Properties

Modulus 200
Structure \(C_{20}\times C_{2}\times C_{2}\)
Order 80

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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(200)
 
pari: g = idealstar(,200,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 80
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{20}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{200}(177,\cdot)$, $\chi_{200}(151,\cdot)$, $\chi_{200}(101,\cdot)$

First 32 of 80 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
\(\chi_{200}(1,\cdot)\) 200.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{200}(3,\cdot)\) 200.v 20 yes \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{200}(7,\cdot)\) 200.j 4 no \(1\) \(1\) \(i\) \(-i\) \(-1\) \(-1\) \(-i\) \(i\) \(1\) \(1\) \(i\) \(-i\)
\(\chi_{200}(9,\cdot)\) 200.q 10 no \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{200}(11,\cdot)\) 200.n 10 yes \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{200}(13,\cdot)\) 200.x 20 yes \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{200}(17,\cdot)\) 200.u 20 no \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{200}(19,\cdot)\) 200.s 10 yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{200}(21,\cdot)\) 200.t 10 yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{200}(23,\cdot)\) 200.w 20 no \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{200}(27,\cdot)\) 200.v 20 yes \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{200}(29,\cdot)\) 200.o 10 yes \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{200}(31,\cdot)\) 200.r 10 no \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{200}(33,\cdot)\) 200.u 20 no \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{200}(37,\cdot)\) 200.x 20 yes \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{200}(39,\cdot)\) 200.p 10 no \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{200}(41,\cdot)\) 200.m 5 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{200}(43,\cdot)\) 200.k 4 no \(1\) \(1\) \(i\) \(i\) \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(-i\) \(-i\)
\(\chi_{200}(47,\cdot)\) 200.w 20 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{200}(49,\cdot)\) 200.c 2 no \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\)
\(\chi_{200}(51,\cdot)\) 200.g 2 no \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(-1\) \(1\)
\(\chi_{200}(53,\cdot)\) 200.x 20 yes \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{200}(57,\cdot)\) 200.l 4 no \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(1\) \(-i\) \(i\)
\(\chi_{200}(59,\cdot)\) 200.s 10 yes \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{200}(61,\cdot)\) 200.t 10 yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{200}(63,\cdot)\) 200.w 20 no \(1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{200}(67,\cdot)\) 200.v 20 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{200}(69,\cdot)\) 200.o 10 yes \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{200}(71,\cdot)\) 200.r 10 no \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{200}(73,\cdot)\) 200.u 20 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{200}(77,\cdot)\) 200.x 20 yes \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\)
\(\chi_{200}(79,\cdot)\) 200.p 10 no \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\)