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Properties

Label 891.f
Modulus 891891
Conductor 1111
Order 55
Real no
Primitive no
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,4]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(82,891))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 891891
Conductor: 1111
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 55
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 11.c
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ5)\Q(\zeta_{5})
Fixed field: Q(ζ11)+\Q(\zeta_{11})^+

Characters in Galois orbit

Character −1-1 11 22 44 55 77 88 1010 1313 1414 1616 1717
χ891(82,⋅)\chi_{891}(82,\cdot) 11 11 e(25)e\left(\frac{2}{5}\right) e(45)e\left(\frac{4}{5}\right) e(35)e\left(\frac{3}{5}\right) e(45)e\left(\frac{4}{5}\right) e(15)e\left(\frac{1}{5}\right) 11 e(25)e\left(\frac{2}{5}\right) e(15)e\left(\frac{1}{5}\right) e(35)e\left(\frac{3}{5}\right) e(35)e\left(\frac{3}{5}\right)
χ891(163,⋅)\chi_{891}(163,\cdot) 11 11 e(35)e\left(\frac{3}{5}\right) e(15)e\left(\frac{1}{5}\right) e(25)e\left(\frac{2}{5}\right) e(15)e\left(\frac{1}{5}\right) e(45)e\left(\frac{4}{5}\right) 11 e(35)e\left(\frac{3}{5}\right) e(45)e\left(\frac{4}{5}\right) e(25)e\left(\frac{2}{5}\right) e(25)e\left(\frac{2}{5}\right)
χ891(487,⋅)\chi_{891}(487,\cdot) 11 11 e(45)e\left(\frac{4}{5}\right) e(35)e\left(\frac{3}{5}\right) e(15)e\left(\frac{1}{5}\right) e(35)e\left(\frac{3}{5}\right) e(25)e\left(\frac{2}{5}\right) 11 e(45)e\left(\frac{4}{5}\right) e(25)e\left(\frac{2}{5}\right) e(15)e\left(\frac{1}{5}\right) e(15)e\left(\frac{1}{5}\right)
χ891(730,⋅)\chi_{891}(730,\cdot) 11 11 e(15)e\left(\frac{1}{5}\right) e(25)e\left(\frac{2}{5}\right) e(45)e\left(\frac{4}{5}\right) e(25)e\left(\frac{2}{5}\right) e(35)e\left(\frac{3}{5}\right) 11 e(15)e\left(\frac{1}{5}\right) e(35)e\left(\frac{3}{5}\right) e(45)e\left(\frac{4}{5}\right) e(45)e\left(\frac{4}{5}\right)