Properties

Label 1640.1399
Modulus 16401640
Conductor 820820
Order 2020
Real no
Primitive no
Minimal no
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1640, base_ring=CyclotomicField(20)) M = H._module chi = DirichletCharacter(H, M([10,0,10,11]))
 
Copy content pari:[g,chi] = znchar(Mod(1399,1640))
 

Basic properties

Modulus: 16401640
Conductor: 820820
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 χ820(579,)\chi_{820}(579,\cdot)
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)
 

Galois orbit 1640.dh

χ1640(39,)\chi_{1640}(39,\cdot) χ1640(159,)\chi_{1640}(159,\cdot) χ1640(279,)\chi_{1640}(279,\cdot) χ1640(759,)\chi_{1640}(759,\cdot) χ1640(799,)\chi_{1640}(799,\cdot) χ1640(1279,)\chi_{1640}(1279,\cdot) χ1640(1399,)\chi_{1640}(1399,\cdot) χ1640(1519,)\chi_{1640}(1519,\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: 20.0.44998002377408544344171356675696640000000000.1

Values on generators

(1231,821,657,1441)(1231,821,657,1441)(1,1,1,e(1120))(-1,1,-1,e\left(\frac{11}{20}\right))

First values

aa 1-1113377991111131317171919212123232727
χ1640(1399,a) \chi_{ 1640 }(1399, a) 1-111iie(920)e\left(\frac{9}{20}\right)1-1e(320)e\left(\frac{3}{20}\right)e(1120)e\left(\frac{11}{20}\right)e(1320)e\left(\frac{13}{20}\right)e(920)e\left(\frac{9}{20}\right)e(710)e\left(\frac{7}{10}\right)e(45)e\left(\frac{4}{5}\right)i-i
Copy content sage:chi.jacobi_sum(n)
 
χ1640(1399,a)   \chi_{ 1640 }(1399,a) \; at   a=\;a = e.g. 2