# Properties

 Modulus $4800$ Structure $$C_{80}\times C_{4}\times C_{2}\times C_{2}$$ Order $1280$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(4800)

pari: g = idealstar(,4800,2)

## Character group

 sage: G.order()  pari: g.no Order = 1280 sage: H.invariants()  pari: g.cyc Structure = $$C_{80}\times C_{4}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4800}(4351,\cdot)$, $\chi_{4800}(901,\cdot)$, $\chi_{4800}(1601,\cdot)$, $\chi_{4800}(577,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{4800}(1,\cdot)$$ 4800.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4800}(7,\cdot)$$ 4800.cd 8 no $$1$$ $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$
$$\chi_{4800}(11,\cdot)$$ 4800.fe 80 yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{3}{40}\right)$$
$$\chi_{4800}(13,\cdot)$$ 4800.fb 80 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{4800}(17,\cdot)$$ 4800.ds 20 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{4800}(19,\cdot)$$ 4800.fd 80 no $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{61}{80}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{29}{40}\right)$$
$$\chi_{4800}(23,\cdot)$$ 4800.ex 40 no $$-1$$ $$1$$ $$1$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{4800}(29,\cdot)$$ 4800.fg 80 yes $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{21}{40}\right)$$
$$\chi_{4800}(31,\cdot)$$ 4800.ch 10 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{4800}(37,\cdot)$$ 4800.fb 80 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{7}{80}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{80}\right)$$ $$e\left(\frac{27}{40}\right)$$
$$\chi_{4800}(41,\cdot)$$ 4800.em 40 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{4800}(43,\cdot)$$ 4800.cw 16 no $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{4800}(47,\cdot)$$ 4800.du 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4800}(49,\cdot)$$ 4800.bl 4 no $$1$$ $$1$$ $$1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-1$$
$$\chi_{4800}(53,\cdot)$$ 4800.fa 80 yes $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{27}{80}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{39}{80}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{51}{80}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{77}{80}\right)$$ $$e\left(\frac{11}{40}\right)$$
$$\chi_{4800}(59,\cdot)$$ 4800.fc 80 yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{7}{40}\right)$$
$$\chi_{4800}(61,\cdot)$$ 4800.fj 80 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{59}{80}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{57}{80}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{33}{40}\right)$$
$$\chi_{4800}(67,\cdot)$$ 4800.fl 80 no $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{67}{80}\right)$$ $$e\left(\frac{13}{80}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{29}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{43}{80}\right)$$ $$e\left(\frac{9}{40}\right)$$
$$\chi_{4800}(71,\cdot)$$ 4800.eo 40 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{4800}(73,\cdot)$$ 4800.ek 40 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{4800}(77,\cdot)$$ 4800.fa 80 yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{79}{80}\right)$$ $$e\left(\frac{1}{80}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{37}{80}\right)$$ $$e\left(\frac{7}{40}\right)$$ $$e\left(\frac{73}{80}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{71}{80}\right)$$ $$e\left(\frac{33}{40}\right)$$
$$\chi_{4800}(79,\cdot)$$ 4800.dn 20 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{4800}(83,\cdot)$$ 4800.fk 80 yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{33}{80}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{21}{80}\right)$$ $$e\left(\frac{31}{40}\right)$$ $$e\left(\frac{49}{80}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{23}{80}\right)$$ $$e\left(\frac{9}{40}\right)$$
$$\chi_{4800}(89,\cdot)$$ 4800.er 40 no $$-1$$ $$1$$ $$-i$$ $$e\left(\frac{37}{40}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{4800}(91,\cdot)$$ 4800.ff 80 no $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{41}{80}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{80}\right)$$ $$e\left(\frac{23}{40}\right)$$ $$e\left(\frac{47}{80}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{27}{40}\right)$$
$$\chi_{4800}(97,\cdot)$$ 4800.ea 20 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4800}(101,\cdot)$$ 4800.cz 16 no $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{5}{16}\right)$$ $$e\left(\frac{7}{16}\right)$$ $$i$$ $$e\left(\frac{15}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{11}{16}\right)$$ $$-1$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{3}{8}\right)$$
$$\chi_{4800}(103,\cdot)$$ 4800.el 40 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{21}{40}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{27}{40}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{40}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{4800}(107,\cdot)$$ 4800.cx 16 no $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{16}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$-1$$ $$e\left(\frac{11}{16}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{15}{16}\right)$$ $$1$$ $$e\left(\frac{9}{16}\right)$$ $$e\left(\frac{7}{8}\right)$$
$$\chi_{4800}(109,\cdot)$$ 4800.fh 80 no $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{31}{80}\right)$$ $$e\left(\frac{69}{80}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{53}{80}\right)$$ $$e\left(\frac{33}{40}\right)$$ $$e\left(\frac{17}{80}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{80}\right)$$ $$e\left(\frac{37}{40}\right)$$
$$\chi_{4800}(113,\cdot)$$ 4800.ds 20 no $$1$$ $$1$$ $$i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{4800}(119,\cdot)$$ 4800.et 40 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{11}{40}\right)$$ $$e\left(\frac{29}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{40}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{17}{40}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{7}{20}\right)$$