Properties

Modulus 293
Structure \(C_{292}\)
Order 292

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(293)
pari: g = idealstar(,293,2)

Character group

sage: G.order()
pari: g.no
Order = 292
sage: H.invariants()
pari: g.cyc
Structure = \(C_{292}\)
sage: H.gens()
pari: g.gen
Generators = $\chi_{293}(2,\cdot)$

First 32 of 292 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.

orbit label order primitive -1 1 2 3 4 5 6 7 8 9 10 11
\(\chi_{293}(1,\cdot)\) 293.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{293}(2,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{1}{292}\right)\) \(e\left(\frac{157}{292}\right)\) \(e\left(\frac{1}{146}\right)\) \(e\left(\frac{173}{292}\right)\) \(e\left(\frac{79}{146}\right)\) \(e\left(\frac{213}{292}\right)\) \(e\left(\frac{3}{292}\right)\) \(e\left(\frac{11}{146}\right)\) \(e\left(\frac{87}{146}\right)\) \(e\left(\frac{115}{292}\right)\)
\(\chi_{293}(3,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{157}{292}\right)\) \(e\left(\frac{121}{292}\right)\) \(e\left(\frac{11}{146}\right)\) \(e\left(\frac{5}{292}\right)\) \(e\left(\frac{139}{146}\right)\) \(e\left(\frac{153}{292}\right)\) \(e\left(\frac{179}{292}\right)\) \(e\left(\frac{121}{146}\right)\) \(e\left(\frac{81}{146}\right)\) \(e\left(\frac{243}{292}\right)\)
\(\chi_{293}(4,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{1}{146}\right)\) \(e\left(\frac{11}{146}\right)\) \(e\left(\frac{1}{73}\right)\) \(e\left(\frac{27}{146}\right)\) \(e\left(\frac{6}{73}\right)\) \(e\left(\frac{67}{146}\right)\) \(e\left(\frac{3}{146}\right)\) \(e\left(\frac{11}{73}\right)\) \(e\left(\frac{14}{73}\right)\) \(e\left(\frac{115}{146}\right)\)
\(\chi_{293}(5,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{173}{292}\right)\) \(e\left(\frac{5}{292}\right)\) \(e\left(\frac{27}{146}\right)\) \(e\left(\frac{145}{292}\right)\) \(e\left(\frac{89}{146}\right)\) \(e\left(\frac{57}{292}\right)\) \(e\left(\frac{227}{292}\right)\) \(e\left(\frac{5}{146}\right)\) \(e\left(\frac{13}{146}\right)\) \(e\left(\frac{39}{292}\right)\)
\(\chi_{293}(6,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{79}{146}\right)\) \(e\left(\frac{139}{146}\right)\) \(e\left(\frac{6}{73}\right)\) \(e\left(\frac{89}{146}\right)\) \(e\left(\frac{36}{73}\right)\) \(e\left(\frac{37}{146}\right)\) \(e\left(\frac{91}{146}\right)\) \(e\left(\frac{66}{73}\right)\) \(e\left(\frac{11}{73}\right)\) \(e\left(\frac{33}{146}\right)\)
\(\chi_{293}(7,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{213}{292}\right)\) \(e\left(\frac{153}{292}\right)\) \(e\left(\frac{67}{146}\right)\) \(e\left(\frac{57}{292}\right)\) \(e\left(\frac{37}{146}\right)\) \(e\left(\frac{109}{292}\right)\) \(e\left(\frac{55}{292}\right)\) \(e\left(\frac{7}{146}\right)\) \(e\left(\frac{135}{146}\right)\) \(e\left(\frac{259}{292}\right)\)
\(\chi_{293}(8,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{3}{292}\right)\) \(e\left(\frac{179}{292}\right)\) \(e\left(\frac{3}{146}\right)\) \(e\left(\frac{227}{292}\right)\) \(e\left(\frac{91}{146}\right)\) \(e\left(\frac{55}{292}\right)\) \(e\left(\frac{9}{292}\right)\) \(e\left(\frac{33}{146}\right)\) \(e\left(\frac{115}{146}\right)\) \(e\left(\frac{53}{292}\right)\)
