Properties

Label 6384.5357
Modulus 63846384
Conductor 63846384
Order 1212
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6384, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([0,9,6,4,6]))
 
Copy content pari:[g,chi] = znchar(Mod(5357,6384))
 

Basic properties

Modulus: 63846384
Conductor: 63846384
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1212
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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)
 

Galois orbit 6384.im

χ6384(2165,)\chi_{6384}(2165,\cdot) χ6384(3077,)\chi_{6384}(3077,\cdot) χ6384(5357,)\chi_{6384}(5357,\cdot) χ6384(6269,)\chi_{6384}(6269,\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(ζ12)\Q(\zeta_{12})
Fixed field: Number field defined by a degree 12 polynomial

Values on generators

(799,4789,2129,913,1009)(799,4789,2129,913,1009)(1,i,1,e(13),1)(1,-i,-1,e\left(\frac{1}{3}\right),-1)

First values

aa 1-11155111113131717232325252929313137374141
χ6384(5357,a) \chi_{ 6384 }(5357, a) 1111e(1112)e\left(\frac{11}{12}\right)e(712)e\left(\frac{7}{12}\right)i-ie(56)e\left(\frac{5}{6}\right)e(23)e\left(\frac{2}{3}\right)e(56)e\left(\frac{5}{6}\right)iie(56)e\left(\frac{5}{6}\right)e(1112)e\left(\frac{11}{12}\right)1-1
Copy content sage:chi.jacobi_sum(n)
 
χ6384(5357,a)   \chi_{ 6384 }(5357,a) \; at   a=\;a = e.g. 2