Properties

Modulus $4830$
Structure \(C_{132}\times C_{2}\times C_{2}\times C_{2}\)
Order $1056$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4830)
 
pari: g = idealstar(,4830,2)
 

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 = $\chi_{4830}(3221,\cdot)$, $\chi_{4830}(967,\cdot)$, $\chi_{4830}(2761,\cdot)$, $\chi_{4830}(1891,\cdot)$

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.

Character Orbit Order Primitive \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{4830}(1,\cdot)\) 4830.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4830}(11,\cdot)\) 4830.de 66 no \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(13,\cdot)\) 4830.co 44 no \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(i\)
\(\chi_{4830}(17,\cdot)\) 4830.do 132 no \(1\) \(1\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4830}(19,\cdot)\) 4830.cx 66 no \(1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4830}(29,\cdot)\) 4830.cj 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(1\)
\(\chi_{4830}(31,\cdot)\) 4830.dg 66 no \(-1\) \(1\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(37,\cdot)\) 4830.dn 132 no \(1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4830}(41,\cdot)\) 4830.cl 22 no \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(1\)
\(\chi_{4830}(43,\cdot)\) 4830.cs 44 no \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(-i\)
\(\chi_{4830}(47,\cdot)\) 4830.bu 12 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-i\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4830}(53,\cdot)\) 4830.dq 132 no \(-1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{29}{132}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4830}(59,\cdot)\) 4830.cw 66 no \(1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(61,\cdot)\) 4830.db 66 no \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(67,\cdot)\) 4830.dn 132 no \(1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{7}{132}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4830}(71,\cdot)\) 4830.cf 22 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(-1\)
\(\chi_{4830}(73,\cdot)\) 4830.dr 132 no \(1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4830}(79,\cdot)\) 4830.cz 66 no \(-1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(83,\cdot)\) 4830.cp 44 no \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(-i\)
\(\chi_{4830}(89,\cdot)\) 4830.df 66 no \(-1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(97,\cdot)\) 4830.cu 44 no \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(-i\)
\(\chi_{4830}(101,\cdot)\) 4830.da 66 no \(1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{4830}(103,\cdot)\) 4830.dl 132 no \(-1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{59}{132}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4830}(107,\cdot)\) 4830.dq 132 no \(-1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{65}{132}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4830}(109,\cdot)\) 4830.cz 66 no \(-1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(113,\cdot)\) 4830.cn 44 no \(-1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(i\)
\(\chi_{4830}(121,\cdot)\) 4830.cm 33 no \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4830}(127,\cdot)\) 4830.cq 44 no \(-1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(i\)
\(\chi_{4830}(131,\cdot)\) 4830.da 66 no \(1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{4830}(137,\cdot)\) 4830.bq 12 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4830}(139,\cdot)\) 4830.o 2 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{4830}(143,\cdot)\) 4830.do 132 no \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{12}\right)\)