Properties

Conductor 4033
Order 36
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.ew

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[459]
 
pari: [g,chi] = znchar(Mod(459,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 36
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.ew
Orbit index = 127

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 ]
 

\(\chi_{4033}(459,\cdot)\) \(\chi_{4033}(782,\cdot)\) \(\chi_{4033}(1197,\cdot)\) \(\chi_{4033}(1667,\cdot)\) \(\chi_{4033}(1907,\cdot)\) \(\chi_{4033}(1979,\cdot)\) \(\chi_{4033}(2054,\cdot)\) \(\chi_{4033}(2126,\cdot)\) \(\chi_{4033}(2366,\cdot)\) \(\chi_{4033}(2836,\cdot)\) \(\chi_{4033}(3251,\cdot)\) \(\chi_{4033}(3574,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{11}{36}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{19}{36}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{11}{36}\right)\)\(e\left(\frac{7}{36}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{36})\)