Properties

Modulus $6825$
Structure \(C_{2}\times C_{2}\times C_{12}\times C_{60}\)
Order $2880$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(6825)
 
pari: g = idealstar(,6825,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2880
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{12}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6825}(2276,\cdot)$, $\chi_{6825}(3277,\cdot)$, $\chi_{6825}(976,\cdot)$, $\chi_{6825}(4201,\cdot)$

First 32 of 2880 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 \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(16\) \(17\) \(19\) \(22\) \(23\) \(29\)
\(\chi_{6825}(1,\cdot)\) 6825.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6825}(2,\cdot)\) 6825.pj 60 yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{6825}(4,\cdot)\) 6825.jn 30 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{6825}(8,\cdot)\) 6825.jg 20 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{6825}(11,\cdot)\) 6825.np 60 yes \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{6825}(16,\cdot)\) 6825.ii 15 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{6825}(17,\cdot)\) 6825.or 60 yes \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{6825}(19,\cdot)\) 6825.my 60 no \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{6825}(22,\cdot)\) 6825.nt 60 no \(-1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{6825}(23,\cdot)\) 6825.ot 60 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{14}{15}\right)\)
\(\chi_{6825}(29,\cdot)\) 6825.kx 30 no \(-1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\)
\(\chi_{6825}(31,\cdot)\) 6825.ng 60 no \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{6825}(32,\cdot)\) 6825.eq 12 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{6825}(34,\cdot)\) 6825.ja 20 no \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{6825}(37,\cdot)\) 6825.ph 60 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{6825}(38,\cdot)\) 6825.ns 60 yes \(-1\) \(1\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{6825}(41,\cdot)\) 6825.nd 60 yes \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\)
\(\chi_{6825}(43,\cdot)\) 6825.hi 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{6825}(44,\cdot)\) 6825.ne 60 yes \(1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{6825}(46,\cdot)\) 6825.op 60 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{6825}(47,\cdot)\) 6825.ov 60 yes \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{6825}(53,\cdot)\) 6825.mm 60 no \(1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{6825}(58,\cdot)\) 6825.ma 60 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{29}{30}\right)\)
\(\chi_{6825}(59,\cdot)\) 6825.oj 60 yes \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\)
\(\chi_{6825}(61,\cdot)\) 6825.kq 30 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{6825}(62,\cdot)\) 6825.nu 60 yes \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{6825}(64,\cdot)\) 6825.eh 10 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{6825}(67,\cdot)\) 6825.ox 60 no \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{6825}(68,\cdot)\) 6825.fs 12 no \(-1\) \(1\) \(i\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{6825}(71,\cdot)\) 6825.no 60 no \(1\) \(1\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{6825}(73,\cdot)\) 6825.pf 60 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{6825}(74,\cdot)\) 6825.ea 6 no \(-1\) \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)
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