Properties

Modulus 4020
Structure \(C_{132}\times C_{2}\times C_{2}\times C_{2}\)
Order 1056

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(4020)
 
pari: g = idealstar(,4020,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1056
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{132}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4020}(3553,\cdot)$, $\chi_{4020}(1741,\cdot)$, $\chi_{4020}(2681,\cdot)$, $\chi_{4020}(2011,\cdot)$

First 32 of 1056 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 7 11 13 17 19 23 29 31 37 41
\(\chi_{4020}(1,\cdot)\) 4020.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4020}(7,\cdot)\) 4020.dr 132 No \(-1\) \(1\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{66}\right)\)
\(\chi_{4020}(11,\cdot)\) 4020.de 66 No \(-1\) \(1\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{4020}(13,\cdot)\) 4020.dl 132 No \(1\) \(1\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{66}\right)\)
\(\chi_{4020}(17,\cdot)\) 4020.dk 132 No \(1\) \(1\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{107}{132}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{59}{66}\right)\)
\(\chi_{4020}(19,\cdot)\) 4020.dd 66 No \(-1\) \(1\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{4020}(23,\cdot)\) 4020.dq 132 Yes \(-1\) \(1\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{4020}(29,\cdot)\) 4020.bn 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4020}(31,\cdot)\) 4020.dh 66 No \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{49}{66}\right)\)
\(\chi_{4020}(37,\cdot)\) 4020.bs 12 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4020}(41,\cdot)\) 4020.da 66 No \(1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{4020}(43,\cdot)\) 4020.cn 44 No \(-1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(-1\) \(e\left(\frac{10}{11}\right)\) \(-i\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{4020}(47,\cdot)\) 4020.dq 132 Yes \(-1\) \(1\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{31}{132}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{43}{66}\right)\)
\(\chi_{4020}(49,\cdot)\) 4020.cz 66 No \(1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{33}\right)\)
\(\chi_{4020}(53,\cdot)\) 4020.cq 44 No \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(1\) \(e\left(\frac{13}{22}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{4020}(59,\cdot)\) 4020.by 22 Yes \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(-1\) \(e\left(\frac{3}{22}\right)\) \(-1\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{4020}(61,\cdot)\) 4020.cv 66 No \(-1\) \(1\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{41}{66}\right)\)
\(\chi_{4020}(71,\cdot)\) 4020.dc 66 No \(1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{66}\right)\)
\(\chi_{4020}(73,\cdot)\) 4020.dp 132 No \(-1\) \(1\) \(e\left(\frac{91}{132}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{4020}(77,\cdot)\) 4020.dk 132 No \(1\) \(1\) \(e\left(\frac{109}{132}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{4020}(79,\cdot)\) 4020.db 66 No \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{4020}(83,\cdot)\) 4020.dq 132 Yes \(-1\) \(1\) \(e\left(\frac{85}{132}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{125}{132}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{47}{66}\right)\)
\(\chi_{4020}(89,\cdot)\) 4020.ck 22 No \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(-1\) \(e\left(\frac{8}{11}\right)\) \(-1\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{4020}(91,\cdot)\) 4020.cj 22 No \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(1\) \(e\left(\frac{9}{22}\right)\) \(1\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{4020}(97,\cdot)\) 4020.bw 12 No \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4020}(101,\cdot)\) 4020.da 66 No \(1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{4020}(103,\cdot)\) 4020.dn 132 No \(1\) \(1\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{43}{132}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{91}{132}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{8}{33}\right)\)
\(\chi_{4020}(107,\cdot)\) 4020.co 44 Yes \(-1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(1\) \(e\left(\frac{7}{22}\right)\) \(i\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{4020}(109,\cdot)\) 4020.cb 22 No \(-1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(1\) \(e\left(\frac{19}{22}\right)\) \(-1\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{4020}(113,\cdot)\) 4020.do 132 No \(-1\) \(1\) \(e\left(\frac{113}{132}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{79}{132}\right)\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{26}{33}\right)\)
\(\chi_{4020}(119,\cdot)\) 4020.ci 22 Yes \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(-1\) \(e\left(\frac{5}{11}\right)\) \(-1\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{4020}(121,\cdot)\) 4020.cm 33 No \(1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{33}\right)\)