Properties

Modulus 4014
Structure \(C_{222}\times C_{6}\)
Order 1332

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4014)
 
pari: g = idealstar(,4014,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1332
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{222}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4014}(2233,\cdot)$, $\chi_{4014}(893,\cdot)$

First 32 of 1332 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 5 7 11 13 17 19 23 25 29 31
\(\chi_{4014}(1,\cdot)\) 4014.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4014}(5,\cdot)\) 4014.bk 222 No \(1\) \(1\) \(e\left(\frac{94}{111}\right)\) \(e\left(\frac{58}{111}\right)\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{133}{222}\right)\) \(e\left(\frac{17}{74}\right)\) \(e\left(\frac{106}{111}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{77}{111}\right)\) \(e\left(\frac{11}{74}\right)\) \(e\left(\frac{20}{37}\right)\)
\(\chi_{4014}(7,\cdot)\) 4014.bb 111 No \(1\) \(1\) \(e\left(\frac{58}{111}\right)\) \(e\left(\frac{35}{111}\right)\) \(e\left(\frac{98}{111}\right)\) \(e\left(\frac{43}{111}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{58}{111}\right)\) \(e\left(\frac{5}{111}\right)\) \(e\left(\frac{83}{111}\right)\) \(e\left(\frac{100}{111}\right)\)
\(\chi_{4014}(11,\cdot)\) 4014.bc 222 No \(1\) \(1\) \(e\left(\frac{27}{37}\right)\) \(e\left(\frac{98}{111}\right)\) \(e\left(\frac{82}{111}\right)\) \(e\left(\frac{41}{222}\right)\) \(e\left(\frac{67}{74}\right)\) \(e\left(\frac{100}{111}\right)\) \(e\left(\frac{44}{111}\right)\) \(e\left(\frac{17}{37}\right)\) \(e\left(\frac{191}{222}\right)\) \(e\left(\frac{95}{111}\right)\)
\(\chi_{4014}(13,\cdot)\) 4014.bf 222 No \(-1\) \(1\) \(e\left(\frac{133}{222}\right)\) \(e\left(\frac{43}{111}\right)\) \(e\left(\frac{41}{222}\right)\) \(e\left(\frac{1}{222}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{33}{37}\right)\) \(e\left(\frac{133}{222}\right)\) \(e\left(\frac{22}{111}\right)\) \(e\left(\frac{10}{111}\right)\) \(e\left(\frac{107}{111}\right)\)
\(\chi_{4014}(17,\cdot)\) 4014.w 74 No \(-1\) \(1\) \(e\left(\frac{17}{74}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{67}{74}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{67}{74}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{17}{74}\right)\) \(e\left(\frac{17}{37}\right)\) \(e\left(\frac{39}{74}\right)\) \(e\left(\frac{7}{37}\right)\)
\(\chi_{4014}(19,\cdot)\) 4014.z 111 No \(1\) \(1\) \(e\left(\frac{106}{111}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{100}{111}\right)\) \(e\left(\frac{33}{37}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{29}{111}\right)\) \(e\left(\frac{32}{111}\right)\) \(e\left(\frac{101}{111}\right)\) \(e\left(\frac{19}{111}\right)\) \(e\left(\frac{59}{111}\right)\)
\(\chi_{4014}(23,\cdot)\) 4014.bc 222 No \(1\) \(1\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{58}{111}\right)\) \(e\left(\frac{44}{111}\right)\) \(e\left(\frac{133}{222}\right)\) \(e\left(\frac{17}{74}\right)\) \(e\left(\frac{32}{111}\right)\) \(e\left(\frac{94}{111}\right)\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{181}{222}\right)\) \(e\left(\frac{97}{111}\right)\)
