Properties

Modulus $4800$
Structure \(C_{80}\times C_{4}\times C_{2}\times C_{2}\)
Order $1280$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(4800)
 
pari: g = idealstar(,4800,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1280
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{80}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4800}(4351,\cdot)$, $\chi_{4800}(901,\cdot)$, $\chi_{4800}(1601,\cdot)$, $\chi_{4800}(577,\cdot)$

First 32 of 1280 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{4800}(1,\cdot)\) 4800.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4800}(7,\cdot)\) 4800.cd 8 no \(1\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\)
\(\chi_{4800}(11,\cdot)\) 4800.fe 80 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{3}{40}\right)\)
\(\chi_{4800}(13,\cdot)\) 4800.fb 80 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{4800}(17,\cdot)\) 4800.ds 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{4800}(19,\cdot)\) 4800.fd 80 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{61}{80}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{29}{40}\right)\)
\(\chi_{4800}(23,\cdot)\) 4800.ex 40 no \(-1\) \(1\) \(1\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{4800}(29,\cdot)\) 4800.fg 80 yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{21}{80}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{21}{40}\right)\)
\(\chi_{4800}(31,\cdot)\) 4800.ch 10 no \(-1\) \(1\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{4800}(37,\cdot)\) 4800.fb 80 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{80}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{80}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{4800}(41,\cdot)\) 4800.em 40 no \(-1\) \(1\) \(-i\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{4800}(43,\cdot)\) 4800.cw 16 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4800}(47,\cdot)\) 4800.du 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{4800}(49,\cdot)\) 4800.bl 4 no \(1\) \(1\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(1\) \(-i\) \(1\) \(-i\) \(-1\)
\(\chi_{4800}(53,\cdot)\) 4800.fa 80 yes \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{27}{80}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{39}{80}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{51}{80}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{77}{80}\right)\) \(e\left(\frac{11}{40}\right)\)
\(\chi_{4800}(59,\cdot)\) 4800.fc 80 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{7}{40}\right)\)
\(\chi_{4800}(61,\cdot)\) 4800.fj 80 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{59}{80}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{57}{80}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{4800}(67,\cdot)\) 4800.fl 80 no \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{67}{80}\right)\) \(e\left(\frac{13}{80}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{29}{80}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{43}{80}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{4800}(71,\cdot)\) 4800.eo 40 no \(1\) \(1\) \(-i\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{4800}(73,\cdot)\) 4800.ek 40 no \(-1\) \(1\) \(-1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{4800}(77,\cdot)\) 4800.fa 80 yes \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{79}{80}\right)\) \(e\left(\frac{1}{80}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{37}{80}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{73}{80}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{71}{80}\right)\) \(e\left(\frac{33}{40}\right)\)
\(\chi_{4800}(79,\cdot)\) 4800.dn 20 no \(-1\) \(1\) \(-1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{4800}(83,\cdot)\) 4800.fk 80 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{33}{80}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{21}{80}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{49}{80}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{23}{80}\right)\) \(e\left(\frac{9}{40}\right)\)
\(\chi_{4800}(89,\cdot)\) 4800.er 40 no \(-1\) \(1\) \(-i\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{4800}(91,\cdot)\) 4800.ff 80 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{41}{80}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{80}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{47}{80}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{27}{40}\right)\)
\(\chi_{4800}(97,\cdot)\) 4800.ea 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{4800}(101,\cdot)\) 4800.cz 16 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4800}(103,\cdot)\) 4800.el 40 no \(1\) \(1\) \(-1\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{4800}(107,\cdot)\) 4800.cx 16 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4800}(109,\cdot)\) 4800.fh 80 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{31}{80}\right)\) \(e\left(\frac{69}{80}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{53}{80}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{80}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{80}\right)\) \(e\left(\frac{37}{40}\right)\)
\(\chi_{4800}(113,\cdot)\) 4800.ds 20 no \(1\) \(1\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{4800}(119,\cdot)\) 4800.et 40 no \(1\) \(1\) \(-i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{40}\right)\) \(e\left(\frac{7}{20}\right)\)