Properties

Modulus $920$
Structure \(C_{44}\times C_{2}\times C_{2}\times C_{2}\)
Order $352$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(920)
 
pari: g = idealstar(,920,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 352
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{44}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{920}(231,\cdot)$, $\chi_{920}(461,\cdot)$, $\chi_{920}(737,\cdot)$, $\chi_{920}(281,\cdot)$

First 32 of 352 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(27\) \(29\)
\(\chi_{920}(1,\cdot)\) 920.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{920}(3,\cdot)\) 920.bq 44 yes \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{920}(7,\cdot)\) 920.br 44 no \(-1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{920}(9,\cdot)\) 920.bk 22 no \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{920}(11,\cdot)\) 920.bb 22 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{920}(13,\cdot)\) 920.bu 44 yes \(-1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{920}(17,\cdot)\) 920.bv 44 no \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{920}(19,\cdot)\) 920.bn 22 yes \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{920}(21,\cdot)\) 920.bl 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{920}(27,\cdot)\) 920.bq 44 yes \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{920}(29,\cdot)\) 920.bf 22 yes \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{920}(31,\cdot)\) 920.bm 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{920}(33,\cdot)\) 920.bv 44 no \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{920}(37,\cdot)\) 920.bo 44 yes \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{920}(39,\cdot)\) 920.ba 22 no \(-1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{920}(41,\cdot)\) 920.y 11 no \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{920}(43,\cdot)\) 920.bs 44 yes \(-1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{920}(47,\cdot)\) 920.s 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(1\) \(1\) \(-i\) \(-1\)
\(\chi_{920}(49,\cdot)\) 920.bk 22 no \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{920}(51,\cdot)\) 920.bb 22 no \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{920}(53,\cdot)\) 920.bo 44 yes \(1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{920}(57,\cdot)\) 920.bv 44 no \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{920}(59,\cdot)\) 920.bh 22 yes \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{920}(61,\cdot)\) 920.bl 22 no \(-1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{920}(63,\cdot)\) 920.br 44 no \(-1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{920}(67,\cdot)\) 920.bs 44 yes \(-1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{920}(71,\cdot)\) 920.bm 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{920}(73,\cdot)\) 920.bp 44 no \(-1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{920}(77,\cdot)\) 920.bu 44 yes \(-1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\)
\(\chi_{920}(79,\cdot)\) 920.bc 22 no \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{920}(81,\cdot)\) 920.y 11 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{920}(83,\cdot)\) 920.bs 44 yes \(-1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\)