Properties

Modulus $1600$
Structure \(C_{80}\times C_{4}\times C_{2}\)
Order $640$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1600)
 
pari: g = idealstar(,1600,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 640
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{80}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1600}(1151,\cdot)$, $\chi_{1600}(901,\cdot)$, $\chi_{1600}(577,\cdot)$

First 32 of 640 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1600}(1,\cdot)\) 1600.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1600}(3,\cdot)\) 1600.cm 80 yes \(1\) \(1\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{43}{80}\right)\)
\(\chi_{1600}(7,\cdot)\) 1600.bb 8 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(1\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{1600}(9,\cdot)\) 1600.cg 40 no \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{1600}(11,\cdot)\) 1600.cp 80 yes \(-1\) \(1\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{9}{80}\right)\)
\(\chi_{1600}(13,\cdot)\) 1600.cn 80 yes \(-1\) \(1\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{31}{80}\right)\)
\(\chi_{1600}(17,\cdot)\) 1600.bs 20 no \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(-i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1600}(19,\cdot)\) 1600.co 80 yes \(-1\) \(1\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{27}{80}\right)\)
\(\chi_{1600}(21,\cdot)\) 1600.cr 80 yes \(1\) \(1\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{73}{80}\right)\)
\(\chi_{1600}(23,\cdot)\) 1600.cl 40 no \(1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{1600}(27,\cdot)\) 1600.cm 80 yes \(1\) \(1\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{49}{80}\right)\)
\(\chi_{1600}(29,\cdot)\) 1600.cq 80 yes \(1\) \(1\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{11}{80}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{23}{80}\right)\)
\(\chi_{1600}(31,\cdot)\) 1600.bd 10 no \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1600}(33,\cdot)\) 1600.bz 20 no \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{1600}(37,\cdot)\) 1600.cn 80 yes \(-1\) \(1\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{41}{80}\right)\)
\(\chi_{1600}(39,\cdot)\) 1600.ch 40 no \(-1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{1600}(41,\cdot)\) 1600.ci 40 no \(1\) \(1\) \(e\left(\frac{1}{40}\right)\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{1600}(43,\cdot)\) 1600.bl 16 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{1600}(47,\cdot)\) 1600.cc 20 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1600}(49,\cdot)\) 1600.q 4 no \(1\) \(1\) \(i\) \(1\) \(-1\) \(i\) \(i\) \(-1\) \(-i\) \(i\) \(1\) \(-i\)
\(\chi_{1600}(51,\cdot)\) 1600.bo 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{1600}(53,\cdot)\) 1600.ct 80 yes \(-1\) \(1\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{21}{80}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{13}{80}\right)\)
\(\chi_{1600}(57,\cdot)\) 1600.w 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{1600}(59,\cdot)\) 1600.co 80 yes \(-1\) \(1\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{61}{80}\right)\)
\(\chi_{1600}(61,\cdot)\) 1600.cr 80 yes \(1\) \(1\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{39}{80}\right)\)
\(\chi_{1600}(63,\cdot)\) 1600.by 20 no \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{1600}(67,\cdot)\) 1600.cs 80 yes \(1\) \(1\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{67}{80}\right)\)
\(\chi_{1600}(69,\cdot)\) 1600.cq 80 yes \(1\) \(1\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{37}{80}\right)\)
\(\chi_{1600}(71,\cdot)\) 1600.cj 40 no \(-1\) \(1\) \(e\left(\frac{23}{40}\right)\) \(-i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{1600}(73,\cdot)\) 1600.ce 40 no \(-1\) \(1\) \(e\left(\frac{39}{40}\right)\) \(-1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{1600}(77,\cdot)\) 1600.ct 80 yes \(-1\) \(1\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{63}{80}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{39}{80}\right)\)
\(\chi_{1600}(79,\cdot)\) 1600.bv 20 no \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\)