Properties

Modulus 640
Structure \(C_{32}\times C_{4}\times C_{2}\)
Order 256

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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(640)
 
pari: g = idealstar(,640,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 256
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{32}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{640}(261,\cdot)$, $\chi_{640}(257,\cdot)$, $\chi_{640}(511,\cdot)$

First 32 of 256 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
\(\chi_{640}(1,\cdot)\) 640.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{640}(3,\cdot)\) 640.bl 32 yes \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{640}(7,\cdot)\) 640.bj 16 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{640}(9,\cdot)\) 640.bf 16 no \(1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{640}(11,\cdot)\) 640.bp 32 no \(-1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{640}(13,\cdot)\) 640.bk 32 yes \(-1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{640}(17,\cdot)\) 640.bb 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{640}(19,\cdot)\) 640.bn 32 yes \(-1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{640}(21,\cdot)\) 640.bm 32 no \(1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{640}(23,\cdot)\) 640.bj 16 no \(1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{640}(27,\cdot)\) 640.bl 32 yes \(1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{640}(29,\cdot)\) 640.bo 32 yes \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{640}(31,\cdot)\) 640.r 4 no \(-1\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(-i\) \(1\) \(i\) \(i\) \(1\) \(-i\)
\(\chi_{640}(33,\cdot)\) 640.i 4 no \(-1\) \(1\) \(-1\) \(i\) \(1\) \(-i\) \(-1\) \(-i\) \(-i\) \(-i\) \(-i\) \(-1\)
\(\chi_{640}(37,\cdot)\) 640.bk 32 yes \(-1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{640}(39,\cdot)\) 640.bh 16 no \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{640}(41,\cdot)\) 640.be 16 no \(1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{640}(43,\cdot)\) 640.br 32 yes \(1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{640}(47,\cdot)\) 640.u 8 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{640}(49,\cdot)\) 640.z 8 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{640}(51,\cdot)\) 640.bp 32 no \(-1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{640}(53,\cdot)\) 640.bq 32 yes \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{640}(57,\cdot)\) 640.bi 16 no \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{640}(59,\cdot)\) 640.bn 32 yes \(-1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{640}(61,\cdot)\) 640.bm 32 no \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{640}(63,\cdot)\) 640.o 4 no \(1\) \(1\) \(i\) \(i\) \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(-i\) \(-i\)
\(\chi_{640}(67,\cdot)\) 640.br 32 yes \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{640}(69,\cdot)\) 640.bo 32 yes \(1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{640}(71,\cdot)\) 640.bg 16 no \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{640}(73,\cdot)\) 640.bi 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{640}(77,\cdot)\) 640.bq 32 yes \(-1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{640}(79,\cdot)\) 640.y 8 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\)