Properties

Modulus $429$
Structure \(C_{2}\times C_{2}\times C_{60}\)
Order $240$

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(429)
 
pari: g = idealstar(,429,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 240
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{429}(287,\cdot)$, $\chi_{429}(79,\cdot)$, $\chi_{429}(67,\cdot)$

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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{429}(1,\cdot)\) 429.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{429}(2,\cdot)\) 429.bt 60 yes \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{43}{60}\right)\)
\(\chi_{429}(4,\cdot)\) 429.bn 30 no \(1\) \(1\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{30}\right)\)
\(\chi_{429}(5,\cdot)\) 429.bi 20 yes \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{429}(7,\cdot)\) 429.bs 60 no \(1\) \(1\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{41}{60}\right)\)
\(\chi_{429}(8,\cdot)\) 429.bk 20 yes \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{429}(10,\cdot)\) 429.o 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{429}(14,\cdot)\) 429.ba 10 no \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{429}(16,\cdot)\) 429.bg 15 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{429}(17,\cdot)\) 429.bm 30 yes \(1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{429}(19,\cdot)\) 429.bs 60 no \(1\) \(1\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{59}{60}\right)\)
\(\chi_{429}(20,\cdot)\) 429.bv 60 yes \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{23}{60}\right)\)
\(\chi_{429}(23,\cdot)\) 429.q 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{429}(25,\cdot)\) 429.bb 10 no \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{429}(28,\cdot)\) 429.bs 60 no \(1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{60}\right)\)
\(\chi_{429}(29,\cdot)\) 429.bq 30 yes \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{23}{30}\right)\)
\(\chi_{429}(31,\cdot)\) 429.bh 20 no \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{429}(32,\cdot)\) 429.bc 12 yes \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{429}(34,\cdot)\) 429.k 4 no \(-1\) \(1\) \(i\) \(-1\) \(i\) \(-i\) \(-i\) \(-1\) \(1\) \(1\) \(-1\) \(i\)
\(\chi_{429}(35,\cdot)\) 429.bq 30 yes \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\)
\(\chi_{429}(37,\cdot)\) 429.bu 60 no \(-1\) \(1\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{31}{60}\right)\)
\(\chi_{429}(38,\cdot)\) 429.v 10 yes \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{429}(40,\cdot)\) 429.z 10 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{429}(41,\cdot)\) 429.bt 60 yes \(-1\) \(1\) \(e\left(\frac{53}{60}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{60}\right)\)
\(\chi_{429}(43,\cdot)\) 429.o 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{429}(46,\cdot)\) 429.bs 60 no \(1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{47}{60}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{53}{60}\right)\)
\(\chi_{429}(47,\cdot)\) 429.bi 20 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{429}(49,\cdot)\) 429.bn 30 no \(1\) \(1\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{30}\right)\)
\(\chi_{429}(50,\cdot)\) 429.bt 60 yes \(-1\) \(1\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{37}{60}\right)\)
\(\chi_{429}(53,\cdot)\) 429.ba 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{429}(56,\cdot)\) 429.q 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{429}(58,\cdot)\) 429.bu 60 no \(-1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{29}{60}\right)\)
Click here to search among the remaining 208 characters.