\(\chi_{293}(9,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{11}{146}\right)\) \(e\left(\frac{121}{146}\right)\) \(e\left(\frac{11}{73}\right)\) \(e\left(\frac{5}{146}\right)\) \(e\left(\frac{66}{73}\right)\) \(e\left(\frac{7}{146}\right)\) \(e\left(\frac{33}{146}\right)\) \(e\left(\frac{48}{73}\right)\) \(e\left(\frac{8}{73}\right)\) \(e\left(\frac{97}{146}\right)\)
\(\chi_{293}(10,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{87}{146}\right)\) \(e\left(\frac{81}{146}\right)\) \(e\left(\frac{14}{73}\right)\) \(e\left(\frac{13}{146}\right)\) \(e\left(\frac{11}{73}\right)\) \(e\left(\frac{135}{146}\right)\) \(e\left(\frac{115}{146}\right)\) \(e\left(\frac{8}{73}\right)\) \(e\left(\frac{50}{73}\right)\) \(e\left(\frac{77}{146}\right)\)
\(\chi_{293}(11,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{115}{292}\right)\) \(e\left(\frac{243}{292}\right)\) \(e\left(\frac{115}{146}\right)\) \(e\left(\frac{39}{292}\right)\) \(e\left(\frac{33}{146}\right)\) \(e\left(\frac{259}{292}\right)\) \(e\left(\frac{53}{292}\right)\) \(e\left(\frac{97}{146}\right)\) \(e\left(\frac{77}{146}\right)\) \(e\left(\frac{85}{292}\right)\)
\(\chi_{293}(12,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{159}{292}\right)\) \(e\left(\frac{143}{292}\right)\) \(e\left(\frac{13}{146}\right)\) \(e\left(\frac{59}{292}\right)\) \(e\left(\frac{5}{146}\right)\) \(e\left(\frac{287}{292}\right)\) \(e\left(\frac{185}{292}\right)\) \(e\left(\frac{143}{146}\right)\) \(e\left(\frac{109}{146}\right)\) \(e\left(\frac{181}{292}\right)\)
\(\chi_{293}(13,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{243}{292}\right)\) \(e\left(\frac{191}{292}\right)\) \(e\left(\frac{97}{146}\right)\) \(e\left(\frac{283}{292}\right)\) \(e\left(\frac{71}{146}\right)\) \(e\left(\frac{75}{292}\right)\) \(e\left(\frac{145}{292}\right)\) \(e\left(\frac{45}{146}\right)\) \(e\left(\frac{117}{146}\right)\) \(e\left(\frac{205}{292}\right)\)
\(\chi_{293}(14,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{107}{146}\right)\) \(e\left(\frac{9}{146}\right)\) \(e\left(\frac{34}{73}\right)\) \(e\left(\frac{115}{146}\right)\) \(e\left(\frac{58}{73}\right)\) \(e\left(\frac{15}{146}\right)\) \(e\left(\frac{29}{146}\right)\) \(e\left(\frac{9}{73}\right)\) \(e\left(\frac{38}{73}\right)\) \(e\left(\frac{41}{146}\right)\)
\(\chi_{293}(15,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{19}{146}\right)\) \(e\left(\frac{63}{146}\right)\) \(e\left(\frac{19}{73}\right)\) \(e\left(\frac{75}{146}\right)\) \(e\left(\frac{41}{73}\right)\) \(e\left(\frac{105}{146}\right)\) \(e\left(\frac{57}{146}\right)\) \(e\left(\frac{63}{73}\right)\) \(e\left(\frac{47}{73}\right)\) \(e\left(\frac{141}{146}\right)\)
\(\chi_{293}(16,\cdot)\) 293.d 73 Yes \(1\) \(1\) \(e\left(\frac{1}{73}\right)\) \(e\left(\frac{11}{73}\right)\) \(e\left(\frac{2}{73}\right)\) \(e\left(\frac{27}{73}\right)\) \(e\left(\frac{12}{73}\right)\) \(e\left(\frac{67}{73}\right)\) \(e\left(\frac{3}{73}\right)\) \(e\left(\frac{22}{73}\right)\) \(e\left(\frac{28}{73}\right)\) \(e\left(\frac{42}{73}\right)\)
