# Properties

 Modulus $2415$ Structure $$C_{132}\times C_{2}\times C_{2}\times C_{2}$$ Order $1056$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2415)

pari: g = idealstar(,2415,2)

## 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 = $\chi_{2415}(806,\cdot)$, $\chi_{2415}(967,\cdot)$, $\chi_{2415}(346,\cdot)$, $\chi_{2415}(1891,\cdot)$

## 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.

Character Orbit Order Primitive $$-1$$ $$1$$ $$2$$ $$4$$ $$8$$ $$11$$ $$13$$ $$16$$ $$17$$ $$19$$ $$22$$ $$26$$
$$\chi_{2415}(1,\cdot)$$ 2415.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2415}(2,\cdot)$$ 2415.dk 132 yes $$1$$ $$1$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$i$$ $$e\left(\frac{41}{66}\right)$$
$$\chi_{2415}(4,\cdot)$$ 2415.db 66 no $$1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$-1$$ $$e\left(\frac{8}{33}\right)$$
$$\chi_{2415}(8,\cdot)$$ 2415.ct 44 no $$1$$ $$1$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$-i$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{2415}(11,\cdot)$$ 2415.da 66 no $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$-1$$ $$e\left(\frac{25}{66}\right)$$
$$\chi_{2415}(13,\cdot)$$ 2415.co 44 no $$1$$ $$1$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$-i$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{2415}(16,\cdot)$$ 2415.cm 33 no $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$1$$ $$e\left(\frac{16}{33}\right)$$
$$\chi_{2415}(17,\cdot)$$ 2415.do 132 yes $$1$$ $$1$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$-i$$ $$e\left(\frac{14}{33}\right)$$
$$\chi_{2415}(19,\cdot)$$ 2415.cv 66 no $$1$$ $$1$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$1$$ $$e\left(\frac{5}{66}\right)$$
$$\chi_{2415}(22,\cdot)$$ 2415.t 4 no $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$1$$
$$\chi_{2415}(26,\cdot)$$ 2415.cy 66 no $$1$$ $$1$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$1$$ $$e\left(\frac{10}{33}\right)$$
$$\chi_{2415}(29,\cdot)$$ 2415.cd 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$-1$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{2415}(31,\cdot)$$ 2415.di 66 no $$-1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$1$$ $$e\left(\frac{13}{66}\right)$$
$$\chi_{2415}(32,\cdot)$$ 2415.dk 132 yes $$1$$ $$1$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$i$$ $$e\left(\frac{7}{66}\right)$$
$$\chi_{2415}(34,\cdot)$$ 2415.ci 22 no $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$1$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{2415}(37,\cdot)$$ 2415.dn 132 no $$1$$ $$1$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$-i$$ $$e\left(\frac{31}{33}\right)$$
$$\chi_{2415}(38,\cdot)$$ 2415.do 132 yes $$1$$ $$1$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$i$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{2415}(41,\cdot)$$ 2415.cl 22 no $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$1$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{2415}(43,\cdot)$$ 2415.cs 44 no $$1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$i$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{2415}(44,\cdot)$$ 2415.dj 66 yes $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$1$$ $$e\left(\frac{41}{66}\right)$$
$$\chi_{2415}(47,\cdot)$$ 2415.bu 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2415}(52,\cdot)$$ 2415.dr 132 no $$1$$ $$1$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$i$$ $$e\left(\frac{61}{66}\right)$$
$$\chi_{2415}(53,\cdot)$$ 2415.dq 132 yes $$-1$$ $$1$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$i$$ $$e\left(\frac{43}{66}\right)$$
$$\chi_{2415}(58,\cdot)$$ 2415.dp 132 no $$-1$$ $$1$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{59}{132}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$-i$$ $$e\left(\frac{7}{33}\right)$$
$$\chi_{2415}(59,\cdot)$$ 2415.de 66 yes $$1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$-1$$ $$e\left(\frac{17}{33}\right)$$
$$\chi_{2415}(61,\cdot)$$ 2415.df 66 no $$1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$-1$$ $$e\left(\frac{35}{66}\right)$$
$$\chi_{2415}(62,\cdot)$$ 2415.cr 44 yes $$-1$$ $$1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$i$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{2415}(64,\cdot)$$ 2415.cg 22 no $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$-1$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{2415}(67,\cdot)$$ 2415.dn 132 no $$1$$ $$1$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{7}{132}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$-i$$ $$e\left(\frac{26}{33}\right)$$
$$\chi_{2415}(68,\cdot)$$ 2415.bs 12 yes $$1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{2415}(71,\cdot)$$ 2415.cj 22 no $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$1$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{2415}(73,\cdot)$$ 2415.dr 132 no $$1$$ $$1$$ $$e\left(\frac{59}{132}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$-i$$ $$e\left(\frac{49}{66}\right)$$