Properties

Label 475.t
Modulus $475$
Conductor $95$
Order $18$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(18)) M = H._module chi = DirichletCharacter(H, M([9,17])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(124,475)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(475\)
Conductor: \(95\)
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 95.o
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: 18.0.10703880581610941769412109375.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(11\) \(12\) \(13\)
\(\chi_{475}(124,\cdot)\) \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{475}(174,\cdot)\) \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{475}(224,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{475}(249,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{475}(299,\cdot)\) \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{475}(374,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{9}\right)\)