Properties

Modulus $5520$
Structure \(C_{44}\times C_{4}\times C_{2}\times C_{2}\times C_{2}\)
Order $1408$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(5520)
 
pari: g = idealstar(,5520,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1408
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{44}\times C_{4}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{5520}(4831,\cdot)$, $\chi_{5520}(1381,\cdot)$, $\chi_{5520}(1841,\cdot)$, $\chi_{5520}(4417,\cdot)$, $\chi_{5520}(1201,\cdot)$

First 32 of 1408 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{5520}(1,\cdot)\) 5520.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{5520}(7,\cdot)\) 5520.fp 44 no \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{5520}(11,\cdot)\) 5520.fz 44 no \(-1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{5520}(13,\cdot)\) 5520.fj 44 no \(-1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{5520}(17,\cdot)\) 5520.eq 44 no \(-1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{5520}(19,\cdot)\) 5520.el 44 no \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{5520}(29,\cdot)\) 5520.ej 44 yes \(-1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{5520}(31,\cdot)\) 5520.ea 22 no \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{5520}(37,\cdot)\) 5520.fh 44 no \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{5520}(41,\cdot)\) 5520.di 22 no \(-1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{5520}(43,\cdot)\) 5520.ff 44 no \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{5520}(47,\cdot)\) 5520.cs 4 no \(-1\) \(1\) \(-i\) \(1\) \(-i\) \(-i\) \(1\) \(1\) \(-1\) \(i\) \(-1\) \(i\)
\(\chi_{5520}(49,\cdot)\) 5520.dy 22 no \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{5520}(53,\cdot)\) 5520.fa 44 yes \(-1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{5520}(59,\cdot)\) 5520.fy 44 yes \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{5520}(61,\cdot)\) 5520.en 44 no \(-1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{5520}(67,\cdot)\) 5520.ff 44 no \(-1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{5520}(71,\cdot)\) 5520.eg 22 no \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{5520}(73,\cdot)\) 5520.fo 44 no \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{5520}(77,\cdot)\) 5520.ey 44 yes \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{5520}(79,\cdot)\) 5520.dw 22 no \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{5520}(83,\cdot)\) 5520.fk 44 yes \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{5520}(89,\cdot)\) 5520.dm 22 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{5520}(91,\cdot)\) 5520.bg 4 no \(1\) \(1\) \(-1\) \(i\) \(-i\) \(-1\) \(-i\) \(-i\) \(-1\) \(-i\) \(-1\) \(i\)
\(\chi_{5520}(97,\cdot)\) 5520.fq 44 no \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{5520}(101,\cdot)\) 5520.ga 44 no \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{5520}(103,\cdot)\) 5520.fp 44 no \(-1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{5520}(107,\cdot)\) 5520.fk 44 yes \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{5520}(109,\cdot)\) 5520.fw 44 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{5520}(113,\cdot)\) 5520.eq 44 no \(-1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{5520}(119,\cdot)\) 5520.dk 22 no \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{5520}(121,\cdot)\) 5520.dp 22 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{22}\right)\)