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Properties

Label 9576.uf
Modulus $9576$
Conductor $1197$
Order $18$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9576, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([0,0,12,9,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(97,9576)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(9576\)
Conductor: \(1197\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(18\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 1197.gg
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: Number field defined by a degree 18 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{9576}(97,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{9576}(1105,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{9576}(1777,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{9576}(2617,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{9576}(4801,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{9576}(6817,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{9}\right)\)