Properties

Modulus $441$
Structure \(C_{42}\times C_{6}\)
Order $252$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(441)
 
pari: g = idealstar(,441,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 252
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{42}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{441}(344,\cdot)$, $\chi_{441}(199,\cdot)$

First 32 of 252 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{441}(1,\cdot)\) 441.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{441}(2,\cdot)\) 441.bi 42 yes \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(4,\cdot)\) 441.z 21 yes \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(5,\cdot)\) 441.bn 42 yes \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(8,\cdot)\) 441.x 14 no \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\)
\(\chi_{441}(10,\cdot)\) 441.bj 42 no \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(11,\cdot)\) 441.bm 42 yes \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(13,\cdot)\) 441.bk 42 yes \(-1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(-1\)
\(\chi_{441}(16,\cdot)\) 441.z 21 yes \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(17,\cdot)\) 441.bg 42 no \(1\) \(1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(19,\cdot)\) 441.m 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(20,\cdot)\) 441.bh 42 yes \(1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(-1\)
\(\chi_{441}(22,\cdot)\) 441.ba 21 yes \(1\) \(1\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\)
\(\chi_{441}(23,\cdot)\) 441.bm 42 yes \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(25,\cdot)\) 441.y 21 yes \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(26,\cdot)\) 441.bg 42 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(29,\cdot)\) 441.be 42 yes \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\)
\(\chi_{441}(31,\cdot)\) 441.k 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(32,\cdot)\) 441.bi 42 yes \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(34,\cdot)\) 441.bk 42 yes \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\)
\(\chi_{441}(37,\cdot)\) 441.bb 21 no \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(38,\cdot)\) 441.bn 42 yes \(1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(40,\cdot)\) 441.bc 42 yes \(-1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(41,\cdot)\) 441.bh 42 yes \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\)
\(\chi_{441}(43,\cdot)\) 441.ba 21 yes \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(1\)
\(\chi_{441}(44,\cdot)\) 441.bf 42 no \(-1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{441}(46,\cdot)\) 441.bb 21 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(47,\cdot)\) 441.bd 42 yes \(1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{441}(50,\cdot)\) 441.r 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\)
\(\chi_{441}(52,\cdot)\) 441.bc 42 yes \(-1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{441}(53,\cdot)\) 441.bf 42 no \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{441}(55,\cdot)\) 441.v 14 no \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\)