Properties

Label 8033.17
Modulus $8033$
Conductor $8033$
Order $276$
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([207,103]))
 
pari: [g,chi] = znchar(Mod(17,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(276\)
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.cd

\(\chi_{8033}(17,\cdot)\) \(\chi_{8033}(46,\cdot)\) \(\chi_{8033}(162,\cdot)\) \(\chi_{8033}(510,\cdot)\) \(\chi_{8033}(534,\cdot)\) \(\chi_{8033}(597,\cdot)\) \(\chi_{8033}(766,\cdot)\) \(\chi_{8033}(887,\cdot)\) \(\chi_{8033}(911,\cdot)\) \(\chi_{8033}(945,\cdot)\) \(\chi_{8033}(998,\cdot)\) \(\chi_{8033}(1119,\cdot)\) \(\chi_{8033}(1206,\cdot)\) \(\chi_{8033}(1235,\cdot)\) \(\chi_{8033}(1380,\cdot)\) \(\chi_{8033}(1438,\cdot)\) \(\chi_{8033}(1462,\cdot)\) \(\chi_{8033}(1496,\cdot)\) \(\chi_{8033}(1520,\cdot)\) \(\chi_{8033}(1612,\cdot)\) \(\chi_{8033}(1781,\cdot)\) \(\chi_{8033}(1815,\cdot)\) \(\chi_{8033}(1984,\cdot)\) \(\chi_{8033}(2076,\cdot)\) \(\chi_{8033}(2192,\cdot)\) \(\chi_{8033}(2274,\cdot)\) \(\chi_{8033}(2390,\cdot)\) \(\chi_{8033}(2511,\cdot)\) \(\chi_{8033}(2598,\cdot)\) \(\chi_{8033}(2627,\cdot)\) ...

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

\((5541,1944)\) → \((-i,e\left(\frac{103}{276}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{251}{276}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{241}{276}\right)\)\(e\left(\frac{143}{276}\right)\)\(e\left(\frac{29}{138}\right)\)\(e\left(\frac{19}{23}\right)\)\(e\left(\frac{113}{138}\right)\)\(e\left(\frac{133}{276}\right)\)\(e\left(\frac{25}{69}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{276})$
Fixed field: Number field defined by a degree %d polynomial (not computed)