# Properties

 Modulus $4840$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{220}$$ Order $1760$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4840)

pari: g = idealstar(,4840,2)

## Character group

 sage: G.order()  pari: g.no Order = 1760 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{220}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4840}(3631,\cdot)$, $\chi_{4840}(2421,\cdot)$, $\chi_{4840}(1937,\cdot)$, $\chi_{4840}(4721,\cdot)$

## First 32 of 1760 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$ $$29$$
$$\chi_{4840}(1,\cdot)$$ 4840.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4840}(3,\cdot)$$ 4840.bt 20 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{4840}(7,\cdot)$$ 4840.dm 220 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{43}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{81}{220}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{32}{55}\right)$$
$$\chi_{4840}(9,\cdot)$$ 4840.bn 10 no $$1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{4840}(13,\cdot)$$ 4840.dl 220 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{39}{220}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{107}{220}\right)$$ $$e\left(\frac{163}{220}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{67}{110}\right)$$
$$\chi_{4840}(17,\cdot)$$ 4840.dr 220 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{81}{220}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{163}{220}\right)$$ $$e\left(\frac{17}{220}\right)$$ $$e\left(\frac{26}{55}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{55}\right)$$
$$\chi_{4840}(19,\cdot)$$ 4840.dd 110 yes $$1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{31}{110}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{23}{110}\right)$$ $$e\left(\frac{26}{55}\right)$$ $$e\left(\frac{69}{110}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{18}{55}\right)$$
$$\chi_{4840}(21,\cdot)$$ 4840.cc 22 no $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{22}\right)$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$-1$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{4840}(23,\cdot)$$ 4840.cm 44 no $$1$$ $$1$$ $$-i$$ $$e\left(\frac{31}{44}\right)$$ $$-1$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$i$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{4840}(27,\cdot)$$ 4840.bt 20 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$i$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{4840}(29,\cdot)$$ 4840.da 110 yes $$-1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{67}{110}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{18}{55}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{55}\right)$$
$$\chi_{4840}(31,\cdot)$$ 4840.df 110 no $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{107}{110}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{53}{55}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{16}{55}\right)$$
$$\chi_{4840}(37,\cdot)$$ 4840.dq 220 yes $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{203}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{179}{220}\right)$$ $$e\left(\frac{211}{220}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{27}{55}\right)$$
$$\chi_{4840}(39,\cdot)$$ 4840.cy 110 no $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{110}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{38}{55}\right)$$ $$e\left(\frac{6}{55}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{110}\right)$$
$$\chi_{4840}(41,\cdot)$$ 4840.cv 110 no $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{51}{110}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{13}{110}\right)$$ $$e\left(\frac{27}{110}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{61}{110}\right)$$
$$\chi_{4840}(43,\cdot)$$ 4840.cn 44 yes $$-1$$ $$1$$ $$i$$ $$e\left(\frac{37}{44}\right)$$ $$-1$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$-i$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{4840}(47,\cdot)$$ 4840.dp 220 no $$1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{217}{220}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{161}{220}\right)$$ $$e\left(\frac{199}{220}\right)$$ $$e\left(\frac{52}{55}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{71}{110}\right)$$
$$\chi_{4840}(49,\cdot)$$ 4840.dc 110 no $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{43}{110}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{39}{110}\right)$$ $$e\left(\frac{81}{110}\right)$$ $$e\left(\frac{31}{55}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{55}\right)$$
$$\chi_{4840}(51,\cdot)$$ 4840.db 110 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{12}{55}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{16}{55}\right)$$ $$e\left(\frac{3}{110}\right)$$ $$e\left(\frac{41}{110}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{37}{55}\right)$$
$$\chi_{4840}(53,\cdot)$$ 4840.dq 220 yes $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{109}{220}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{17}{220}\right)$$ $$e\left(\frac{213}{220}\right)$$ $$e\left(\frac{54}{55}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{21}{55}\right)$$
$$\chi_{4840}(57,\cdot)$$ 4840.dr 220 no $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{29}{220}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{167}{220}\right)$$ $$e\left(\frac{93}{220}\right)$$ $$e\left(\frac{29}{55}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{51}{55}\right)$$
$$\chi_{4840}(59,\cdot)$$ 4840.di 110 yes $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{55}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{21}{55}\right)$$ $$e\left(\frac{83}{110}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{49}{110}\right)$$
$$\chi_{4840}(61,\cdot)$$ 4840.de 110 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{103}{110}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{32}{55}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{41}{55}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{55}\right)$$
$$\chi_{4840}(63,\cdot)$$ 4840.dm 220 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{197}{220}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{61}{220}\right)$$ $$e\left(\frac{59}{220}\right)$$ $$e\left(\frac{9}{110}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{43}{55}\right)$$
$$\chi_{4840}(67,\cdot)$$ 4840.cs 44 yes $$1$$ $$1$$ $$-i$$ $$e\left(\frac{5}{44}\right)$$ $$-1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$i$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{4840}(69,\cdot)$$ 4840.cx 110 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{61}{110}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{4}{55}\right)$$ $$e\left(\frac{97}{110}\right)$$ $$e\left(\frac{79}{110}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{101}{110}\right)$$
$$\chi_{4840}(71,\cdot)$$ 4840.df 110 no $$-1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{53}{110}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{55}\right)$$ $$e\left(\frac{48}{55}\right)$$ $$e\left(\frac{47}{110}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{29}{55}\right)$$
$$\chi_{4840}(73,\cdot)$$ 4840.dr 220 no $$1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{23}{220}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{49}{220}\right)$$ $$e\left(\frac{51}{220}\right)$$ $$e\left(\frac{23}{55}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{12}{55}\right)$$
$$\chi_{4840}(79,\cdot)$$ 4840.cy 110 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{67}{110}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{8}{55}\right)$$ $$e\left(\frac{42}{55}\right)$$ $$e\left(\frac{24}{55}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{37}{110}\right)$$
$$\chi_{4840}(81,\cdot)$$ 4840.y 5 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4840}(83,\cdot)$$ 4840.do 220 yes $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{21}{220}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{83}{220}\right)$$ $$e\left(\frac{147}{220}\right)$$ $$e\left(\frac{21}{55}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{53}{110}\right)$$
$$\chi_{4840}(87,\cdot)$$ 4840.ct 44 no $$-1$$ $$1$$ $$i$$ $$e\left(\frac{19}{44}\right)$$ $$-1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$-i$$ $$e\left(\frac{8}{11}\right)$$