# Properties

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

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 $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$