Properties

Label 8033.434
Modulus $8033$
Conductor $8033$
Order $46$
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([23,36]))
 
pari: [g,chi] = znchar(Mod(434,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(46\)
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.bl

\(\chi_{8033}(434,\cdot)\) \(\chi_{8033}(550,\cdot)\) \(\chi_{8033}(1681,\cdot)\) \(\chi_{8033}(1826,\cdot)\) \(\chi_{8033}(2203,\cdot)\) \(\chi_{8033}(2232,\cdot)\) \(\chi_{8033}(2696,\cdot)\) \(\chi_{8033}(3131,\cdot)\) \(\chi_{8033}(3479,\cdot)\) \(\chi_{8033}(3537,\cdot)\) \(\chi_{8033}(3653,\cdot)\) \(\chi_{8033}(4668,\cdot)\) \(\chi_{8033}(5016,\cdot)\) \(\chi_{8033}(5161,\cdot)\) \(\chi_{8033}(5567,\cdot)\) \(\chi_{8033}(5741,\cdot)\) \(\chi_{8033}(5886,\cdot)\) \(\chi_{8033}(6263,\cdot)\) \(\chi_{8033}(6350,\cdot)\) \(\chi_{8033}(6582,\cdot)\) \(\chi_{8033}(7887,\cdot)\) \(\chi_{8033}(7974,\cdot)\)

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

\((5541,1944)\) → \((-1,e\left(\frac{18}{23}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{25}{46}\right)\)\(e\left(\frac{29}{46}\right)\)\(e\left(\frac{2}{23}\right)\)\(e\left(\frac{18}{23}\right)\)\(e\left(\frac{4}{23}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{29}{46}\right)\)\(e\left(\frac{6}{23}\right)\)\(e\left(\frac{15}{46}\right)\)\(e\left(\frac{45}{46}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{23})\)
Fixed field: Number field defined by a degree 46 polynomial