# Properties

 Modulus 4020 Structure $$C_{132}\times C_{2}\times C_{2}\times C_{2}$$ Order 1056

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(4020)

pari: g = idealstar(,4020,2)

## Character group

 sage: G.order()  pari: g.no Order = 1056 sage: H.invariants()  pari: g.cyc Structure = $$C_{132}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4020}(3553,\cdot)$, $\chi_{4020}(1741,\cdot)$, $\chi_{4020}(2681,\cdot)$, $\chi_{4020}(2011,\cdot)$

## First 32 of 1056 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.

orbit label order primitive -1 1 7 11 13 17 19 23 29 31 37 41
$$\chi_{4020}(1,\cdot)$$ 4020.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4020}(7,\cdot)$$ 4020.dr 132 no $$-1$$ $$1$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{49}{132}\right)$$ $$e\left(\frac{73}{132}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{1}{132}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{31}{66}\right)$$
$$\chi_{4020}(11,\cdot)$$ 4020.de 66 no $$-1$$ $$1$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{33}\right)$$
$$\chi_{4020}(13,\cdot)$$ 4020.dl 132 no $$1$$ $$1$$ $$e\left(\frac{49}{132}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{17}{66}\right)$$
$$\chi_{4020}(17,\cdot)$$ 4020.dk 132 no $$1$$ $$1$$ $$e\left(\frac{73}{132}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{107}{132}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{53}{132}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{59}{66}\right)$$
$$\chi_{4020}(19,\cdot)$$ 4020.dd 66 no $$-1$$ $$1$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{4020}(23,\cdot)$$ 4020.dq 132 yes $$-1$$ $$1$$ $$e\left(\frac{1}{132}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{53}{132}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{65}{66}\right)$$
$$\chi_{4020}(29,\cdot)$$ 4020.bn 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{4020}(31,\cdot)$$ 4020.dh 66 no $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{49}{66}\right)$$
$$\chi_{4020}(37,\cdot)$$ 4020.bs 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{4020}(41,\cdot)$$ 4020.da 66 no $$1$$ $$1$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{4020}(43,\cdot)$$ 4020.cn 44 no $$-1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$-1$$ $$e\left(\frac{10}{11}\right)$$ $$-i$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{4020}(47,\cdot)$$ 4020.dq 132 yes $$-1$$ $$1$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{43}{66}\right)$$
$$\chi_{4020}(49,\cdot)$$ 4020.cz 66 no $$1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{4020}(53,\cdot)$$ 4020.cq 44 no $$-1$$ $$1$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$-i$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{4020}(59,\cdot)$$ 4020.by 22 yes $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$-1$$ $$e\left(\frac{3}{22}\right)$$ $$-1$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{4020}(61,\cdot)$$ 4020.cv 66 no $$-1$$ $$1$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{41}{66}\right)$$
$$\chi_{4020}(71,\cdot)$$ 4020.dc 66 no $$1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{4020}(73,\cdot)$$ 4020.dp 132 no $$-1$$ $$1$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{71}{132}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{4}{33}\right)$$
$$\chi_{4020}(77,\cdot)$$ 4020.dk 132 no $$1$$ $$1$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{23}{66}\right)$$
$$\chi_{4020}(79,\cdot)$$ 4020.db 66 no $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{4020}(83,\cdot)$$ 4020.dq 132 yes $$-1$$ $$1$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{53}{132}\right)$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{125}{132}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{47}{66}\right)$$
$$\chi_{4020}(89,\cdot)$$ 4020.ck 22 no $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$-1$$ $$e\left(\frac{8}{11}\right)$$ $$-1$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{4020}(91,\cdot)$$ 4020.cj 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$1$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{4020}(97,\cdot)$$ 4020.bw 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{4020}(101,\cdot)$$ 4020.da 66 no $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{4020}(103,\cdot)$$ 4020.dn 132 no $$1$$ $$1$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{37}{132}\right)$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{8}{33}\right)$$
$$\chi_{4020}(107,\cdot)$$ 4020.co 44 yes $$-1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$i$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{4020}(109,\cdot)$$ 4020.cb 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$-1$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{4020}(113,\cdot)$$ 4020.do 132 no $$-1$$ $$1$$ $$e\left(\frac{113}{132}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{49}{132}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{7}{132}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{4020}(119,\cdot)$$ 4020.ci 22 yes $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$-1$$ $$e\left(\frac{5}{11}\right)$$ $$-1$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{4020}(121,\cdot)$$ 4020.cm 33 no $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{25}{33}\right)$$