Properties

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

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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 \(1\) \(1\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{14}{33}\right)\)
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