Properties

Modulus $2563$
Structure \(C_{2}\times C_{1160}\)
Order $2320$

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Show commands: PariGP / SageMath

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 \(1\) \(1\) \(e\left(\frac{59}{290}\right)\) \(e\left(\frac{543}{1160}\right)\) \(e\left(\frac{59}{145}\right)\) \(e\left(\frac{739}{1160}\right)\) \(e\left(\frac{779}{1160}\right)\) \(e\left(\frac{11}{580}\right)\) \(e\left(\frac{177}{290}\right)\) \(e\left(\frac{543}{580}\right)\) \(e\left(\frac{195}{232}\right)\) \(e\left(\frac{7}{8}\right)\)
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