Properties

Label 8033.883
Modulus $8033$
Conductor $8033$
Order $322$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([207,280]))
 
pari: [g,chi] = znchar(Mod(883,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(322\)
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.cj

\(\chi_{8033}(236,\cdot)\) \(\chi_{8033}(296,\cdot)\) \(\chi_{8033}(361,\cdot)\) \(\chi_{8033}(441,\cdot)\) \(\chi_{8033}(573,\cdot)\) \(\chi_{8033}(584,\cdot)\) \(\chi_{8033}(709,\cdot)\) \(\chi_{8033}(718,\cdot)\) \(\chi_{8033}(729,\cdot)\) \(\chi_{8033}(767,\cdot)\) \(\chi_{8033}(818,\cdot)\) \(\chi_{8033}(847,\cdot)\) \(\chi_{8033}(850,\cdot)\) \(\chi_{8033}(883,\cdot)\) \(\chi_{8033}(962,\cdot)\) \(\chi_{8033}(995,\cdot)\) \(\chi_{8033}(1049,\cdot)\) \(\chi_{8033}(1095,\cdot)\) \(\chi_{8033}(1124,\cdot)\) \(\chi_{8033}(1135,\cdot)\) \(\chi_{8033}(1309,\cdot)\) \(\chi_{8033}(1311,\cdot)\) \(\chi_{8033}(1372,\cdot)\) \(\chi_{8033}(1401,\cdot)\) \(\chi_{8033}(1454,\cdot)\) \(\chi_{8033}(1542,\cdot)\) \(\chi_{8033}(1588,\cdot)\) \(\chi_{8033}(1658,\cdot)\) \(\chi_{8033}(1746,\cdot)\) \(\chi_{8033}(1831,\cdot)\) ...

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

Values on generators

\((5541,1944)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{20}{23}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{151}{322}\right)\)\(e\left(\frac{223}{322}\right)\)\(e\left(\frac{151}{161}\right)\)\(e\left(\frac{2}{161}\right)\)\(e\left(\frac{26}{161}\right)\)\(e\left(\frac{136}{161}\right)\)\(e\left(\frac{131}{322}\right)\)\(e\left(\frac{62}{161}\right)\)\(e\left(\frac{155}{322}\right)\)\(e\left(\frac{51}{322}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{161})$
Fixed field: Number field defined by a degree 322 polynomial