Properties

Label 8033.22
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([897,539]))
 
pari: [g,chi] = znchar(Mod(22,8033))
 

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.cv

\(\chi_{8033}(22,\cdot)\) \(\chi_{8033}(34,\cdot)\) \(\chi_{8033}(62,\cdot)\) \(\chi_{8033}(63,\cdot)\) \(\chi_{8033}(92,\cdot)\) \(\chi_{8033}(121,\cdot)\) \(\chi_{8033}(187,\cdot)\) \(\chi_{8033}(196,\cdot)\) \(\chi_{8033}(254,\cdot)\) \(\chi_{8033}(267,\cdot)\) \(\chi_{8033}(274,\cdot)\) \(\chi_{8033}(299,\cdot)\) \(\chi_{8033}(324,\cdot)\) \(\chi_{8033}(352,\cdot)\) \(\chi_{8033}(383,\cdot)\) \(\chi_{8033}(410,\cdot)\) \(\chi_{8033}(469,\cdot)\) \(\chi_{8033}(473,\cdot)\) \(\chi_{8033}(497,\cdot)\) \(\chi_{8033}(499,\cdot)\) \(\chi_{8033}(506,\cdot)\) \(\chi_{8033}(526,\cdot)\) \(\chi_{8033}(531,\cdot)\) \(\chi_{8033}(544,\cdot)\) \(\chi_{8033}(593,\cdot)\) \(\chi_{8033}(643,\cdot)\) \(\chi_{8033}(660,\cdot)\) \(\chi_{8033}(731,\cdot)\) \(\chi_{8033}(760,\cdot)\) \(\chi_{8033}(776,\cdot)\) ...

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

\((5541,1944)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{77}{138}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{153}{161}\right)\)\(e\left(\frac{523}{966}\right)\)\(e\left(\frac{145}{161}\right)\)\(e\left(\frac{953}{966}\right)\)\(e\left(\frac{475}{966}\right)\)\(e\left(\frac{202}{483}\right)\)\(e\left(\frac{137}{161}\right)\)\(e\left(\frac{40}{483}\right)\)\(e\left(\frac{905}{966}\right)\)\(e\left(\frac{58}{483}\right)\)
value at e.g. 2

Related number fields

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