Properties

Conductor 4033
Order 54
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.hq

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[206]
 
pari: [g,chi] = znchar(Mod(206,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 54
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.hq
Orbit index = 199

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 ]
 

\(\chi_{4033}(206,\cdot)\) \(\chi_{4033}(657,\cdot)\) \(\chi_{4033}(881,\cdot)\) \(\chi_{4033}(1224,\cdot)\) \(\chi_{4033}(1779,\cdot)\) \(\chi_{4033}(1817,\cdot)\) \(\chi_{4033}(2556,\cdot)\) \(\chi_{4033}(2631,\cdot)\) \(\chi_{4033}(2694,\cdot)\) \(\chi_{4033}(2914,\cdot)\) \(\chi_{4033}(2964,\cdot)\) \(\chi_{4033}(3133,\cdot)\) \(\chi_{4033}(3166,\cdot)\) \(\chi_{4033}(3277,\cdot)\) \(\chi_{4033}(3318,\cdot)\) \(\chi_{4033}(3577,\cdot)\) \(\chi_{4033}(3619,\cdot)\) \(\chi_{4033}(3950,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{1}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{22}{27}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{47}{54}\right)\)\(e\left(\frac{29}{54}\right)\)\(e\left(\frac{1}{27}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{11}{27}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{27})\)