# Properties

 Modulus $8280$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{132}$$ Order $2112$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8280)

pari: g = idealstar(,8280,2)

## 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 = $\chi_{8280}(2071,\cdot)$, $\chi_{8280}(4141,\cdot)$, $\chi_{8280}(4601,\cdot)$, $\chi_{8280}(1657,\cdot)$, $\chi_{8280}(3961,\cdot)$

## 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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$
$$\chi_{8280}(1,\cdot)$$ 8280.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{8280}(7,\cdot)$$ 8280.hg 132 no $$-1$$ $$1$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{31}{132}\right)$$
$$\chi_{8280}(11,\cdot)$$ 8280.go 66 no $$-1$$ $$1$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{47}{66}\right)$$
$$\chi_{8280}(13,\cdot)$$ 8280.gx 132 yes $$-1$$ $$1$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{35}{132}\right)$$
$$\chi_{8280}(17,\cdot)$$ 8280.ez 44 no $$-1$$ $$1$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{44}\right)$$
$$\chi_{8280}(19,\cdot)$$ 8280.er 22 no $$1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{8280}(29,\cdot)$$ 8280.gc 66 yes $$-1$$ $$1$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{25}{33}\right)$$
$$\chi_{8280}(31,\cdot)$$ 8280.fu 66 no $$-1$$ $$1$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$
$$\chi_{8280}(37,\cdot)$$ 8280.fd 44 no $$1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{44}\right)$$
$$\chi_{8280}(41,\cdot)$$ 8280.gl 66 no $$-1$$ $$1$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{2}{33}\right)$$
$$\chi_{8280}(43,\cdot)$$ 8280.gw 132 yes $$-1$$ $$1$$ $$e\left(\frac{31}{132}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{35}{132}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{7}{132}\right)$$
$$\chi_{8280}(47,\cdot)$$ 8280.di 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{8280}(49,\cdot)$$ 8280.ga 66 no $$1$$ $$1$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{31}{66}\right)$$
$$\chi_{8280}(53,\cdot)$$ 8280.fn 44 no $$-1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$
$$\chi_{8280}(59,\cdot)$$ 8280.gk 66 yes $$1$$ $$1$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$
$$\chi_{8280}(61,\cdot)$$ 8280.fz 66 no $$-1$$ $$1$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{1}{33}\right)$$
$$\chi_{8280}(67,\cdot)$$ 8280.gw 132 yes $$-1$$ $$1$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{132}\right)$$
$$\chi_{8280}(71,\cdot)$$ 8280.el 22 no $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{8280}(73,\cdot)$$ 8280.ff 44 no $$-1$$ $$1$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{1}{44}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$
$$\chi_{8280}(77,\cdot)$$ 8280.hd 132 yes $$1$$ $$1$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{125}{132}\right)$$
$$\chi_{8280}(79,\cdot)$$ 8280.fy 66 no $$1$$ $$1$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$
$$\chi_{8280}(83,\cdot)$$ 8280.hc 132 yes $$1$$ $$1$$ $$e\left(\frac{7}{132}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{59}{132}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{91}{132}\right)$$
$$\chi_{8280}(89,\cdot)$$ 8280.dz 22 no $$1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{8280}(91,\cdot)$$ 8280.r 2 no $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{8280}(97,\cdot)$$ 8280.gv 132 no $$1$$ $$1$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{95}{132}\right)$$ $$e\left(\frac{25}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{85}{132}\right)$$
$$\chi_{8280}(101,\cdot)$$ 8280.gq 66 no $$-1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{29}{66}\right)$$
$$\chi_{8280}(103,\cdot)$$ 8280.hg 132 no $$-1$$ $$1$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{17}{132}\right)$$
$$\chi_{8280}(107,\cdot)$$ 8280.fc 44 no $$1$$ $$1$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$
$$\chi_{8280}(109,\cdot)$$ 8280.dt 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{8280}(113,\cdot)$$ 8280.hf 132 no $$-1$$ $$1$$ $$e\left(\frac{41}{132}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{25}{132}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{71}{132}\right)$$
$$\chi_{8280}(119,\cdot)$$ 8280.gn 66 no $$1$$ $$1$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{25}{66}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$
$$\chi_{8280}(121,\cdot)$$ 8280.ey 33 no $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$