Properties

Label 7800.4519
Modulus 78007800
Conductor 13001300
Order 2020
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(7800, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([10,0,0,18,5]))
 
Copy content pari:[g,chi] = znchar(Mod(4519,7800))
 

Basic properties

Modulus: 78007800
Conductor: 13001300
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 2020
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1300(619,)\chi_{1300}(619,\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 7800.ig

χ7800(1279,)\chi_{7800}(1279,\cdot) χ7800(2839,)\chi_{7800}(2839,\cdot) χ7800(2959,)\chi_{7800}(2959,\cdot) χ7800(4519,)\chi_{7800}(4519,\cdot) χ7800(5959,)\chi_{7800}(5959,\cdot) χ7800(6079,)\chi_{7800}(6079,\cdot) χ7800(7519,)\chi_{7800}(7519,\cdot) χ7800(7639,)\chi_{7800}(7639,\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(ζ20)\Q(\zeta_{20})
Fixed field: 20.20.31241389779108128051757812500000000000000000000.1

Values on generators

(1951,3901,5201,7177,4201)(1951,3901,5201,7177,4201)(1,1,1,e(910),i)(-1,1,1,e\left(\frac{9}{10}\right),i)

First values

aa 1-11177111117171919232329293131373741414343
χ7800(4519,a) \chi_{ 7800 }(4519, a) 1111i-ie(1320)e\left(\frac{13}{20}\right)e(15)e\left(\frac{1}{5}\right)e(1920)e\left(\frac{19}{20}\right)e(910)e\left(\frac{9}{10}\right)e(45)e\left(\frac{4}{5}\right)e(1920)e\left(\frac{19}{20}\right)e(1720)e\left(\frac{17}{20}\right)e(1720)e\left(\frac{17}{20}\right)1-1
Copy content sage:chi.jacobi_sum(n)
 
χ7800(4519,a)   \chi_{ 7800 }(4519,a) \; at   a=\;a = e.g. 2