\(\chi_{4014}(25,\cdot)\) 4014.ba 111 No \(1\) \(1\) \(e\left(\frac{77}{111}\right)\) \(e\left(\frac{5}{111}\right)\) \(e\left(\frac{17}{37}\right)\) \(e\left(\frac{22}{111}\right)\) \(e\left(\frac{17}{37}\right)\) \(e\left(\frac{101}{111}\right)\) \(e\left(\frac{1}{37}\right)\) \(e\left(\frac{43}{111}\right)\) \(e\left(\frac{11}{37}\right)\) \(e\left(\frac{3}{37}\right)\)
\(\chi_{4014}(29,\cdot)\) 4014.bn 222 No \(-1\) \(1\) \(e\left(\frac{11}{74}\right)\) \(e\left(\frac{83}{111}\right)\) \(e\left(\frac{191}{222}\right)\) \(e\left(\frac{10}{111}\right)\) \(e\left(\frac{39}{74}\right)\) \(e\left(\frac{19}{111}\right)\) \(e\left(\frac{181}{222}\right)\) \(e\left(\frac{11}{37}\right)\) \(e\left(\frac{215}{222}\right)\) \(e\left(\frac{68}{111}\right)\)
\(\chi_{4014}(31,\cdot)\) 4014.y 111 No \(1\) \(1\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{100}{111}\right)\) \(e\left(\frac{95}{111}\right)\) \(e\left(\frac{107}{111}\right)\) \(e\left(\frac{7}{37}\right)\) \(e\left(\frac{59}{111}\right)\) \(e\left(\frac{97}{111}\right)\) \(e\left(\frac{3}{37}\right)\) \(e\left(\frac{68}{111}\right)\) \(e\left(\frac{106}{111}\right)\)
\(\chi_{4014}(35,\cdot)\) 4014.bj 222 No \(1\) \(1\) \(e\left(\frac{41}{111}\right)\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{68}{111}\right)\) \(e\left(\frac{73}{74}\right)\) \(e\left(\frac{33}{74}\right)\) \(e\left(\frac{73}{111}\right)\) \(e\left(\frac{4}{111}\right)\) \(e\left(\frac{82}{111}\right)\) \(e\left(\frac{199}{222}\right)\) \(e\left(\frac{49}{111}\right)\)
\(\chi_{4014}(37,\cdot)\) 4014.z 111 No \(1\) \(1\) \(e\left(\frac{104}{111}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{29}{111}\right)\) \(e\left(\frac{24}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{85}{111}\right)\) \(e\left(\frac{67}{111}\right)\) \(e\left(\frac{97}{111}\right)\) \(e\left(\frac{71}{111}\right)\) \(e\left(\frac{16}{111}\right)\)
\(\chi_{4014}(41,\cdot)\) 4014.bg 222 No \(-1\) \(1\) \(e\left(\frac{211}{222}\right)\) \(e\left(\frac{34}{111}\right)\) \(e\left(\frac{35}{222}\right)\) \(e\left(\frac{83}{111}\right)\) \(e\left(\frac{61}{74}\right)\) \(e\left(\frac{2}{37}\right)\) \(e\left(\frac{211}{222}\right)\) \(e\left(\frac{100}{111}\right)\) \(e\left(\frac{101}{222}\right)\) \(e\left(\frac{2}{111}\right)\)
\(\chi_{4014}(43,\cdot)\) 4014.ba 111 No \(1\) \(1\) \(e\left(\frac{71}{111}\right)\) \(e\left(\frac{32}{111}\right)\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{52}{111}\right)\) \(e\left(\frac{20}{37}\right)\) \(e\left(\frac{47}{111}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{31}{111}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{34}{37}\right)\)
\(\chi_{4014}(47,\cdot)\) 4014.bn 222 No \(-1\) \(1\) \(e\left(\frac{65}{74}\right)\) \(e\left(\frac{107}{111}\right)\) \(e\left(\frac{59}{222}\right)\) \(e\left(\frac{49}{111}\right)\) \(e\left(\frac{69}{74}\right)\) \(e\left(\frac{82}{111}\right)\) \(e\left(\frac{121}{222}\right)\) \(e\left(\frac{28}{37}\right)\) \(e\left(\frac{221}{222}\right)\) \(e\left(\frac{89}{111}\right)\)
