sage: H = DirichletGroup(669)
pari: g = idealstar(,669,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 444 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{222}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{669}(224,\cdot)$, $\chi_{669}(226,\cdot)$ |
First 32 of 444 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 | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{669}(1,\cdot)\) | 669.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{669}(2,\cdot)\) | 669.l | 74 | yes | \(-1\) | \(1\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{49}{74}\right)\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{19}{74}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{29}{37}\right)\) |
\(\chi_{669}(4,\cdot)\) | 669.i | 37 | no | \(1\) | \(1\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{29}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) |
\(\chi_{669}(5,\cdot)\) | 669.p | 222 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{74}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{20}{111}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{187}{222}\right)\) | \(e\left(\frac{44}{111}\right)\) | \(e\left(\frac{69}{74}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{24}{37}\right)\) |
\(\chi_{669}(7,\cdot)\) | 669.i | 37 | no | \(1\) | \(1\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{34}{37}\right)\) | \(e\left(\frac{3}{37}\right)\) |
\(\chi_{669}(8,\cdot)\) | 669.l | 74 | yes | \(-1\) | \(1\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{1}{74}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{11}{74}\right)\) | \(e\left(\frac{13}{37}\right)\) |
\(\chi_{669}(10,\cdot)\) | 669.n | 222 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{187}{222}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{211}{222}\right)\) | \(e\left(\frac{145}{222}\right)\) | \(e\left(\frac{9}{74}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) |
\(\chi_{669}(11,\cdot)\) | 669.p | 222 | yes | \(1\) | \(1\) | \(e\left(\frac{19}{74}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{44}{111}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{145}{222}\right)\) | \(e\left(\frac{8}{111}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{35}{74}\right)\) | \(e\left(\frac{1}{37}\right)\) |
\(\chi_{669}(13,\cdot)\) | 669.j | 74 | no | \(-1\) | \(1\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{69}{74}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{9}{74}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{9}{37}\right)\) | \(e\left(\frac{28}{37}\right)\) |
\(\chi_{669}(14,\cdot)\) | 669.l | 74 | yes | \(-1\) | \(1\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{34}{37}\right)\) | \(e\left(\frac{11}{74}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{35}{74}\right)\) | \(e\left(\frac{9}{37}\right)\) | \(e\left(\frac{47}{74}\right)\) | \(e\left(\frac{32}{37}\right)\) |
\(\chi_{669}(16,\cdot)\) | 669.i | 37 | no | \(1\) | \(1\) | \(e\left(\frac{29}{37}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{28}{37}\right)\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{5}{37}\right)\) |
\(\chi_{669}(17,\cdot)\) | 669.l | 74 | yes | \(-1\) | \(1\) | \(e\left(\frac{19}{74}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{35}{74}\right)\) | \(e\left(\frac{1}{37}\right)\) |
\(\chi_{669}(19,\cdot)\) | 669.m | 111 | no | \(1\) | \(1\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{34}{37}\right)\) | \(e\left(\frac{106}{111}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{46}{111}\right)\) | \(e\left(\frac{100}{111}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{31}{37}\right)\) |
\(\chi_{669}(20,\cdot)\) | 669.p | 222 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{74}\right)\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{56}{111}\right)\) | \(e\left(\frac{27}{37}\right)\) | \(e\left(\frac{49}{74}\right)\) | \(e\left(\frac{13}{222}\right)\) | \(e\left(\frac{101}{111}\right)\) | \(e\left(\frac{23}{74}\right)\) | \(e\left(\frac{21}{74}\right)\) | \(e\left(\frac{8}{37}\right)\) |
\(\chi_{669}(22,\cdot)\) | 669.n | 222 | no | \(-1\) | \(1\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{13}{222}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{169}{222}\right)\) | \(e\left(\frac{73}{222}\right)\) | \(e\left(\frac{3}{74}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{30}{37}\right)\) |
\(\chi_{669}(23,\cdot)\) | 669.p | 222 | yes | \(1\) | \(1\) | \(e\left(\frac{49}{74}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{94}{111}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{113}{222}\right)\) | \(e\left(\frac{7}{111}\right)\) | \(e\left(\frac{69}{74}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{24}{37}\right)\) |
\(\chi_{669}(25,\cdot)\) | 669.m | 111 | no | \(1\) | \(1\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{40}{111}\right)\) | \(e\left(\frac{14}{37}\right)\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{76}{111}\right)\) | \(e\left(\frac{88}{111}\right)\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) |
