Properties

Label 7800.961
Modulus 78007800
Conductor 325325
Order 1010
Real no
Primitive no
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(7800, base_ring=CyclotomicField(10)) M = H._module chi = DirichletCharacter(H, M([0,0,0,8,5]))
 
Copy content pari:[g,chi] = znchar(Mod(961,7800))
 

Basic properties

Modulus: 78007800
Conductor: 325325
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1010
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ325(311,)\chi_{325}(311,\cdot)
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 7800.et

χ7800(961,)\chi_{7800}(961,\cdot) χ7800(2521,)\chi_{7800}(2521,\cdot) χ7800(4081,)\chi_{7800}(4081,\cdot) χ7800(5641,)\chi_{7800}(5641,\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(ζ5)\Q(\zeta_{5})
Fixed field: 10.10.56654815673828125.1

Values on generators

(1951,3901,5201,7177,4201)(1951,3901,5201,7177,4201)(1,1,1,e(45),1)(1,1,1,e\left(\frac{4}{5}\right),-1)

First values

aa 1-11177111117171919232329293131373741414343
χ7800(961,a) \chi_{ 7800 }(961, a) 11111-1e(310)e\left(\frac{3}{10}\right)e(25)e\left(\frac{2}{5}\right)e(910)e\left(\frac{9}{10}\right)e(45)e\left(\frac{4}{5}\right)e(35)e\left(\frac{3}{5}\right)e(910)e\left(\frac{9}{10}\right)e(710)e\left(\frac{7}{10}\right)e(710)e\left(\frac{7}{10}\right)11
Copy content sage:chi.jacobi_sum(n)
 
χ7800(961,a)   \chi_{ 7800 }(961,a) \; at   a=\;a = e.g. 2