Properties

Modulus $2400$
Structure \(C_{2}\times C_{2}\times C_{4}\times C_{40}\)
Order $640$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2400)
 
pari: g = idealstar(,2400,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 640
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{4}\times C_{40}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2400}(1951,\cdot)$, $\chi_{2400}(901,\cdot)$, $\chi_{2400}(1601,\cdot)$, $\chi_{2400}(577,\cdot)$

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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{2400}(1,\cdot)\) 2400.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2400}(7,\cdot)\) 2400.y 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-i\) \(-i\) \(i\) \(-1\) \(-1\) \(-1\)
\(\chi_{2400}(11,\cdot)\) 2400.dy 40 yes \(1\) \(1\) \(-i\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{2400}(13,\cdot)\) 2400.du 40 no \(-1\) \(1\) \(-1\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{2400}(17,\cdot)\) 2400.cz 20 no \(1\) \(1\) \(i\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2400}(19,\cdot)\) 2400.dz 40 no \(-1\) \(1\) \(-i\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{2400}(23,\cdot)\) 2400.di 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{2400}(29,\cdot)\) 2400.eb 40 yes \(-1\) \(1\) \(i\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{21}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{2400}(31,\cdot)\) 2400.cj 10 no \(-1\) \(1\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{2400}(37,\cdot)\) 2400.du 40 no \(-1\) \(1\) \(-1\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{2400}(41,\cdot)\) 2400.cw 20 no \(-1\) \(1\) \(-1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2400}(43,\cdot)\) 2400.bp 8 no \(1\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{2400}(47,\cdot)\) 2400.dn 20 no \(-1\) \(1\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{2400}(49,\cdot)\) 2400.d 2 no \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\)
\(\chi_{2400}(53,\cdot)\) 2400.eg 40 yes \(1\) \(1\) \(1\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{2400}(59,\cdot)\) 2400.ed 40 yes \(1\) \(1\) \(i\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{2400}(61,\cdot)\) 2400.ea 40 no \(1\) \(1\) \(-i\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{2400}(67,\cdot)\) 2400.dv 40 no \(1\) \(1\) \(-1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{33}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{2400}(71,\cdot)\) 2400.dr 20 no \(1\) \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2400}(73,\cdot)\) 2400.dh 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{2400}(77,\cdot)\) 2400.eg 40 yes \(1\) \(1\) \(1\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{3}{40}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{2400}(79,\cdot)\) 2400.cn 10 no \(-1\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2400}(83,\cdot)\) 2400.eh 40 yes \(-1\) \(1\) \(1\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{40}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{2400}(89,\cdot)\) 2400.dp 20 no \(-1\) \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{2400}(91,\cdot)\) 2400.ec 40 no \(-1\) \(1\) \(-i\) \(e\left(\frac{13}{40}\right)\) \(e\left(\frac{27}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{39}{40}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{31}{40}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{37}{40}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{2400}(97,\cdot)\) 2400.db 20 no \(-1\) \(1\) \(i\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2400}(101,\cdot)\) 2400.ca 8 no \(-1\) \(1\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{2400}(103,\cdot)\) 2400.df 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{2400}(107,\cdot)\) 2400.cb 8 no \(-1\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(i\)
\(\chi_{2400}(109,\cdot)\) 2400.dx 40 no \(1\) \(1\) \(i\) \(e\left(\frac{23}{40}\right)\) \(e\left(\frac{17}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{29}{40}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{40}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{40}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{2400}(113,\cdot)\) 2400.cz 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{2400}(119,\cdot)\) 2400.cu 20 no \(1\) \(1\) \(-1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
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