sage: H = DirichletGroup(2563)
pari: g = idealstar(,2563,2)
Character group
sage: G.order()
pari: g.no
| ||
Order | = | 2320 |
sage: H.invariants()
pari: g.cyc
| ||
Structure | = | \(C_{2}\times C_{1160}\) |
sage: H.gens()
pari: g.gen
| ||
Generators | = | $\chi_{2563}(1399,\cdot)$, $\chi_{2563}(2333,\cdot)$ |
First 32 of 2320 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 | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\chi_{2563}(1,\cdot)\) | 2563.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
\(\chi_{2563}(2,\cdot)\) | 2563.ba | 290 | yes | \(-1\) | \(1\) | \(e\left(\frac{129}{290}\right)\) | \(e\left(\frac{16}{145}\right)\) | \(e\left(\frac{129}{145}\right)\) | \(e\left(\frac{88}{145}\right)\) | \(e\left(\frac{161}{290}\right)\) | \(e\left(\frac{173}{290}\right)\) | \(e\left(\frac{97}{290}\right)\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(1\) |
\(\chi_{2563}(3,\cdot)\) | 2563.bf | 1160 | yes | \(-1\) | \(1\) | \(e\left(\frac{16}{145}\right)\) | \(e\left(\frac{469}{1160}\right)\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{1057}{1160}\right)\) | \(e\left(\frac{597}{1160}\right)\) | \(e\left(\frac{323}{580}\right)\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{469}{580}\right)\) | \(e\left(\frac{5}{232}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2563}(4,\cdot)\) | 2563.w | 145 | yes | \(1\) | \(1\) | \(e\left(\frac{129}{145}\right)\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{113}{145}\right)\) | \(e\left(\frac{31}{145}\right)\) | \(e\left(\frac{16}{145}\right)\) | \(e\left(\frac{28}{145}\right)\) | \(e\left(\frac{97}{145}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(1\) |
\(\chi_{2563}(5,\cdot)\) | 2563.bf | 1160 | yes | \(-1\) | \(1\) | \(e\left(\frac{88}{145}\right)\) | \(e\left(\frac{1057}{1160}\right)\) | \(e\left(\frac{31}{145}\right)\) | \(e\left(\frac{1101}{1160}\right)\) | \(e\left(\frac{601}{1160}\right)\) | \(e\left(\frac{399}{580}\right)\) | \(e\left(\frac{119}{145}\right)\) | \(e\left(\frac{477}{580}\right)\) | \(e\left(\frac{129}{232}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{2563}(6,\cdot)\) | 2563.be | 1160 | yes | \(1\) | \(1\) | \(e\left(\frac{161}{290}\right)\) | \(e\left(\frac{597}{1160}\right)\) | \(e\left(\frac{16}{145}\right)\) | \(e\left(\frac{601}{1160}\right)\) | \(e\left(\frac{81}{1160}\right)\) | \(e\left(\frac{89}{580}\right)\) | \(e\left(\frac{193}{290}\right)\) | \(e\left(\frac{17}{580}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2563}(7,\cdot)\) | 2563.bc | 580 | yes | \(-1\) | \(1\) | \(e\left(\frac{173}{290}\right)\) | \(e\left(\frac{323}{580}\right)\) | \(e\left(\frac{28}{145}\right)\) | \(e\left(\frac{399}{580}\right)\) | \(e\left(\frac{89}{580}\right)\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{229}{290}\right)\) | \(e\left(\frac{33}{290}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(-i\) |
