Properties

Label 8033.7
Modulus $8033$
Conductor $8033$
Order $966$
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([414,77]))
 
pari: [g,chi] = znchar(Mod(7,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(966\)
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.ct

\(\chi_{8033}(7,\cdot)\) \(\chi_{8033}(25,\cdot)\) \(\chi_{8033}(36,\cdot)\) \(\chi_{8033}(83,\cdot)\) \(\chi_{8033}(112,\cdot)\) \(\chi_{8033}(123,\cdot)\) \(\chi_{8033}(141,\cdot)\) \(\chi_{8033}(198,\cdot)\) \(\chi_{8033}(210,\cdot)\) \(\chi_{8033}(228,\cdot)\) \(\chi_{8033}(268,\cdot)\) \(\chi_{8033}(284,\cdot)\) \(\chi_{8033}(306,\cdot)\) \(\chi_{8033}(313,\cdot)\) \(\chi_{8033}(339,\cdot)\) \(\chi_{8033}(364,\cdot)\) \(\chi_{8033}(400,\cdot)\) \(\chi_{8033}(487,\cdot)\) \(\chi_{8033}(545,\cdot)\) \(\chi_{8033}(576,\cdot)\) \(\chi_{8033}(616,\cdot)\) \(\chi_{8033}(629,\cdot)\) \(\chi_{8033}(687,\cdot)\) \(\chi_{8033}(741,\cdot)\) \(\chi_{8033}(750,\cdot)\) \(\chi_{8033}(774,\cdot)\) \(\chi_{8033}(803,\cdot)\) \(\chi_{8033}(808,\cdot)\) \(\chi_{8033}(828,\cdot)\) \(\chi_{8033}(865,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{11}{138}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{47}{322}\right)\)\(e\left(\frac{62}{483}\right)\)\(e\left(\frac{47}{161}\right)\)\(e\left(\frac{491}{966}\right)\)\(e\left(\frac{265}{966}\right)\)\(e\left(\frac{433}{483}\right)\)\(e\left(\frac{141}{322}\right)\)\(e\left(\frac{124}{483}\right)\)\(e\left(\frac{316}{483}\right)\)\(e\left(\frac{263}{966}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{483})$
Fixed field: Number field defined by a degree 966 polynomial