Properties

Conductor 4033
Order 18
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.cz

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4033)
 
sage: chi = H[300]
 
pari: [g,chi] = znchar(Mod(300,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 18
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4033.cz
Orbit index = 78

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4033}(300,\cdot)\) \(\chi_{4033}(1510,\cdot)\) \(\chi_{4033}(2223,\cdot)\) \(\chi_{4033}(2578,\cdot)\) \(\chi_{4033}(2729,\cdot)\) \(\chi_{4033}(2759,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{17}{18}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{1}{18}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{9})\)