\(\chi_{2563}(8,\cdot)\) | 2563.ba | 290 | yes | \(-1\) | \(1\) | \(e\left(\frac{97}{290}\right)\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{97}{145}\right)\) | \(e\left(\frac{119}{145}\right)\) | \(e\left(\frac{193}{290}\right)\) | \(e\left(\frac{229}{290}\right)\) | \(e\left(\frac{1}{290}\right)\) | \(e\left(\frac{96}{145}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(1\) |
\(\chi_{2563}(9,\cdot)\) | 2563.bd | 580 | yes | \(1\) | \(1\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{469}{580}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{477}{580}\right)\) | \(e\left(\frac{17}{580}\right)\) | \(e\left(\frac{33}{290}\right)\) | \(e\left(\frac{96}{145}\right)\) | \(e\left(\frac{179}{290}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(i\) |
\(\chi_{2563}(10,\cdot)\) | 2563.y | 232 | yes | \(1\) | \(1\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{5}{232}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{129}{232}\right)\) | \(e\left(\frac{17}{232}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{5}{116}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{2563}(12,\cdot)\) | 2563.i | 8 | no | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{8}\right)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(-i\) | \(1\) | \(i\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2563}(13,\cdot)\) | 2563.bc | 580 | yes | \(-1\) | \(1\) | \(e\left(\frac{39}{290}\right)\) | \(e\left(\frac{279}{580}\right)\) | \(e\left(\frac{39}{145}\right)\) | \(e\left(\frac{447}{580}\right)\) | \(e\left(\frac{357}{580}\right)\) | \(e\left(\frac{129}{145}\right)\) | \(e\left(\frac{117}{290}\right)\) | \(e\left(\frac{279}{290}\right)\) | \(e\left(\frac{105}{116}\right)\) | \(-i\) |
\(\chi_{2563}(14,\cdot)\) | 2563.bd | 580 | yes | \(1\) | \(1\) | \(e\left(\frac{6}{145}\right)\) | \(e\left(\frac{387}{580}\right)\) | \(e\left(\frac{12}{145}\right)\) | \(e\left(\frac{171}{580}\right)\) | \(e\left(\frac{411}{580}\right)\) | \(e\left(\frac{269}{290}\right)\) | \(e\left(\frac{18}{145}\right)\) | \(e\left(\frac{97}{290}\right)\) | \(e\left(\frac{39}{116}\right)\) | \(-i\) |
\(\chi_{2563}(15,\cdot)\) | 2563.bd | 580 | yes | \(1\) | \(1\) | \(e\left(\frac{104}{145}\right)\) | \(e\left(\frac{183}{580}\right)\) | \(e\left(\frac{63}{145}\right)\) | \(e\left(\frac{499}{580}\right)\) | \(e\left(\frac{19}{580}\right)\) | \(e\left(\frac{71}{290}\right)\) | \(e\left(\frac{22}{145}\right)\) | \(e\left(\frac{183}{290}\right)\) | \(e\left(\frac{67}{116}\right)\) | \(-i\) |
\(\chi_{2563}(16,\cdot)\) | 2563.w | 145 | yes | \(1\) | \(1\) | \(e\left(\frac{113}{145}\right)\) | \(e\left(\frac{64}{145}\right)\) | \(e\left(\frac{81}{145}\right)\) | \(e\left(\frac{62}{145}\right)\) | \(e\left(\frac{32}{145}\right)\) | \(e\left(\frac{56}{145}\right)\) | \(e\left(\frac{49}{145}\right)\) | \(e\left(\frac{128}{145}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(1\) |
