Properties

Modulus $2200$
Structure \(C_{2}\times C_{2}\times C_{10}\times C_{20}\)
Order $800$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2200)
 
pari: g = idealstar(,2200,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 800
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{10}\times C_{20}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2200}(551,\cdot)$, $\chi_{2200}(1101,\cdot)$, $\chi_{2200}(177,\cdot)$, $\chi_{2200}(1201,\cdot)$

First 32 of 800 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\) \(29\)
\(\chi_{2200}(1,\cdot)\) 2200.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2200}(3,\cdot)\) 2200.gd 20 yes \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2200}(7,\cdot)\) 2200.ft 20 no \(-1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2200}(9,\cdot)\) 2200.dx 10 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{2200}(13,\cdot)\) 2200.fv 20 yes \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2200}(17,\cdot)\) 2200.et 20 no \(1\) \(1\) \(-i\) \(e\left(\frac{11}{20}\right)\) \(-1\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(i\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{2200}(19,\cdot)\) 2200.dz 10 yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2200}(21,\cdot)\) 2200.cw 10 yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{2200}(23,\cdot)\) 2200.fg 20 no \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(i\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2200}(27,\cdot)\) 2200.gd 20 yes \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2200}(29,\cdot)\) 2200.bv 10 yes \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{2200}(31,\cdot)\) 2200.dq 10 no \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\)
\(\chi_{2200}(37,\cdot)\) 2200.es 20 yes \(-1\) \(1\) \(i\) \(e\left(\frac{13}{20}\right)\) \(-1\) \(i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(-i\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2200}(39,\cdot)\) 2200.cj 10 no \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{2200}(41,\cdot)\) 2200.co 10 no \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\)
\(\chi_{2200}(43,\cdot)\) 2200.w 4 no \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(1\) \(-i\) \(-i\) \(-1\)
\(\chi_{2200}(47,\cdot)\) 2200.fh 20 no \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(i\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{2200}(49,\cdot)\) 2200.ec 10 no \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2200}(51,\cdot)\) 2200.bt 10 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(-1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2200}(53,\cdot)\) 2200.es 20 yes \(-1\) \(1\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(-1\) \(-i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(i\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2200}(57,\cdot)\) 2200.fc 20 no \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{2200}(59,\cdot)\) 2200.bh 10 yes \(-1\) \(1\) \(-1\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{2200}(61,\cdot)\) 2200.dp 10 yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{2200}(63,\cdot)\) 2200.fb 20 no \(-1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(1\)
\(\chi_{2200}(67,\cdot)\) 2200.gc 20 no \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{2200}(69,\cdot)\) 2200.ci 10 yes \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{2200}(71,\cdot)\) 2200.dq 10 no \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\)
\(\chi_{2200}(73,\cdot)\) 2200.gk 20 no \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(1\)
\(\chi_{2200}(79,\cdot)\) 2200.eo 10 no \(1\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{2200}(81,\cdot)\) 2200.bb 5 no \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{2200}(83,\cdot)\) 2200.eq 20 yes \(-1\) \(1\) \(i\) \(e\left(\frac{11}{20}\right)\) \(-1\) \(i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{20}\right)\) \(-i\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{2200}(87,\cdot)\) 2200.ge 20 no \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(i\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
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