Properties

Label 8033.9
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([345,350]))
 
pari: [g,chi] = znchar(Mod(9,8033))
 

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.cu

\(\chi_{8033}(9,\cdot)\) \(\chi_{8033}(67,\cdot)\) \(\chi_{8033}(71,\cdot)\) \(\chi_{8033}(91,\cdot)\) \(\chi_{8033}(100,\cdot)\) \(\chi_{8033}(154,\cdot)\) \(\chi_{8033}(207,\cdot)\) \(\chi_{8033}(237,\cdot)\) \(\chi_{8033}(238,\cdot)\) \(\chi_{8033}(241,\cdot)\) \(\chi_{8033}(265,\cdot)\) \(\chi_{8033}(270,\cdot)\) \(\chi_{8033}(325,\cdot)\) \(\chi_{8033}(332,\cdot)\) \(\chi_{8033}(448,\cdot)\) \(\chi_{8033}(468,\cdot)\) \(\chi_{8033}(515,\cdot)\) \(\chi_{8033}(557,\cdot)\) \(\chi_{8033}(564,\cdot)\) \(\chi_{8033}(602,\cdot)\) \(\chi_{8033}(642,\cdot)\) \(\chi_{8033}(644,\cdot)\) \(\chi_{8033}(701,\cdot)\) \(\chi_{8033}(792,\cdot)\) \(\chi_{8033}(834,\cdot)\) \(\chi_{8033}(854,\cdot)\) \(\chi_{8033}(879,\cdot)\) \(\chi_{8033}(912,\cdot)\) \(\chi_{8033}(921,\cdot)\) \(\chi_{8033}(1019,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{25}{69}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{199}{322}\right)\)\(e\left(\frac{871}{966}\right)\)\(e\left(\frac{38}{161}\right)\)\(e\left(\frac{106}{483}\right)\)\(e\left(\frac{251}{483}\right)\)\(e\left(\frac{124}{483}\right)\)\(e\left(\frac{275}{322}\right)\)\(e\left(\frac{388}{483}\right)\)\(e\left(\frac{809}{966}\right)\)\(e\left(\frac{449}{966}\right)\)
value at e.g. 2

Related number fields

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