Properties

Modulus $837$
Structure \(C_{90}\times C_{6}\)
Order $540$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(837)
 
pari: g = idealstar(,837,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 540
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{90}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{837}(218,\cdot)$, $\chi_{837}(406,\cdot)$

First 32 of 540 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{837}(1,\cdot)\) 837.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{837}(2,\cdot)\) 837.cg 90 yes \(-1\) \(1\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{1}{45}\right)\)
\(\chi_{837}(4,\cdot)\) 837.cc 45 yes \(1\) \(1\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{2}{45}\right)\)
\(\chi_{837}(5,\cdot)\) 837.bn 18 yes \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{837}(7,\cdot)\) 837.ca 45 yes \(1\) \(1\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{16}{45}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{7}{45}\right)\)
\(\chi_{837}(8,\cdot)\) 837.br 30 no \(-1\) \(1\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{15}\right)\)
\(\chi_{837}(10,\cdot)\) 837.be 15 no \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{15}\right)\)
\(\chi_{837}(11,\cdot)\) 837.cf 90 yes \(1\) \(1\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{22}{45}\right)\)
\(\chi_{837}(13,\cdot)\) 837.cj 90 yes \(-1\) \(1\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{53}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{44}{45}\right)\)
\(\chi_{837}(14,\cdot)\) 837.ci 90 yes \(-1\) \(1\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{8}{45}\right)\)
\(\chi_{837}(16,\cdot)\) 837.cc 45 yes \(1\) \(1\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{22}{45}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{4}{45}\right)\)
\(\chi_{837}(17,\cdot)\) 837.bt 30 no \(1\) \(1\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{15}\right)\)
\(\chi_{837}(19,\cdot)\) 837.be 15 no \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{15}\right)\)
\(\chi_{837}(20,\cdot)\) 837.ci 90 yes \(-1\) \(1\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{7}{45}\right)\)
\(\chi_{837}(22,\cdot)\) 837.cj 90 yes \(-1\) \(1\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{23}{45}\right)\)
\(\chi_{837}(23,\cdot)\) 837.ch 90 yes \(1\) \(1\) \(e\left(\frac{19}{90}\right)\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{29}{45}\right)\) \(e\left(\frac{71}{90}\right)\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{38}{45}\right)\)
\(\chi_{837}(25,\cdot)\) 837.x 9 yes \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{837}(26,\cdot)\) 837.j 6 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\)
\(\chi_{837}(28,\cdot)\) 837.bb 15 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{837}(29,\cdot)\) 837.ch 90 yes \(1\) \(1\) \(e\left(\frac{23}{90}\right)\) \(e\left(\frac{23}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{28}{45}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{49}{90}\right)\) \(e\left(\frac{1}{45}\right)\)
\(\chi_{837}(32,\cdot)\) 837.bk 18 no \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{837}(34,\cdot)\) 837.cj 90 yes \(-1\) \(1\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{43}{90}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{34}{45}\right)\)
\(\chi_{837}(35,\cdot)\) 837.br 30 no \(-1\) \(1\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\)
\(\chi_{837}(37,\cdot)\) 837.l 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{837}(38,\cdot)\) 837.cd 90 yes \(-1\) \(1\) \(e\left(\frac{11}{90}\right)\) \(e\left(\frac{11}{45}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{77}{90}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{73}{90}\right)\) \(e\left(\frac{22}{45}\right)\)
\(\chi_{837}(40,\cdot)\) 837.ca 45 yes \(1\) \(1\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{4}{45}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{44}{45}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{1}{45}\right)\) \(e\left(\frac{8}{45}\right)\)
\(\chi_{837}(41,\cdot)\) 837.cd 90 yes \(-1\) \(1\) \(e\left(\frac{13}{90}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{8}{45}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{31}{45}\right)\) \(e\left(\frac{29}{90}\right)\) \(e\left(\frac{26}{45}\right)\)
\(\chi_{837}(43,\cdot)\) 837.cj 90 yes \(-1\) \(1\) \(e\left(\frac{19}{45}\right)\) \(e\left(\frac{38}{45}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{41}{90}\right)\) \(e\left(\frac{67}{90}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{31}{45}\right)\)
\(\chi_{837}(44,\cdot)\) 837.bq 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{8}{15}\right)\)
\(\chi_{837}(46,\cdot)\) 837.bv 30 no \(-1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\)
\(\chi_{837}(47,\cdot)\) 837.cg 90 yes \(-1\) \(1\) \(e\left(\frac{17}{90}\right)\) \(e\left(\frac{17}{45}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{37}{45}\right)\) \(e\left(\frac{17}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{59}{90}\right)\) \(e\left(\frac{14}{45}\right)\) \(e\left(\frac{1}{90}\right)\) \(e\left(\frac{34}{45}\right)\)
\(\chi_{837}(49,\cdot)\) 837.ca 45 yes \(1\) \(1\) \(e\left(\frac{26}{45}\right)\) \(e\left(\frac{7}{45}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{32}{45}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{45}\right)\) \(e\left(\frac{34}{45}\right)\) \(e\left(\frac{13}{45}\right)\) \(e\left(\frac{14}{45}\right)\)