Properties

Modulus 90
Structure \(C_{12}\times C_{2}\)
Order 24

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(90)
 
pari: g = idealstar(,90,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 24
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{12}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{90}(83,\cdot)$, $\chi_{90}(89,\cdot)$

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 7 11 13 17 19 23 29 31 37 41
\(\chi_{90}(1,\cdot)\) 90.a 1 No \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{90}(7,\cdot)\) 90.k 12 No \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{90}(11,\cdot)\) 90.h 6 No \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{90}(13,\cdot)\) 90.k 12 No \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{90}(17,\cdot)\) 90.f 4 No \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(-1\) \(i\) \(1\) \(1\) \(i\) \(-1\)
\(\chi_{90}(19,\cdot)\) 90.c 2 No \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{90}(23,\cdot)\) 90.l 12 No \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{90}(29,\cdot)\) 90.j 6 No \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{90}(31,\cdot)\) 90.e 3 No \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{90}(37,\cdot)\) 90.g 4 No \(-1\) \(1\) \(i\) \(1\) \(-i\) \(i\) \(-1\) \(-i\) \(-1\) \(1\) \(i\) \(1\)
\(\chi_{90}(41,\cdot)\) 90.h 6 No \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{90}(43,\cdot)\) 90.k 12 No \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{90}(47,\cdot)\) 90.l 12 No \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{90}(49,\cdot)\) 90.i 6 No \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{90}(53,\cdot)\) 90.f 4 No \(1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(-1\) \(-i\) \(1\) \(1\) \(-i\) \(-1\)
\(\chi_{90}(59,\cdot)\) 90.j 6 No \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{90}(61,\cdot)\) 90.e 3 No \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{90}(67,\cdot)\) 90.k 12 No \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{90}(71,\cdot)\) 90.d 2 No \(-1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(-1\)
\(\chi_{90}(73,\cdot)\) 90.g 4 No \(-1\) \(1\) \(-i\) \(1\) \(i\) \(-i\) \(-1\) \(i\) \(-1\) \(1\) \(-i\) \(1\)
\(\chi_{90}(77,\cdot)\) 90.l 12 No \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{90}(79,\cdot)\) 90.i 6 No \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{90}(83,\cdot)\) 90.l 12 No \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{90}(89,\cdot)\) 90.b 2 No \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\)