\(\chi_{4014}(49,\cdot)\) 4014.bb 111 No \(1\) \(1\) \(e\left(\frac{5}{111}\right)\) \(e\left(\frac{70}{111}\right)\) \(e\left(\frac{85}{111}\right)\) \(e\left(\frac{86}{111}\right)\) \(e\left(\frac{16}{37}\right)\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{5}{111}\right)\) \(e\left(\frac{10}{111}\right)\) \(e\left(\frac{55}{111}\right)\) \(e\left(\frac{89}{111}\right)\)
\(\chi_{4014}(53,\cdot)\) 4014.bd 222 No \(-1\) \(1\) \(e\left(\frac{127}{222}\right)\) \(e\left(\frac{25}{37}\right)\) \(e\left(\frac{13}{222}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{29}{74}\right)\) \(e\left(\frac{109}{111}\right)\) \(e\left(\frac{53}{222}\right)\) \(e\left(\frac{16}{111}\right)\) \(e\left(\frac{139}{222}\right)\) \(e\left(\frac{61}{111}\right)\)
\(\chi_{4014}(55,\cdot)\) 4014.z 111 No \(1\) \(1\) \(e\left(\frac{64}{111}\right)\) \(e\left(\frac{15}{37}\right)\) \(e\left(\frac{52}{111}\right)\) \(e\left(\frac{29}{37}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{95}{111}\right)\) \(e\left(\frac{101}{111}\right)\) \(e\left(\frac{17}{111}\right)\) \(e\left(\frac{1}{111}\right)\) \(e\left(\frac{44}{111}\right)\)
\(\chi_{4014}(59,\cdot)\) 4014.bl 222 No \(1\) \(1\) \(e\left(\frac{86}{111}\right)\) \(e\left(\frac{94}{111}\right)\) \(e\left(\frac{19}{111}\right)\) \(e\left(\frac{139}{222}\right)\) \(e\left(\frac{25}{74}\right)\) \(e\left(\frac{36}{37}\right)\) \(e\left(\frac{86}{111}\right)\) \(e\left(\frac{61}{111}\right)\) \(e\left(\frac{5}{222}\right)\) \(e\left(\frac{110}{111}\right)\)
\(\chi_{4014}(61,\cdot)\) 4014.bh 222 No \(-1\) \(1\) \(e\left(\frac{133}{222}\right)\) \(e\left(\frac{80}{111}\right)\) \(e\left(\frac{63}{74}\right)\) \(e\left(\frac{149}{222}\right)\) \(e\left(\frac{13}{37}\right)\) \(e\left(\frac{62}{111}\right)\) \(e\left(\frac{69}{74}\right)\) \(e\left(\frac{22}{111}\right)\) \(e\left(\frac{28}{37}\right)\) \(e\left(\frac{11}{37}\right)\)
\(\chi_{4014}(65,\cdot)\) 4014.bn 222 No \(-1\) \(1\) \(e\left(\frac{33}{74}\right)\) \(e\left(\frac{101}{111}\right)\) \(e\left(\frac{203}{222}\right)\) \(e\left(\frac{67}{111}\right)\) \(e\left(\frac{43}{74}\right)\) \(e\left(\frac{94}{111}\right)\) \(e\left(\frac{25}{222}\right)\) \(e\left(\frac{33}{37}\right)\) \(e\left(\frac{53}{222}\right)\) \(e\left(\frac{56}{111}\right)\)
\(\chi_{4014}(67,\cdot)\) 4014.bm 222 No \(-1\) \(1\) \(e\left(\frac{61}{74}\right)\) \(e\left(\frac{97}{111}\right)\) \(e\left(\frac{151}{222}\right)\) \(e\left(\frac{121}{222}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{65}{111}\right)\) \(e\left(\frac{35}{222}\right)\) \(e\left(\frac{24}{37}\right)\) \(e\left(\frac{26}{111}\right)\) \(e\left(\frac{34}{111}\right)\)
\(\chi_{4014}(71,\cdot)\) 4014.bj 222 No \(1\) \(1\) \(e\left(\frac{49}{111}\right)\) \(e\left(\frac{19}{37}\right)\) \(e\left(\frac{19}{111}\right)\) \(e\left(\frac{71}{74}\right)\) \(e\left(\frac{25}{74}\right)\) \(e\left(\frac{71}{111}\right)\) \(e\left(\frac{86}{111}\right)\) \(e\left(\frac{98}{111}\right)\) \(e\left(\frac{5}{222}\right)\) \(e\left(\frac{110}{111}\right)\)
