Properties

Modulus 54
Structure \(C_{18}\)
Order 18

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(54)
 
pari: g = idealstar(,54,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 18
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{18}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{54}(29,\cdot)$

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 5 7 11 13 17 19 23 25 29 31
\(\chi_{54}(1,\cdot)\) 54.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{54}(5,\cdot)\) 54.f 18 No \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{54}(7,\cdot)\) 54.e 9 No \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{54}(11,\cdot)\) 54.f 18 No \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{54}(13,\cdot)\) 54.e 9 No \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{54}(17,\cdot)\) 54.d 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{54}(19,\cdot)\) 54.c 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{54}(23,\cdot)\) 54.f 18 No \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{54}(25,\cdot)\) 54.e 9 No \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{54}(29,\cdot)\) 54.f 18 No \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{54}(31,\cdot)\) 54.e 9 No \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{54}(35,\cdot)\) 54.d 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{54}(37,\cdot)\) 54.c 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{54}(41,\cdot)\) 54.f 18 No \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{54}(43,\cdot)\) 54.e 9 No \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{54}(47,\cdot)\) 54.f 18 No \(-1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{54}(49,\cdot)\) 54.e 9 No \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{54}(53,\cdot)\) 54.b 2 No \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(1\)