\(\chi_{293}(17,\cdot)\) 293.d 73 Yes \(1\) \(1\) \(e\left(\frac{55}{73}\right)\) \(e\left(\frac{21}{73}\right)\) \(e\left(\frac{37}{73}\right)\) \(e\left(\frac{25}{73}\right)\) \(e\left(\frac{3}{73}\right)\) \(e\left(\frac{35}{73}\right)\) \(e\left(\frac{19}{73}\right)\) \(e\left(\frac{42}{73}\right)\) \(e\left(\frac{7}{73}\right)\) \(e\left(\frac{47}{73}\right)\)
\(\chi_{293}(18,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{23}{292}\right)\) \(e\left(\frac{107}{292}\right)\) \(e\left(\frac{23}{146}\right)\) \(e\left(\frac{183}{292}\right)\) \(e\left(\frac{65}{146}\right)\) \(e\left(\frac{227}{292}\right)\) \(e\left(\frac{69}{292}\right)\) \(e\left(\frac{107}{146}\right)\) \(e\left(\frac{103}{146}\right)\) \(e\left(\frac{17}{292}\right)\)
\(\chi_{293}(19,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{111}{292}\right)\) \(e\left(\frac{199}{292}\right)\) \(e\left(\frac{111}{146}\right)\) \(e\left(\frac{223}{292}\right)\) \(e\left(\frac{9}{146}\right)\) \(e\left(\frac{283}{292}\right)\) \(e\left(\frac{41}{292}\right)\) \(e\left(\frac{53}{146}\right)\) \(e\left(\frac{21}{146}\right)\) \(e\left(\frac{209}{292}\right)\)
\(\chi_{293}(20,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{175}{292}\right)\) \(e\left(\frac{27}{292}\right)\) \(e\left(\frac{29}{146}\right)\) \(e\left(\frac{199}{292}\right)\) \(e\left(\frac{101}{146}\right)\) \(e\left(\frac{191}{292}\right)\) \(e\left(\frac{233}{292}\right)\) \(e\left(\frac{27}{146}\right)\) \(e\left(\frac{41}{146}\right)\) \(e\left(\frac{269}{292}\right)\)
\(\chi_{293}(21,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{39}{146}\right)\) \(e\left(\frac{137}{146}\right)\) \(e\left(\frac{39}{73}\right)\) \(e\left(\frac{31}{146}\right)\) \(e\left(\frac{15}{73}\right)\) \(e\left(\frac{131}{146}\right)\) \(e\left(\frac{117}{146}\right)\) \(e\left(\frac{64}{73}\right)\) \(e\left(\frac{35}{73}\right)\) \(e\left(\frac{105}{146}\right)\)
\(\chi_{293}(22,\cdot)\) 293.d 73 Yes \(1\) \(1\) \(e\left(\frac{29}{73}\right)\) \(e\left(\frac{27}{73}\right)\) \(e\left(\frac{58}{73}\right)\) \(e\left(\frac{53}{73}\right)\) \(e\left(\frac{56}{73}\right)\) \(e\left(\frac{45}{73}\right)\) \(e\left(\frac{14}{73}\right)\) \(e\left(\frac{54}{73}\right)\) \(e\left(\frac{9}{73}\right)\) \(e\left(\frac{50}{73}\right)\)
\(\chi_{293}(23,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{207}{292}\right)\) \(e\left(\frac{87}{292}\right)\) \(e\left(\frac{61}{146}\right)\) \(e\left(\frac{187}{292}\right)\) \(e\left(\frac{1}{146}\right)\) \(e\left(\frac{291}{292}\right)\) \(e\left(\frac{37}{292}\right)\) \(e\left(\frac{87}{146}\right)\) \(e\left(\frac{51}{146}\right)\) \(e\left(\frac{153}{292}\right)\)
\(\chi_{293}(24,\cdot)\) 293.d 73 Yes \(1\) \(1\) \(e\left(\frac{40}{73}\right)\) \(e\left(\frac{2}{73}\right)\) \(e\left(\frac{7}{73}\right)\) \(e\left(\frac{58}{73}\right)\) \(e\left(\frac{42}{73}\right)\) \(e\left(\frac{52}{73}\right)\) \(e\left(\frac{47}{73}\right)\) \(e\left(\frac{4}{73}\right)\) \(e\left(\frac{25}{73}\right)\) \(e\left(\frac{1}{73}\right)\)
