}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{259}{270}\right)\) | \(e\left(\frac{88}{135}\right)\) | \(e\left(\frac{239}{270}\right)\) | \(e\left(\frac{98}{135}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) |
| \(\chi_{2025}(43,\cdot)\) | 2025.bm | 108 | no | \(-1\) | \(1\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) |
| \(\chi_{2025}(44,\cdot)\) | 2025.bl | 90 | no | \(-1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) |
| \(\chi_{2025}(46,\cdot)\) | 2025.bd | 45 | no | \(1\) | \(1\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) |
| \(\chi_{2025}(47,\cdot)\) | 2025.bv | 540 | yes | \(1\) | \(1\) | \(e\left(\frac{529}{540}\right)\) | \(e\left(\frac{259}{270}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{77}{270}\right)\) | \(e\left(\frac{101}{540}\right)\) | \(e\left(\frac{41}{135}\right)\) | \(e\left(\frac{124}{135}\right)\) | \(e\left(\frac{59}{180}\right)\) | \(e\left(\frac{47}{90}\right)\) |
| \(\chi_{2025}(49,\cdot)\) | 2025.be | 54 | no | \(1\) | \(1\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{4}{9}\right)\) |
| \(\chi_{2025}(52,\cdot)\) | 2025.bu | 540 | yes | \(-1\) | \(1\) | \(e\left(\frac{127}{540}\right)\) | \(e\left(\frac{127}{270}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{127}{180}\right)\) | \(e\left(\frac{28}{135}\right)\) | \(e\left(\frac{233}{540}\right)\) | \(e\left(\frac{121}{270}\right)\) | \(e\left(\frac{127}{135}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{71}{90}\right)\) |
| \(\chi_{2025}(53,\cdot)\) | 2025.bh | 60 | no | \(1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{10}\right)\) |
| \(\chi_{2025}(56,\cdot)\) | 2025.bt | 270 | yes | \(-1\) | \(1\) | \(e\left(\frac{203}{270}\right)\) | \(e\left(\frac{68}{135}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{263}{270}\right)\) | \(e\left(\frac{56}{135}\right)\) | \(e\left(\frac{103}{270}\right)\) | \(e\left(\frac{1}{135}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{4}{45}\right)\) |
| \(\chi_{2025}(58,\cdot)\) | 2025.bu | 540 | yes | \(-1\) | \(1\) | \(e\left(\frac{461}{540}\right)\) | \(e\left(\frac{191}{270}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{101}{180}\right)\) | \(e\left(\frac{74}{135}\right)\) | \(e\left(\frac{259}{540}\right)\) | \(e\left(\frac{233}{270}\right)\) | \(e\left(\frac{56}{135}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{43}{90}\right)\) |
| \(\chi_{2025}(59,\cdot)\) | 2025.bs | 270 | yes | \(-1\) | \(1\) | \(e\left(\frac{62}{135}\right)\) | \(e\left(\frac{124}{135}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{19}{270}\right)\) | \(e\left(\frac{101}{270}\right)\) | \(e\left(\frac{29}{270}\right)\) | \(e\left(\frac{113}{135}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) |