\(\chi_{4014}(73,\cdot)\) 4014.z 111 No \(1\) \(1\) \(e\left(\frac{47}{111}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{59}{111}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{32}{37}\right)\) \(e\left(\frac{16}{111}\right)\) \(e\left(\frac{10}{111}\right)\) \(e\left(\frac{94}{111}\right)\) \(e\left(\frac{110}{111}\right)\) \(e\left(\frac{67}{111}\right)\)
\(\chi_{4014}(77,\cdot)\) 4014.bk 222 No \(1\) \(1\) \(e\left(\frac{28}{111}\right)\) \(e\left(\frac{22}{111}\right)\) \(e\left(\frac{23}{37}\right)\) \(e\left(\frac{127}{222}\right)\) \(e\left(\frac{9}{74}\right)\) \(e\left(\frac{67}{111}\right)\) \(e\left(\frac{34}{37}\right)\) \(e\left(\frac{56}{111}\right)\) \(e\left(\frac{45}{74}\right)\) \(e\left(\frac{28}{37}\right)\)
\(\chi_{4014}(79,\cdot)\) 4014.bm 222 No \(-1\) \(1\) \(e\left(\frac{21}{74}\right)\) \(e\left(\frac{71}{111}\right)\) \(e\left(\frac{35}{222}\right)\) \(e\left(\frac{203}{222}\right)\) \(e\left(\frac{12}{37}\right)\) \(e\left(\frac{43}{111}\right)\) \(e\left(\frac{211}{222}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{106}{111}\right)\) \(e\left(\frac{2}{111}\right)\)
\(\chi_{4014}(83,\cdot)\) 4014.bn 222 No \(-1\) \(1\) \(e\left(\frac{39}{74}\right)\) \(e\left(\frac{5}{111}\right)\) \(e\left(\frac{65}{222}\right)\) \(e\left(\frac{22}{111}\right)\) \(e\left(\frac{71}{74}\right)\) \(e\left(\frac{64}{111}\right)\) \(e\left(\frac{43}{222}\right)\) \(e\left(\frac{2}{37}\right)\) \(e\left(\frac{29}{222}\right)\) \(e\left(\frac{83}{111}\right)\)
\(\chi_{4014}(85,\cdot)\) 4014.bh 222 No \(-1\) \(1\) \(e\left(\frac{17}{222}\right)\) \(e\left(\frac{82}{111}\right)\) \(e\left(\frac{47}{74}\right)\) \(e\left(\frac{211}{222}\right)\) \(e\left(\frac{5}{37}\right)\) \(e\left(\frac{58}{111}\right)\) \(e\left(\frac{55}{74}\right)\) \(e\left(\frac{17}{111}\right)\) \(e\left(\frac{25}{37}\right)\) \(e\left(\frac{27}{37}\right)\)
\(\chi_{4014}(89,\cdot)\) 4014.bd 222 No \(-1\) \(1\) \(e\left(\frac{71}{222}\right)\) \(e\left(\frac{30}{37}\right)\) \(e\left(\frac{23}{222}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{57}{74}\right)\) \(e\left(\frac{5}{111}\right)\) \(e\left(\frac{145}{222}\right)\) \(e\left(\frac{71}{111}\right)\) \(e\left(\frac{41}{222}\right)\) \(e\left(\frac{14}{111}\right)\)
\(\chi_{4014}(91,\cdot)\) 4014.x 74 No \(-1\) \(1\) \(e\left(\frac{9}{74}\right)\) \(e\left(\frac{26}{37}\right)\) \(e\left(\frac{5}{74}\right)\) \(e\left(\frac{29}{74}\right)\) \(e\left(\frac{21}{37}\right)\) \(e\left(\frac{22}{37}\right)\) \(e\left(\frac{9}{74}\right)\) \(e\left(\frac{9}{37}\right)\) \(e\left(\frac{31}{37}\right)\) \(e\left(\frac{32}{37}\right)\)
\(\chi_{4014}(95,\cdot)\) 4014.bl 222 No \(1\) \(1\) \(e\left(\frac{89}{111}\right)\) \(e\left(\frac{25}{111}\right)\) \(e\left(\frac{70}{111}\right)\) \(e\left(\frac{109}{222}\right)\) \(e\left(\frac{59}{74}\right)\) \(e\left(\frac{8}{37}\right)\) \(e\left(\frac{89}{111}\right)\) \(e\left(\frac{67}{111}\right)\) \(e\left(\frac{71}{222}\right)\) \(e\left(\frac{8}{111}\right)\)