\(\chi_{2563}(17,\cdot)\) | 2563.be | 1160 | yes | \(1\) | \(1\) | \(e\left(\frac{251}{290}\right)\) | \(e\left(\frac{747}{1160}\right)\) | \(e\left(\frac{106}{145}\right)\) | \(e\left(\frac{991}{1160}\right)\) | \(e\left(\frac{591}{1160}\right)\) | \(e\left(\frac{499}{580}\right)\) | \(e\left(\frac{173}{290}\right)\) | \(e\left(\frac{167}{580}\right)\) | \(e\left(\frac{167}{232}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2563}(18,\cdot)\) | 2563.bc | 580 | yes | \(-1\) | \(1\) | \(e\left(\frac{193}{290}\right)\) | \(e\left(\frac{533}{580}\right)\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{249}{580}\right)\) | \(e\left(\frac{339}{580}\right)\) | \(e\left(\frac{103}{145}\right)\) | \(e\left(\frac{289}{290}\right)\) | \(e\left(\frac{243}{290}\right)\) | \(e\left(\frac{11}{116}\right)\) | \(i\) |
\(\chi_{2563}(19,\cdot)\) | 2563.ba | 290 | yes | \(-1\) | \(1\) | \(e\left(\frac{147}{290}\right)\) | \(e\left(\frac{143}{145}\right)\) | \(e\left(\frac{2}{145}\right)\) | \(e\left(\frac{134}{145}\right)\) | \(e\left(\frac{143}{290}\right)\) | \(e\left(\frac{69}{290}\right)\) | \(e\left(\frac{151}{290}\right)\) | \(e\left(\frac{141}{145}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(1\) |
\(\chi_{2563}(20,\cdot)\) | 2563.bf | 1160 | yes | \(-1\) | \(1\) | \(e\left(\frac{72}{145}\right)\) | \(e\left(\frac{153}{1160}\right)\) | \(e\left(\frac{144}{145}\right)\) | \(e\left(\frac{189}{1160}\right)\) | \(e\left(\frac{729}{1160}\right)\) | \(e\left(\frac{511}{580}\right)\) | \(e\left(\frac{71}{145}\right)\) | \(e\left(\frac{153}{580}\right)\) | \(e\left(\frac{153}{232}\right)\) | \(e\left(\frac{1}{8}\right)\) |
\(\chi_{2563}(21,\cdot)\) | 2563.y | 232 | yes | \(1\) | \(1\) | \(e\left(\frac{41}{58}\right)\) | \(e\left(\frac{223}{232}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(e\left(\frac{139}{232}\right)\) | \(e\left(\frac{155}{232}\right)\) | \(e\left(\frac{103}{116}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(e\left(\frac{71}{232}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2563}(23,\cdot)\) | 2563.o | 29 | no | \(1\) | \(1\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{12}{29}\right)\) | \(1\) |
\(\chi_{2563}(24,\cdot)\) | 2563.be | 1160 | yes | \(1\) | \(1\) | \(e\left(\frac{129}{290}\right)\) | \(e\left(\frac{853}{1160}\right)\) | \(e\left(\frac{129}{145}\right)\) | \(e\left(\frac{849}{1160}\right)\) | \(e\left(\frac{209}{1160}\right)\) | \(e\left(\frac{201}{580}\right)\) | \(e\left(\frac{97}{290}\right)\) | \(e\left(\frac{273}{580}\right)\) | \(e\left(\frac{41}{232}\right)\) | \(e\left(\frac{5}{8}\right)\) |
\(\chi_{2563}(25,\cdot)\) | 2563.bd | 580 | yes | \(1\) | \(1\) | \(e\left(\frac{31}{145}\right)\) | \(e\left(\frac{477}{580}\right)\) | \(e\left(\frac{62}{145}\right)\) | \(e\left(\frac{521}{580}\right)\) | \(e\left(\frac{21}{580}\right)\) | \(e\left(\frac{109}{290}\right)\) | \(e\left(\frac{93}{145}\right)\) | \(e\left(\frac{187}{290}\right)\) | \(e\left(\frac{13}{116}\right)\) | \(i\) |
\(\chi_{2563}(26,\cdot)\) | 2563.bd | 580 | yes | \(1\) | \(1\) | \(e\left(\frac{84}{145}\right)\) | \(e\left(\frac{343}{580}\right)\) | \(e\left(\frac{23}{145}\right)\) | \(e\left(\frac{219}{580}\right)\) | \(e\left(\frac{99}{580}\right)\) | \(e\left(\frac{141}{290}\right)\) | \(e\left(\frac{107}{145}\right)\) | \(e\left(\frac{53}{290}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(-i\) |
