sage: H = DirichletGroup(1441)
pari: g = idealstar(,1441,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 1300 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{10}\times C_{130}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{1441}(1311,\cdot)$, $\chi_{1441}(133,\cdot)$ |
First 32 of 1300 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{1441}(1,\cdot)\) | 1441.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{1441}(2,\cdot)\) | 1441.by | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) |
\(\chi_{1441}(3,\cdot)\) | 1441.bj | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) |
\(\chi_{1441}(4,\cdot)\) | 1441.bi | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) |
\(\chi_{1441}(5,\cdot)\) | 1441.bj | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) |
\(\chi_{1441}(6,\cdot)\) | 1441.bm | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) |
\(\chi_{1441}(7,\cdot)\) | 1441.bn | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{57}{130}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{42}{65}\right)\) |
\(\chi_{1441}(8,\cdot)\) | 1441.by | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) |
\(\chi_{1441}(9,\cdot)\) | 1441.bj | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) |
\(\chi_{1441}(10,\cdot)\) | 1441.ca | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{27}{130}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) |
\(\chi_{1441}(12,\cdot)\) | 1441.bl | 65 | no | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) |
\(\chi_{1441}(13,\cdot)\) | 1441.bn | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{129}{130}\right)\) | \(e\left(\frac{93}{130}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{1}{130}\right)\) | \(e\left(\frac{16}{65}\right)\) |
\(\chi_{1441}(14,\cdot)\) | 1441.bp | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{71}{130}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{9}{130}\right)\) | \(e\left(\frac{14}{65}\right)\) |
\(\chi_{1441}(15,\cdot)\) | 1441.bj | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{21}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{11}{65}\right)\) |
\(\chi_{1441}(16,\cdot)\) | 1441.bi | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{27}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{19}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{18}{65}\right)\) |
\(\chi_{1441}(17,\cdot)\) | 1441.bm | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{7}{130}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) |
\(\chi_{1441}(18,\cdot)\) | 1441.bz | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{41}{65}\right)\) | \(e\left(\frac{7}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) |
\(\chi_{1441}(19,\cdot)\) | 1441.bz | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{12}{13}\right)\) |
\(\chi_{1441}(20,\cdot)\) | 1441.bh | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{21}{65}\right)\) |
\(\chi_{1441}(21,\cdot)\) | 1441.bq | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{103}{130}\right)\) | \(e\left(\frac{3}{65}\right)\) | \(e\left(\frac{38}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{49}{130}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{31}{130}\right)\) | \(e\left(\frac{41}{65}\right)\) |
\(\chi_{1441}(23,\cdot)\) | 1441.bs | 130 | no | \(-1\) | \(1\) | \(e\left(\frac{23}{130}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{9}{65}\right)\) | \(e\left(\frac{119}{130}\right)\) | \(e\left(\frac{64}{65}\right)\) | \(e\left(\frac{69}{130}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{41}{130}\right)\) | \(e\left(\frac{6}{65}\right)\) |
\(\chi_{1441}(24,\cdot)\) | 1441.bz | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{11}{130}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{9}{13}\right)\) |
\(\chi_{1441}(25,\cdot)\) | 1441.bj | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{33}{65}\right)\) | \(e\left(\frac{23}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{49}{65}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) |
\(\chi_{1441}(26,\cdot)\) | 1441.cd | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{16}{65}\right)\) | \(e\left(\frac{113}{130}\right)\) | \(e\left(\frac{53}{65}\right)\) |
\(\chi_{1441}(27,\cdot)\) | 1441.bj | 65 | yes | \(1\) | \(1\) | \(e\left(\frac{4}{65}\right)\) | \(e\left(\frac{54}{65}\right)\) | \(e\left(\frac{8}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{62}{65}\right)\) |
\(\chi_{1441}(28,\cdot)\) | 1441.cc | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{87}{130}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{62}{65}\right)\) | \(e\left(\frac{121}{130}\right)\) | \(e\left(\frac{51}{65}\right)\) |
\(\chi_{1441}(29,\cdot)\) | 1441.bx | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{12}{65}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{18}{65}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{2}{65}\right)\) |
\(\chi_{1441}(30,\cdot)\) | 1441.bx | 130 | yes | \(1\) | \(1\) | \(e\left(\frac{14}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{28}{65}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{127}{130}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) |
\(\chi_{1441}(31,\cdot)\) | 1441.bp | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{56}{65}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{43}{65}\right)\) | \(e\left(\frac{89}{130}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{61}{130}\right)\) | \(e\left(\frac{47}{65}\right)\) | \(e\left(\frac{63}{130}\right)\) | \(e\left(\frac{33}{65}\right)\) |
\(\chi_{1441}(32,\cdot)\) | 1441.bd | 26 | yes | \(1\) | \(1\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) |
\(\chi_{1441}(34,\cdot)\) | 1441.bl | 65 | no | \(1\) | \(1\) | \(e\left(\frac{22}{65}\right)\) | \(e\left(\frac{24}{65}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{37}{65}\right)\) | \(e\left(\frac{46}{65}\right)\) | \(e\left(\frac{32}{65}\right)\) | \(e\left(\frac{1}{65}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{59}{65}\right)\) | \(e\left(\frac{3}{65}\right)\) |
\(\chi_{1441}(35,\cdot)\) | 1441.cc | 130 | yes | \(-1\) | \(1\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{83}{130}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{58}{65}\right)\) | \(e\left(\frac{109}{130}\right)\) | \(e\left(\frac{54}{65}\right)\) |