Properties

 Modulus $5610$ Structure $$C_{2}\times C_{2}\times C_{4}\times C_{80}$$ Order $1280$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5610)

pari: g = idealstar(,5610,2)

Character group

 sage: G.order()  pari: g.no Order = 1280 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{4}\times C_{80}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{5610}(1871,\cdot)$, $\chi_{5610}(3367,\cdot)$, $\chi_{5610}(1531,\cdot)$, $\chi_{5610}(3301,\cdot)$

First 32 of 1280 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 $$-1$$ $$1$$ $$7$$ $$13$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$47$$
$$\chi_{5610}(1,\cdot)$$ 5610.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{5610}(7,\cdot)$$ 5610.ez 80 no $$-1$$ $$1$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{5610}(13,\cdot)$$ 5610.dn 20 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$i$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{5610}(19,\cdot)$$ 5610.eu 40 no $$-1$$ $$1$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$-i$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{5610}(23,\cdot)$$ 5610.dj 16 no $$-1$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$
$$\chi_{5610}(29,\cdot)$$ 5610.fi 80 no $$-1$$ $$1$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{5610}(31,\cdot)$$ 5610.fe 80 no $$-1$$ $$1$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{5610}(37,\cdot)$$ 5610.fa 80 no $$1$$ $$1$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{5610}(41,\cdot)$$ 5610.ff 80 no $$-1$$ $$1$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{5610}(43,\cdot)$$ 5610.bz 8 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$i$$
$$\chi_{5610}(47,\cdot)$$ 5610.dl 20 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$i$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{5610}(49,\cdot)$$ 5610.ei 40 no $$1$$ $$1$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$i$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{5610}(53,\cdot)$$ 5610.eq 40 no $$1$$ $$1$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$1$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{5610}(59,\cdot)$$ 5610.ek 40 no $$-1$$ $$1$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$-i$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{5610}(61,\cdot)$$ 5610.fc 80 no $$1$$ $$1$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{5610}(67,\cdot)$$ 5610.ba 4 no $$-1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$
$$\chi_{5610}(71,\cdot)$$ 5610.fd 80 no $$1$$ $$1$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{5610}(73,\cdot)$$ 5610.ez 80 no $$-1$$ $$1$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{39}{40}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{5610}(79,\cdot)$$ 5610.fh 80 no $$1$$ $$1$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{11}{80}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{5610}(83,\cdot)$$ 5610.en 40 no $$-1$$ $$1$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$-1$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{5610}(89,\cdot)$$ 5610.v 4 no $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$i$$ $$i$$ $$-i$$ $$i$$ $$-i$$ $$1$$ $$1$$
$$\chi_{5610}(91,\cdot)$$ 5610.fe 80 no $$-1$$ $$1$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{5610}(97,\cdot)$$ 5610.fa 80 no $$1$$ $$1$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{5610}(101,\cdot)$$ 5610.cl 10 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{5610}(103,\cdot)$$ 5610.dy 20 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$i$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$i$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{5610}(107,\cdot)$$ 5610.fk 80 no $$1$$ $$1$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{5610}(109,\cdot)$$ 5610.de 16 no $$1$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$i$$
$$\chi_{5610}(113,\cdot)$$ 5610.ey 80 no $$-1$$ $$1$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{63}{80}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{5610}(127,\cdot)$$ 5610.eo 40 no $$1$$ $$1$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$-1$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{5610}(131,\cdot)$$ 5610.cy 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{16}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$
$$\chi_{5610}(133,\cdot)$$ 5610.cw 16 no $$1$$ $$1$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{13}{16}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{3}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$
$$\chi_{5610}(137,\cdot)$$ 5610.dw 20 no $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$i$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-i$$ $$e\left(\frac{19}{20}\right)$$