\(\chi_{293}(25,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{27}{146}\right)\) \(e\left(\frac{5}{146}\right)\) \(e\left(\frac{27}{73}\right)\) \(e\left(\frac{145}{146}\right)\) \(e\left(\frac{16}{73}\right)\) \(e\left(\frac{57}{146}\right)\) \(e\left(\frac{81}{146}\right)\) \(e\left(\frac{5}{73}\right)\) \(e\left(\frac{13}{73}\right)\) \(e\left(\frac{39}{146}\right)\)
\(\chi_{293}(26,\cdot)\) 293.d 73 Yes \(1\) \(1\) \(e\left(\frac{61}{73}\right)\) \(e\left(\frac{14}{73}\right)\) \(e\left(\frac{49}{73}\right)\) \(e\left(\frac{41}{73}\right)\) \(e\left(\frac{2}{73}\right)\) \(e\left(\frac{72}{73}\right)\) \(e\left(\frac{37}{73}\right)\) \(e\left(\frac{28}{73}\right)\) \(e\left(\frac{29}{73}\right)\) \(e\left(\frac{7}{73}\right)\)
\(\chi_{293}(27,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{179}{292}\right)\) \(e\left(\frac{71}{292}\right)\) \(e\left(\frac{33}{146}\right)\) \(e\left(\frac{15}{292}\right)\) \(e\left(\frac{125}{146}\right)\) \(e\left(\frac{167}{292}\right)\) \(e\left(\frac{245}{292}\right)\) \(e\left(\frac{71}{146}\right)\) \(e\left(\frac{97}{146}\right)\) \(e\left(\frac{145}{292}\right)\)
\(\chi_{293}(28,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{215}{292}\right)\) \(e\left(\frac{175}{292}\right)\) \(e\left(\frac{69}{146}\right)\) \(e\left(\frac{111}{292}\right)\) \(e\left(\frac{49}{146}\right)\) \(e\left(\frac{243}{292}\right)\) \(e\left(\frac{61}{292}\right)\) \(e\left(\frac{29}{146}\right)\) \(e\left(\frac{17}{146}\right)\) \(e\left(\frac{197}{292}\right)\)
\(\chi_{293}(29,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{129}{292}\right)\) \(e\left(\frac{105}{292}\right)\) \(e\left(\frac{129}{146}\right)\) \(e\left(\frac{125}{292}\right)\) \(e\left(\frac{117}{146}\right)\) \(e\left(\frac{29}{292}\right)\) \(e\left(\frac{95}{292}\right)\) \(e\left(\frac{105}{146}\right)\) \(e\left(\frac{127}{146}\right)\) \(e\left(\frac{235}{292}\right)\)
\(\chi_{293}(30,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{39}{292}\right)\) \(e\left(\frac{283}{292}\right)\) \(e\left(\frac{39}{146}\right)\) \(e\left(\frac{31}{292}\right)\) \(e\left(\frac{15}{146}\right)\) \(e\left(\frac{131}{292}\right)\) \(e\left(\frac{117}{292}\right)\) \(e\left(\frac{137}{146}\right)\) \(e\left(\frac{35}{146}\right)\) \(e\left(\frac{105}{292}\right)\)
\(\chi_{293}(31,\cdot)\) 293.e 146 Yes \(1\) \(1\) \(e\left(\frac{23}{146}\right)\) \(e\left(\frac{107}{146}\right)\) \(e\left(\frac{23}{73}\right)\) \(e\left(\frac{37}{146}\right)\) \(e\left(\frac{65}{73}\right)\) \(e\left(\frac{81}{146}\right)\) \(e\left(\frac{69}{146}\right)\) \(e\left(\frac{34}{73}\right)\) \(e\left(\frac{30}{73}\right)\) \(e\left(\frac{17}{146}\right)\)
\(\chi_{293}(32,\cdot)\) 293.f 292 Yes \(-1\) \(1\) \(e\left(\frac{5}{292}\right)\) \(e\left(\frac{201}{292}\right)\) \(e\left(\frac{5}{146}\right)\) \(e\left(\frac{281}{292}\right)\) \(e\left(\frac{103}{146}\right)\) \(e\left(\frac{189}{292}\right)\) \(e\left(\frac{15}{292}\right)\) \(e\left(\frac{55}{146}\right)\) \(e\left(\frac{143}{146}\right)\) \(e\left(\frac{283}{292}\right)\)