\(\chi_{2563}(27,\cdot)\) | 2563.bf | 1160 | yes | \(-1\) | \(1\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{247}{1160}\right)\) | \(e\left(\frac{96}{145}\right)\) | \(e\left(\frac{851}{1160}\right)\) | \(e\left(\frac{631}{1160}\right)\) | \(e\left(\frac{389}{580}\right)\) | \(e\left(\frac{144}{145}\right)\) | \(e\left(\frac{247}{580}\right)\) | \(e\left(\frac{15}{232}\right)\) | \(e\left(\frac{7}{8}\right)\) |
\(\chi_{2563}(28,\cdot)\) | 2563.bc | 580 | yes | \(-1\) | \(1\) | \(e\left(\frac{141}{290}\right)\) | \(e\left(\frac{451}{580}\right)\) | \(e\left(\frac{141}{145}\right)\) | \(e\left(\frac{523}{580}\right)\) | \(e\left(\frac{153}{580}\right)\) | \(e\left(\frac{76}{145}\right)\) | \(e\left(\frac{133}{290}\right)\) | \(e\left(\frac{161}{290}\right)\) | \(e\left(\frac{45}{116}\right)\) | \(-i\) |
\(\chi_{2563}(29,\cdot)\) | 2563.z | 290 | yes | \(-1\) | \(1\) | \(e\left(\frac{193}{290}\right)\) | \(e\left(\frac{49}{290}\right)\) | \(e\left(\frac{48}{145}\right)\) | \(e\left(\frac{197}{290}\right)\) | \(e\left(\frac{121}{145}\right)\) | \(e\left(\frac{61}{290}\right)\) | \(e\left(\frac{289}{290}\right)\) | \(e\left(\frac{49}{145}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(-1\) |
\(\chi_{2563}(30,\cdot)\) | 2563.bc | 580 | yes | \(-1\) | \(1\) | \(e\left(\frac{47}{290}\right)\) | \(e\left(\frac{247}{580}\right)\) | \(e\left(\frac{47}{145}\right)\) | \(e\left(\frac{271}{580}\right)\) | \(e\left(\frac{341}{580}\right)\) | \(e\left(\frac{122}{145}\right)\) | \(e\left(\frac{141}{290}\right)\) | \(e\left(\frac{247}{290}\right)\) | \(e\left(\frac{73}{116}\right)\) | \(-i\) |
\(\chi_{2563}(31,\cdot)\) | 2563.bd | 580 | yes | \(1\) | \(1\) | \(e\left(\frac{12}{145}\right)\) | \(e\left(\frac{339}{580}\right)\) | \(e\left(\frac{24}{145}\right)\) | \(e\left(\frac{487}{580}\right)\) | \(e\left(\frac{387}{580}\right)\) | \(e\left(\frac{103}{290}\right)\) | \(e\left(\frac{36}{145}\right)\) | \(e\left(\frac{49}{290}\right)\) | \(e\left(\frac{107}{116}\right)\) | \(-i\) |
\(\chi_{2563}(32,\cdot)\) | 2563.s | 58 | yes | \(-1\) | \(1\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) | \(e\left(\frac{39}{58}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(1\) |
\(\chi_{2563}(34,\cdot)\) | 2563.x | 232 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{175}{232}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{107}{232}\right)\) | \(e\left(\frac{15}{232}\right)\) | \(e\left(\frac{53}{116}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{59}{116}\right)\) | \(e\left(\frac{179}{232}\right)\) | \(e\left(\frac{3}{8}\right)\) |
\(\chi_{2563}(35,\cdot)\) | 2563.be | 1160 | yes | \(1\) | \(1\) | \(e\left(\frac{59}{290}\right)\) | \(e\left(\frac{543}{1160}\right)\) | \(e\left(\frac{59}{145}\right)\) | \(e\left(\frac{739}{1160}\right)\) | \(e\left(\frac{779}{1160}\right)\) | \(e\left(\frac{11}{580}\right)\) | \(e\left(\frac{177}{290}\right)\) | \(e\left(\frac{543}{580}\right)\) | \(e\left(\frac{195}{232}\right)\) | \(e\left(\frac{7}{8}\right)\) |