Properties

Modulus $1050$
Structure \(C_{60}\times C_{2}\times C_{2}\)
Order $240$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1050)
 
pari: g = idealstar(,1050,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 240
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{60}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1050}(701,\cdot)$, $\chi_{1050}(127,\cdot)$, $\chi_{1050}(451,\cdot)$

First 32 of 240 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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{1050}(1,\cdot)\) 1050.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1050}(11,\cdot)\) 1050.bm 30 no \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\)
\(\chi_{1050}(13,\cdot)\) 1050.bh 20 no \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\)
\(\chi_{1050}(17,\cdot)\) 1050.bt 60 no \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{1050}(19,\cdot)\) 1050.bp 30 no \(-1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\)
\(\chi_{1050}(23,\cdot)\) 1050.bs 60 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\)
\(\chi_{1050}(29,\cdot)\) 1050.ba 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\)
\(\chi_{1050}(31,\cdot)\) 1050.bq 30 no \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\)
\(\chi_{1050}(37,\cdot)\) 1050.bu 60 no \(-1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\)
\(\chi_{1050}(41,\cdot)\) 1050.bb 10 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\)
\(\chi_{1050}(43,\cdot)\) 1050.l 4 no \(-1\) \(1\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-1\) \(1\) \(-i\) \(1\) \(i\)
\(\chi_{1050}(47,\cdot)\) 1050.bt 60 no \(-1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(-i\)
\(\chi_{1050}(53,\cdot)\) 1050.bs 60 no \(1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\)
\(\chi_{1050}(59,\cdot)\) 1050.bl 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\)
\(\chi_{1050}(61,\cdot)\) 1050.bq 30 no \(-1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\)
\(\chi_{1050}(67,\cdot)\) 1050.bu 60 no \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(-i\)
\(\chi_{1050}(71,\cdot)\) 1050.y 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\)
\(\chi_{1050}(73,\cdot)\) 1050.bv 60 no \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(i\)
\(\chi_{1050}(79,\cdot)\) 1050.br 30 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\)
\(\chi_{1050}(83,\cdot)\) 1050.bj 20 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(i\)
\(\chi_{1050}(89,\cdot)\) 1050.bl 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\)
\(\chi_{1050}(97,\cdot)\) 1050.bh 20 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(-i\)
\(\chi_{1050}(101,\cdot)\) 1050.s 6 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)
\(\chi_{1050}(103,\cdot)\) 1050.bv 60 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{31}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\)
\(\chi_{1050}(107,\cdot)\) 1050.bf 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-i\)
\(\chi_{1050}(109,\cdot)\) 1050.br 30 no \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\)
\(\chi_{1050}(113,\cdot)\) 1050.bk 20 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(i\)
\(\chi_{1050}(121,\cdot)\) 1050.bg 15 no \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\)
\(\chi_{1050}(127,\cdot)\) 1050.bi 20 no \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(-i\)
\(\chi_{1050}(131,\cdot)\) 1050.bn 30 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\)
\(\chi_{1050}(137,\cdot)\) 1050.bs 60 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(-i\)
\(\chi_{1050}(139,\cdot)\) 1050.v 10 no \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\)