Properties

Modulus $1122$
Structure \(C_{80}\times C_{2}\times C_{2}\)
Order $320$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1122)
 
pari: g = idealstar(,1122,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 320
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{80}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1122}(749,\cdot)$, $\chi_{1122}(409,\cdot)$, $\chi_{1122}(1057,\cdot)$

First 32 of 320 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 \(-1\) \(1\) \(5\) \(7\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\) \(37\)
\(\chi_{1122}(1,\cdot)\) 1122.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1122}(5,\cdot)\) 1122.bn 80 no \(1\) \(1\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{80}\right)\)
\(\chi_{1122}(7,\cdot)\) 1122.bm 80 no \(1\) \(1\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{80}\right)\)
\(\chi_{1122}(13,\cdot)\) 1122.bf 20 no \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{1122}(19,\cdot)\) 1122.bh 40 no \(-1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{1122}(23,\cdot)\) 1122.y 16 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{1122}(25,\cdot)\) 1122.bi 40 no \(1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{1122}(29,\cdot)\) 1122.bl 80 no \(-1\) \(1\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{80}\right)\)
\(\chi_{1122}(31,\cdot)\) 1122.bk 80 no \(-1\) \(1\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{61}{80}\right)\)
\(\chi_{1122}(35,\cdot)\) 1122.x 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1122}(37,\cdot)\) 1122.bk 80 no \(-1\) \(1\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{37}{80}\right)\)
\(\chi_{1122}(41,\cdot)\) 1122.bl 80 no \(-1\) \(1\) \(e\left(\frac{11}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{23}{80}\right)\)
\(\chi_{1122}(43,\cdot)\) 1122.p 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(i\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{1122}(47,\cdot)\) 1122.bd 20 no \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{1122}(49,\cdot)\) 1122.bi 40 no \(1\) \(1\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{1122}(53,\cdot)\) 1122.bj 40 no \(-1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{1122}(59,\cdot)\) 1122.bj 40 no \(-1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{1122}(61,\cdot)\) 1122.bm 80 no \(1\) \(1\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{79}{80}\right)\)
\(\chi_{1122}(65,\cdot)\) 1122.ba 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(1\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{1122}(67,\cdot)\) 1122.c 2 no \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\)
\(\chi_{1122}(71,\cdot)\) 1122.bn 80 no \(1\) \(1\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{69}{80}\right)\)
\(\chi_{1122}(73,\cdot)\) 1122.bm 80 no \(1\) \(1\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{57}{80}\right)\)
\(\chi_{1122}(79,\cdot)\) 1122.bm 80 no \(1\) \(1\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{51}{80}\right)\)
\(\chi_{1122}(83,\cdot)\) 1122.bg 40 no \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{1122}(89,\cdot)\) 1122.k 4 no \(-1\) \(1\) \(i\) \(i\) \(1\) \(-1\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\) \(-i\)
\(\chi_{1122}(91,\cdot)\) 1122.bk 80 no \(-1\) \(1\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{63}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{43}{80}\right)\)
\(\chi_{1122}(95,\cdot)\) 1122.bl 80 no \(-1\) \(1\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{47}{80}\right)\)
\(\chi_{1122}(97,\cdot)\) 1122.bk 80 no \(-1\) \(1\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{11}{80}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{80}\right)\)
\(\chi_{1122}(101,\cdot)\) 1122.r 10 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1122}(103,\cdot)\) 1122.m 5 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1122}(107,\cdot)\) 1122.bl 80 no \(-1\) \(1\) \(e\left(\frac{21}{80}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{73}{80}\right)\)
\(\chi_{1122}(109,\cdot)\) 1122.z 16 no \(1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\)