Properties

Label 4033.509
Modulus $4033$
Conductor $4033$
Order $54$
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(4033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([51,28]))
 
pari: [g,chi] = znchar(Mod(509,4033))
 

Basic properties

Modulus: \(4033\)
Conductor: \(4033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(54\)
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 4033.gy

\(\chi_{4033}(25,\cdot)\) \(\chi_{4033}(189,\cdot)\) \(\chi_{4033}(299,\cdot)\) \(\chi_{4033}(484,\cdot)\) \(\chi_{4033}(509,\cdot)\) \(\chi_{4033}(580,\cdot)\) \(\chi_{4033}(659,\cdot)\) \(\chi_{4033}(743,\cdot)\) \(\chi_{4033}(770,\cdot)\) \(\chi_{4033}(1168,\cdot)\) \(\chi_{4033}(1225,\cdot)\) \(\chi_{4033}(1323,\cdot)\) \(\chi_{4033}(1357,\cdot)\) \(\chi_{4033}(1656,\cdot)\) \(\chi_{4033}(1732,\cdot)\) \(\chi_{4033}(1965,\cdot)\) \(\chi_{4033}(2093,\cdot)\) \(\chi_{4033}(3388,\cdot)\)

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

\((1963,2295)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{14}{27}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(-1\)\(e\left(\frac{14}{27}\right)\)\(1\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{1}{54}\right)\)\(e\left(\frac{26}{27}\right)\)\(-1\)\(e\left(\frac{1}{27}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{10}{27}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{27})\)
Fixed field: Number field defined by a degree 54 polynomial