Properties

Modulus 44
Structure \(C_{10}\times C_{2}\)
Order 20

Learn more about

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(44)
 
pari: g = idealstar(,44,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 20
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{10}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{44}(13,\cdot)$, $\chi_{44}(23,\cdot)$

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 5 7 9 13 15 17 19 21 23
\(\chi_{44}(1,\cdot)\) 44.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{44}(3,\cdot)\) 44.h 10 Yes \(-1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(1\) \(-1\)
\(\chi_{44}(5,\cdot)\) 44.e 5 No \(1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(1\)
\(\chi_{44}(7,\cdot)\) 44.g 10 Yes \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\) \(-1\)
\(\chi_{44}(9,\cdot)\) 44.e 5 No \(1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(1\) \(1\)
\(\chi_{44}(13,\cdot)\) 44.f 10 No \(-1\) \(1\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(-1\) \(1\)
\(\chi_{44}(15,\cdot)\) 44.h 10 Yes \(-1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(1\) \(-1\)
\(\chi_{44}(17,\cdot)\) 44.f 10 No \(-1\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(1\)
\(\chi_{44}(19,\cdot)\) 44.g 10 Yes \(1\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(-1\) \(-1\)
\(\chi_{44}(21,\cdot)\) 44.d 2 No \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\)
\(\chi_{44}(23,\cdot)\) 44.b 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\)
\(\chi_{44}(25,\cdot)\) 44.e 5 No \(1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)
\(\chi_{44}(27,\cdot)\) 44.h 10 Yes \(-1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(1\) \(-1\)
\(\chi_{44}(29,\cdot)\) 44.f 10 No \(-1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(1\)
\(\chi_{44}(31,\cdot)\) 44.h 10 Yes \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(-1\)
\(\chi_{44}(35,\cdot)\) 44.g 10 Yes \(1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(-1\) \(-1\)
\(\chi_{44}(37,\cdot)\) 44.e 5 No \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)
\(\chi_{44}(39,\cdot)\) 44.g 10 Yes \(1\) \(1\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(-1\) \(-1\)
\(\chi_{44}(41,\cdot)\) 44.f 10 No \(-1\) \(1\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(-1\) \(1\)
\(\chi_{44}(43,\cdot)\) 44.c 2 Yes \(1\) \(1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\)