Properties

Label 2128.601
Modulus 21282128
Conductor 10641064
Order 66
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2128, base_ring=CyclotomicField(6)) M = H._module chi = DirichletCharacter(H, M([0,3,3,5]))
 
Copy content pari:[g,chi] = znchar(Mod(601,2128))
 

Basic properties

Modulus: 21282128
Conductor: 10641064
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 66
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1064(69,)\chi_{1064}(69,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2128.ck

χ2128(601,)\chi_{2128}(601,\cdot) χ2128(825,)\chi_{2128}(825,\cdot)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: Q(ζ3)\mathbb{Q}(\zeta_3)
Fixed field: 6.6.434842601984.1

Values on generators

(799,533,913,1009)(799,533,913,1009)(1,1,1,e(56))(1,-1,-1,e\left(\frac{5}{6}\right))

First values

aa 1-1113355991111131315151717232325252727
χ2128(601,a) \chi_{ 2128 }(601, a) 1111e(56)e\left(\frac{5}{6}\right)e(13)e\left(\frac{1}{3}\right)e(23)e\left(\frac{2}{3}\right)1-1e(16)e\left(\frac{1}{6}\right)e(16)e\left(\frac{1}{6}\right)e(56)e\left(\frac{5}{6}\right)e(23)e\left(\frac{2}{3}\right)e(23)e\left(\frac{2}{3}\right)1-1
Copy content sage:chi.jacobi_sum(n)
 
χ2128(601,a)   \chi_{ 2128 }(601,a) \; at   a=\;a = e.g. 2