\(\chi_{669}(26,\cdot)\) | 669.k | 74 | yes | \(1\) | \(1\) | \(e\left(\frac{47}{74}\right)\) | \(e\left(\frac{10}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{39}{74}\right)\) | \(e\left(\frac{71}{74}\right)\) | \(e\left(\frac{20}{37}\right)\) |
\(\chi_{669}(28,\cdot)\) | 669.i | 37 | no | \(1\) | \(1\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{19}{37}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{27}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{24}{37}\right)\) |
\(\chi_{669}(29,\cdot)\) | 669.o | 222 | yes | \(-1\) | \(1\) | \(e\left(\frac{21}{74}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{181}{222}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{63}{74}\right)\) | \(e\left(\frac{11}{111}\right)\) | \(e\left(\frac{43}{222}\right)\) | \(e\left(\frac{28}{37}\right)\) | \(e\left(\frac{27}{74}\right)\) | \(e\left(\frac{5}{37}\right)\) |
\(\chi_{669}(31,\cdot)\) | 669.m | 111 | no | \(1\) | \(1\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{97}{111}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{40}{111}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{2}{37}\right)\) | \(e\left(\frac{35}{37}\right)\) |
\(\chi_{669}(32,\cdot)\) | 669.l | 74 | yes | \(-1\) | \(1\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{23}{74}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{51}{74}\right)\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{21}{74}\right)\) | \(e\left(\frac{35}{37}\right)\) | \(e\left(\frac{43}{74}\right)\) | \(e\left(\frac{34}{37}\right)\) |
\(\chi_{669}(34,\cdot)\) | 669.i | 37 | no | \(1\) | \(1\) | \(e\left(\frac{26}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{33}{37}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{22}{37}\right)\) | \(e\left(\frac{6}{37}\right)\) | \(e\left(\frac{20}{37}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{30}{37}\right)\) |
\(\chi_{669}(35,\cdot)\) | 669.p | 222 | yes | \(1\) | \(1\) | \(e\left(\frac{69}{74}\right)\) | \(e\left(\frac{32}{37}\right)\) | \(e\left(\frac{41}{111}\right)\) | \(e\left(\frac{31}{37}\right)\) | \(e\left(\frac{59}{74}\right)\) | \(e\left(\frac{67}{222}\right)\) | \(e\left(\frac{68}{111}\right)\) | \(e\left(\frac{73}{74}\right)\) | \(e\left(\frac{57}{74}\right)\) | \(e\left(\frac{27}{37}\right)\) |
\(\chi_{669}(37,\cdot)\) | 669.m | 111 | no | \(1\) | \(1\) | \(e\left(\frac{9}{37}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{104}{111}\right)\) | \(e\left(\frac{29}{37}\right)\) | \(e\left(\frac{27}{37}\right)\) | \(e\left(\frac{20}{111}\right)\) | \(e\left(\frac{29}{111}\right)\) | \(e\left(\frac{24}{37}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{36}{37}\right)\) |
\(\chi_{669}(38,\cdot)\) | 669.o | 222 | yes | \(-1\) | \(1\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{137}{222}\right)\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{58}{111}\right)\) | \(e\left(\frac{35}{222}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{65}{74}\right)\) | \(e\left(\frac{23}{37}\right)\) |
\(\chi_{669}(40,\cdot)\) | 669.h | 6 | no | \(-1\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
\(\chi_{669}(41,\cdot)\) | 669.l | 74 | yes | \(-1\) | \(1\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{30}{37}\right)\) | \(e\left(\frac{21}{74}\right)\) | \(e\left(\frac{36}{37}\right)\) | \(e\left(\frac{53}{74}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{61}{74}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{65}{74}\right)\) | \(e\left(\frac{23}{37}\right)\) |
\(\chi_{669}(43,\cdot)\) | 669.m | 111 | no | \(1\) | \(1\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{13}{37}\right)\) | \(e\left(\frac{34}{111}\right)\) | \(e\left(\frac{23}{37}\right)\) | \(e\left(\frac{1}{37}\right)\) | \(e\left(\frac{109}{111}\right)\) | \(e\left(\frac{97}{111}\right)\) | \(e\left(\frac{5}{37}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{26}{37}\right)\) |
\(\chi_{669}(44,\cdot)\) | 669.p | 222 | yes | \(1\) | \(1\) | \(e\left(\frac{11}{74}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{80}{111}\right)\) | \(e\left(\frac{28}{37}\right)\) | \(e\left(\frac{33}{74}\right)\) | \(e\left(\frac{193}{222}\right)\) | \(e\left(\frac{65}{111}\right)\) | \(e\left(\frac{17}{74}\right)\) | \(e\left(\frac{67}{74}\right)\) | \(e\left(\frac{22}{37}\right)\) |
\(\chi_{669}(46,\cdot)\) | 669.n | 222 | no | \(-1\) | \(1\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{8}{37}\right)\) | \(e\left(\frac{113}{222}\right)\) | \(e\left(\frac{17}{37}\right)\) | \(e\left(\frac{12}{37}\right)\) | \(e\left(\frac{137}{222}\right)\) | \(e\left(\frac{71}{222}\right)\) | \(e\left(\frac{9}{74}\right)\) | \(e\left(\frac{21}{37}\right)\) | \(e\left(\frac{16}{37}\right)\) |
\(\chi_{669}(47,\cdot)\) | 669.o | 222 | yes | \(-1\) | \(1\) | \(e\left(\frac{3}{74}\right)\) | \(e\left(\frac{3}{37}\right)\) | \(e\left(\frac{121}{222}\right)\) | \(e\left(\frac{11}{37}\right)\) | \(e\left(\frac{9}{74}\right)\) | \(e\left(\frac{65}{111}\right)\) | \(e\left(\frac{133}{222}\right)\) | \(e\left(\frac{4}{37}\right)\) | \(e\left(\frac{25}{74}\right)\) | \(e\left(\frac{6}{37}\right)\) |