Properties

Modulus $7800$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}\)
Order $1920$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(7800)
 
pari: g = idealstar(,7800,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1920
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{7800}(1951,\cdot)$, $\chi_{7800}(3901,\cdot)$, $\chi_{7800}(5201,\cdot)$, $\chi_{7800}(7177,\cdot)$, $\chi_{7800}(4201,\cdot)$

First 32 of 1920 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 \(-1\) \(1\) \(7\) \(11\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{7800}(1,\cdot)\) 7800.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{7800}(7,\cdot)\) 7800.hg 12 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{7800}(11,\cdot)\) 7800.lm 60 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{7800}(17,\cdot)\) 7800.lz 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{7800}(19,\cdot)\) 7800.lk 60 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{7800}(23,\cdot)\) 7800.kx 60 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{7800}(29,\cdot)\) 7800.kj 30 yes \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{7800}(31,\cdot)\) 7800.ij 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(1\)
\(\chi_{7800}(37,\cdot)\) 7800.kq 60 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{7800}(41,\cdot)\) 7800.lp 60 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{7800}(43,\cdot)\) 7800.gv 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{7800}(47,\cdot)\) 7800.hl 20 no \(1\) \(1\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\)
\(\chi_{7800}(49,\cdot)\) 7800.ds 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{7800}(53,\cdot)\) 7800.hw 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{7800}(59,\cdot)\) 7800.lj 60 yes \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{7800}(61,\cdot)\) 7800.jm 30 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{7800}(67,\cdot)\) 7800.ks 60 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{7800}(71,\cdot)\) 7800.ll 60 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{7800}(73,\cdot)\) 7800.hs 20 no \(1\) \(1\) \(-1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(-i\)
\(\chi_{7800}(77,\cdot)\) 7800.ix 20 yes \(1\) \(1\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\)
\(\chi_{7800}(79,\cdot)\) 7800.fm 10 no \(-1\) \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\)
\(\chi_{7800}(83,\cdot)\) 7800.hr 20 yes \(1\) \(1\) \(-1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(-i\)
\(\chi_{7800}(89,\cdot)\) 7800.lc 60 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{7800}(97,\cdot)\) 7800.mb 60 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{7800}(101,\cdot)\) 7800.eg 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{7800}(103,\cdot)\) 7800.ia 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{7800}(107,\cdot)\) 7800.hb 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{7800}(109,\cdot)\) 7800.id 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(-1\)
\(\chi_{7800}(113,\cdot)\) 7800.kw 60 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{7800}(119,\cdot)\) 7800.lg 60 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{7800}(121,\cdot)\) 7800.kb 30 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{7800}(127,\cdot)\) 7800.ls 60 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{12}\right)\)
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