# Properties

 Modulus $7728$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}$$ Order $2112$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7728)

pari: g = idealstar(,7728,2)

## Character group

 sage: G.order()  pari: g.no Order = 2112 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{7728}(4831,\cdot)$, $\chi_{7728}(5797,\cdot)$, $\chi_{7728}(5153,\cdot)$, $\chi_{7728}(6625,\cdot)$, $\chi_{7728}(6721,\cdot)$

## First 32 of 2112 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 $$-1$$ $$1$$ $$5$$ $$11$$ $$13$$ $$17$$ $$19$$ $$25$$ $$29$$ $$31$$ $$37$$ $$41$$
$$\chi_{7728}(1,\cdot)$$ 7728.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7728}(5,\cdot)$$ 7728.gw 132 yes $$-1$$ $$1$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{65}{132}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{115}{132}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{7728}(11,\cdot)$$ 7728.hc 132 yes $$-1$$ $$1$$ $$e\left(\frac{65}{132}\right)$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{7728}(13,\cdot)$$ 7728.fl 44 no $$-1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{7728}(17,\cdot)$$ 7728.gc 66 no $$-1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{7728}(19,\cdot)$$ 7728.hg 132 no $$-1$$ $$1$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{7728}(25,\cdot)$$ 7728.fv 66 no $$1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{7728}(29,\cdot)$$ 7728.fh 44 no $$-1$$ $$1$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{7728}(31,\cdot)$$ 7728.fu 66 no $$1$$ $$1$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{7728}(37,\cdot)$$ 7728.ha 132 no $$-1$$ $$1$$ $$e\left(\frac{115}{132}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{127}{132}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{7728}(41,\cdot)$$ 7728.ei 22 no $$1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{7728}(43,\cdot)$$ 7728.fn 44 no $$1$$ $$1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{7728}(47,\cdot)$$ 7728.bx 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{7728}(53,\cdot)$$ 7728.hh 132 yes $$1$$ $$1$$ $$e\left(\frac{125}{132}\right)$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{7728}(55,\cdot)$$ 7728.dv 22 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{7728}(59,\cdot)$$ 7728.hj 132 yes $$-1$$ $$1$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{83}{132}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{125}{132}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{7728}(61,\cdot)$$ 7728.hd 132 no $$1$$ $$1$$ $$e\left(\frac{91}{132}\right)$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{1}{132}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{7728}(65,\cdot)$$ 7728.gp 66 no $$1$$ $$1$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{7728}(67,\cdot)$$ 7728.gx 132 no $$1$$ $$1$$ $$e\left(\frac{89}{132}\right)$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{125}{132}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{65}{132}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{7728}(71,\cdot)$$ 7728.eg 22 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{7728}(73,\cdot)$$ 7728.gg 66 no $$-1$$ $$1$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{7728}(79,\cdot)$$ 7728.fy 66 no $$1$$ $$1$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{7728}(83,\cdot)$$ 7728.fj 44 yes $$1$$ $$1$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{7728}(85,\cdot)$$ 7728.fc 44 no $$1$$ $$1$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{7728}(89,\cdot)$$ 7728.gf 66 no $$-1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{7728}(95,\cdot)$$ 7728.fx 66 no $$1$$ $$1$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{7728}(97,\cdot)$$ 7728.ee 22 no $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{7728}(101,\cdot)$$ 7728.he 132 yes $$1$$ $$1$$ $$e\left(\frac{5}{132}\right)$$ $$e\left(\frac{67}{132}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{53}{132}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{17}{132}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{7728}(103,\cdot)$$ 7728.fs 66 no $$-1$$ $$1$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{7728}(107,\cdot)$$ 7728.hc 132 yes $$-1$$ $$1$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{71}{132}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{67}{132}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{31}{66}\right)$$ $$e\left(\frac{19}{132}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{7728}(109,\cdot)$$ 7728.ha 132 no $$-1$$ $$1$$ $$e\left(\frac{53}{132}\right)$$ $$e\left(\frac{37}{132}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{59}{66}\right)$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{7728}(113,\cdot)$$ 7728.dt 22 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$