Properties

Modulus 800
Structure \(C_{40}\times C_{4}\times C_{2}\)
Order 320

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(800)
 
pari: g = idealstar(,800,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 320
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{40}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{800}(77,\cdot)$, $\chi_{800}(657,\cdot)$, $\chi_{800}(351,\cdot)$

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.

orbit label order primitive -1 1 3 7 9 11 13 17 19 21 23 27
\(\chi_{800}(1,\cdot)\) 800.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{800}(3,\cdot)\) 800.cd 40 Yes \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{800}(7,\cdot)\) 800.s 4 No \(1\) \(1\) \(1\) \(i\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(i\) \(-i\) \(1\)
\(\chi_{800}(9,\cdot)\) 800.bt 20 No \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{800}(11,\cdot)\) 800.cb 40 Yes \(-1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{800}(13,\cdot)\) 800.bw 40 Yes \(-1\) \(1\) \(e\left(\frac{11}{40}\right)\) \(-1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{800}(17,\cdot)\) 800.br 20 No \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{800}(19,\cdot)\) 800.bz 40 Yes \(-1\) \(1\) \(e\left(\frac{17}{40}\right)\) \(-i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{800}(21,\cdot)\) 800.ca 40 Yes \(1\) \(1\) \(e\left(\frac{3}{40}\right)\) \(i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{800}(23,\cdot)\) 800.bl 20 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{800}(27,\cdot)\) 800.cd 40 Yes \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{800}(29,\cdot)\) 800.by 40 Yes \(1\) \(1\) \(e\left(\frac{33}{40}\right)\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{40}\right)\)
\(\chi_{800}(31,\cdot)\) 800.bh 10 No \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{800}(33,\cdot)\) 800.bo 20 No \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{800}(37,\cdot)\) 800.bw 40 Yes \(-1\) \(1\) \(e\left(\frac{21}{40}\right)\) \(-1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{23}{40}\right)\)
\(\chi_{800}(39,\cdot)\) 800.bn 20 No \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{800}(41,\cdot)\) 800.bm 20 No \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{800}(43,\cdot)\) 800.v 8 No \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{800}(47,\cdot)\) 800.bp 20 No \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{800}(49,\cdot)\) 800.f 2 No \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{800}(51,\cdot)\) 800.x 8 No \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{800}(53,\cdot)\) 800.cc 40 Yes \(-1\) \(1\) \(e\left(\frac{13}{40}\right)\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{39}{40}\right)\)
\(\chi_{800}(57,\cdot)\) 800.i 4 No \(-1\) \(1\) \(-1\) \(-i\) \(1\) \(i\) \(-1\) \(i\) \(i\) \(i\) \(i\) \(-1\)
\(\chi_{800}(59,\cdot)\) 800.bz 40 Yes \(-1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{40}\right)\)
\(\chi_{800}(61,\cdot)\) 800.ca 40 Yes \(1\) \(1\) \(e\left(\frac{29}{40}\right)\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{800}(63,\cdot)\) 800.bq 20 No \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{800}(67,\cdot)\) 800.bx 40 Yes \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{800}(69,\cdot)\) 800.by 40 Yes \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{40}\right)\)
\(\chi_{800}(71,\cdot)\) 800.bs 20 No \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{800}(73,\cdot)\) 800.bv 20 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{800}(77,\cdot)\) 800.cc 40 Yes \(-1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{800}(79,\cdot)\) 800.bi 10 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\)