Properties

Label 4080.hm
Modulus $4080$
Conductor $4080$
Order $8$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4080, base_ring=CyclotomicField(8))
 
M = H._module
 
chi = DirichletCharacter(H, M([4,6,4,6,3]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(83,4080))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4080\)
Conductor: \(4080\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(8\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{8})\)
Fixed field: 8.0.2178248377171968000000.2

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(11\) \(13\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{4080}(83,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{4080}(563,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{4080}(587,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\)
\(\chi_{4080}(2507,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\)