Properties

Label 8033.318
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([23,21]))
 
pari: [g,chi] = znchar(Mod(318,8033))
 

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.bj

\(\chi_{8033}(318,\cdot)\) \(\chi_{8033}(1333,\cdot)\) \(\chi_{8033}(1449,\cdot)\) \(\chi_{8033}(1507,\cdot)\) \(\chi_{8033}(1855,\cdot)\) \(\chi_{8033}(2290,\cdot)\) \(\chi_{8033}(2754,\cdot)\) \(\chi_{8033}(2783,\cdot)\) \(\chi_{8033}(3160,\cdot)\) \(\chi_{8033}(3305,\cdot)\) \(\chi_{8033}(4436,\cdot)\) \(\chi_{8033}(4552,\cdot)\) \(\chi_{8033}(5045,\cdot)\) \(\chi_{8033}(5132,\cdot)\) \(\chi_{8033}(6437,\cdot)\) \(\chi_{8033}(6669,\cdot)\) \(\chi_{8033}(6756,\cdot)\) \(\chi_{8033}(7133,\cdot)\) \(\chi_{8033}(7278,\cdot)\) \(\chi_{8033}(7452,\cdot)\) \(\chi_{8033}(7858,\cdot)\) \(\chi_{8033}(8003,\cdot)\)

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

\((5541,1944)\) → \((-1,e\left(\frac{21}{46}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{15}{46}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{21}{46}\right)\)\(e\left(\frac{43}{46}\right)\)\(e\left(\frac{1}{23}\right)\)\(e\left(\frac{19}{23}\right)\)\(e\left(\frac{15}{23}\right)\)\(e\left(\frac{3}{46}\right)\)\(e\left(\frac{16}{23}\right)\)
value at e.g. 2

Related number fields

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