Properties

Modulus 110
Structure \(C_{20}\times C_{2}\)
Order 40

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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(110)
 
pari: g = idealstar(,110,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 40
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{20}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{110}(13,\cdot)$, $\chi_{110}(21,\cdot)$

First 32 of 40 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 13 17 19 21 23 27 29
\(\chi_{110}(1,\cdot)\) 110.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{110}(3,\cdot)\) 110.l 20 No \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{110}(7,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{110}(9,\cdot)\) 110.j 10 No \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{110}(13,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{110}(17,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(-i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{110}(19,\cdot)\) 110.i 10 No \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{110}(21,\cdot)\) 110.d 2 No \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{110}(23,\cdot)\) 110.e 4 No \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-i\) \(-1\) \(1\) \(i\) \(-i\) \(-1\)
\(\chi_{110}(27,\cdot)\) 110.l 20 No \(-1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(-i\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{110}(29,\cdot)\) 110.i 10 No \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{110}(31,\cdot)\) 110.g 5 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{110}(37,\cdot)\) 110.l 20 No \(-1\) \(1\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(-i\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{110}(39,\cdot)\) 110.i 10 No \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{110}(41,\cdot)\) 110.h 10 No \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{110}(43,\cdot)\) 110.f 4 No \(1\) \(1\) \(i\) \(i\) \(-1\) \(-i\) \(i\) \(1\) \(-1\) \(i\) \(-i\) \(1\)
\(\chi_{110}(47,\cdot)\) 110.l 20 No \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(-i\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{110}(49,\cdot)\) 110.j 10 No \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{110}(51,\cdot)\) 110.h 10 No \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{110}(53,\cdot)\) 110.l 20 No \(-1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(i\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{110}(57,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(-i\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{110}(59,\cdot)\) 110.j 10 No \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{110}(61,\cdot)\) 110.h 10 No \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{110}(63,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(i\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{110}(67,\cdot)\) 110.e 4 No \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(i\) \(-1\) \(1\) \(-i\) \(i\) \(-1\)
\(\chi_{110}(69,\cdot)\) 110.j 10 No \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{110}(71,\cdot)\) 110.g 5 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{110}(73,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(i\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{110}(79,\cdot)\) 110.i 10 No \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(-1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{110}(81,\cdot)\) 110.g 5 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{110}(83,\cdot)\) 110.k 20 No \(1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(i\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{110}(87,\cdot)\) 110.f 4 No \(1\) \(1\) \(-i\) \(-i\) \(-1\) \(i\) \(-i\) \(1\) \(-1\) \(-i\) \(i\) \(1\)