Properties

Modulus $4200$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order $960$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(4200)
 
pari: g = idealstar(,4200,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 960
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{2}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4200}(3151,\cdot)$, $\chi_{4200}(2101,\cdot)$, $\chi_{4200}(2801,\cdot)$, $\chi_{4200}(1177,\cdot)$, $\chi_{4200}(3601,\cdot)$

First 32 of 960 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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{4200}(1,\cdot)\) 4200.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4200}(11,\cdot)\) 4200.ga 30 yes \(1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\)
\(\chi_{4200}(13,\cdot)\) 4200.fm 20 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\)
\(\chi_{4200}(17,\cdot)\) 4200.gy 60 no \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{4200}(19,\cdot)\) 4200.gr 30 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\)
\(\chi_{4200}(23,\cdot)\) 4200.hg 60 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(-i\)
\(\chi_{4200}(29,\cdot)\) 4200.de 10 no \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\)
\(\chi_{4200}(31,\cdot)\) 4200.fz 30 no \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\)
\(\chi_{4200}(37,\cdot)\) 4200.gz 60 no \(-1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(i\)
\(\chi_{4200}(41,\cdot)\) 4200.ed 10 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\)
\(\chi_{4200}(43,\cdot)\) 4200.br 4 no \(1\) \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(-i\) \(1\) \(-1\) \(i\) \(1\) \(i\)
\(\chi_{4200}(47,\cdot)\) 4200.hd 60 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(i\)
\(\chi_{4200}(53,\cdot)\) 4200.hj 60 yes \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{4200}(59,\cdot)\) 4200.fx 30 yes \(-1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\)
\(\chi_{4200}(61,\cdot)\) 4200.fs 30 no \(-1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\)
\(\chi_{4200}(67,\cdot)\) 4200.hc 60 no \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{4200}(71,\cdot)\) 4200.di 10 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\)
\(\chi_{4200}(73,\cdot)\) 4200.hi 60 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\)
\(\chi_{4200}(79,\cdot)\) 4200.fy 30 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\)
\(\chi_{4200}(83,\cdot)\) 4200.fj 20 yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\)
\(\chi_{4200}(89,\cdot)\) 4200.fq 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\)
\(\chi_{4200}(97,\cdot)\) 4200.fc 20 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{4200}(101,\cdot)\) 4200.cg 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)
\(\chi_{4200}(103,\cdot)\) 4200.gx 60 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{4200}(107,\cdot)\) 4200.ev 12 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(-i\)
\(\chi_{4200}(109,\cdot)\) 4200.fp 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\)
\(\chi_{4200}(113,\cdot)\) 4200.fl 20 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\)
\(\chi_{4200}(121,\cdot)\) 4200.ey 15 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\)
\(\chi_{4200}(127,\cdot)\) 4200.fk 20 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(i\)
\(\chi_{4200}(131,\cdot)\) 4200.fu 30 yes \(-1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\)
\(\chi_{4200}(137,\cdot)\) 4200.gv 60 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\)
\(\chi_{4200}(139,\cdot)\) 4200.dm 10 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\)
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