Properties

Label 2600.cs
Modulus 26002600
Conductor 200200
Order 1010
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2600, base_ring=CyclotomicField(10)) M = H._module chi = DirichletCharacter(H, M([0,5,8,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(261,2600)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 26002600
Conductor: 200200
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 200.t
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)
 

Related number fields

Field of values: Q(ζ5)\Q(\zeta_{5})
Fixed field: 10.10.5000000000000000.1

Characters in Galois orbit

Character 1-1 11 33 77 99 1111 1717 1919 2121 2323 2727 2929
χ2600(261,)\chi_{2600}(261,\cdot) 11 11 e(110)e\left(\frac{1}{10}\right) 11 e(15)e\left(\frac{1}{5}\right) e(310)e\left(\frac{3}{10}\right) e(25)e\left(\frac{2}{5}\right) e(910)e\left(\frac{9}{10}\right) e(110)e\left(\frac{1}{10}\right) e(45)e\left(\frac{4}{5}\right) e(310)e\left(\frac{3}{10}\right) e(110)e\left(\frac{1}{10}\right)
χ2600(781,)\chi_{2600}(781,\cdot) 11 11 e(310)e\left(\frac{3}{10}\right) 11 e(35)e\left(\frac{3}{5}\right) e(910)e\left(\frac{9}{10}\right) e(15)e\left(\frac{1}{5}\right) e(710)e\left(\frac{7}{10}\right) e(310)e\left(\frac{3}{10}\right) e(25)e\left(\frac{2}{5}\right) e(910)e\left(\frac{9}{10}\right) e(310)e\left(\frac{3}{10}\right)
χ2600(1821,)\chi_{2600}(1821,\cdot) 11 11 e(710)e\left(\frac{7}{10}\right) 11 e(25)e\left(\frac{2}{5}\right) e(110)e\left(\frac{1}{10}\right) e(45)e\left(\frac{4}{5}\right) e(310)e\left(\frac{3}{10}\right) e(710)e\left(\frac{7}{10}\right) e(35)e\left(\frac{3}{5}\right) e(110)e\left(\frac{1}{10}\right) e(710)e\left(\frac{7}{10}\right)
χ2600(2341,)\chi_{2600}(2341,\cdot) 11 11 e(910)e\left(\frac{9}{10}\right) 11 e(45)e\left(\frac{4}{5}\right) e(710)e\left(\frac{7}{10}\right) e(35)e\left(\frac{3}{5}\right) e(110)e\left(\frac{1}{10}\right) e(910)e\left(\frac{9}{10}\right) e(15)e\left(\frac{1}{5}\right) e(710)e\left(\frac{7}{10}\right) e(910)e\left(\frac{9}{10}\right)