Properties

Label 8033.1984
Modulus $8033$
Conductor $8033$
Order $276$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, base_ring=CyclotomicField(276))
 
M = H._module
 
chi = DirichletCharacter(H, M([69,101]))
 
pari: [g,chi] = znchar(Mod(1984,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(276\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8033.cd

\(\chi_{8033}(17,\cdot)\) \(\chi_{8033}(46,\cdot)\) \(\chi_{8033}(162,\cdot)\) \(\chi_{8033}(510,\cdot)\) \(\chi_{8033}(534,\cdot)\) \(\chi_{8033}(597,\cdot)\) \(\chi_{8033}(766,\cdot)\) \(\chi_{8033}(887,\cdot)\) \(\chi_{8033}(911,\cdot)\) \(\chi_{8033}(945,\cdot)\) \(\chi_{8033}(998,\cdot)\) \(\chi_{8033}(1119,\cdot)\) \(\chi_{8033}(1206,\cdot)\) \(\chi_{8033}(1235,\cdot)\) \(\chi_{8033}(1380,\cdot)\) \(\chi_{8033}(1438,\cdot)\) \(\chi_{8033}(1462,\cdot)\) \(\chi_{8033}(1496,\cdot)\) \(\chi_{8033}(1520,\cdot)\) \(\chi_{8033}(1612,\cdot)\) \(\chi_{8033}(1781,\cdot)\) \(\chi_{8033}(1815,\cdot)\) \(\chi_{8033}(1984,\cdot)\) \(\chi_{8033}(2076,\cdot)\) \(\chi_{8033}(2192,\cdot)\) \(\chi_{8033}(2274,\cdot)\) \(\chi_{8033}(2390,\cdot)\) \(\chi_{8033}(2511,\cdot)\) \(\chi_{8033}(2598,\cdot)\) \(\chi_{8033}(2627,\cdot)\) ...

sage: chi.galois_orbit()
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{276})$
Fixed field: Number field defined by a degree 276 polynomial (not computed)

Values on generators

\((5541,1944)\) → \((i,e\left(\frac{101}{276}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 8033 }(1984, a) \) \(1\)\(1\)\(e\left(\frac{1}{23}\right)\)\(e\left(\frac{13}{276}\right)\)\(e\left(\frac{2}{23}\right)\)\(e\left(\frac{239}{276}\right)\)\(e\left(\frac{25}{276}\right)\)\(e\left(\frac{7}{138}\right)\)\(e\left(\frac{3}{23}\right)\)\(e\left(\frac{13}{138}\right)\)\(e\left(\frac{251}{276}\right)\)\(e\left(\frac{56}{69}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 8033 }(1984,a) \;\) at \(\;a = \) e.g. 2