Properties

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

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[138]
 
pari: [g,chi] = znchar(Mod(138,4033))
 

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.he
Orbit index = 187

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 ]
 

\(\chi_{4033}(138,\cdot)\) \(\chi_{4033}(196,\cdot)\) \(\chi_{4033}(714,\cdot)\) \(\chi_{4033}(1121,\cdot)\) \(\chi_{4033}(1211,\cdot)\) \(\chi_{4033}(1491,\cdot)\) \(\chi_{4033}(1655,\cdot)\) \(\chi_{4033}(1914,\cdot)\) \(\chi_{4033}(2046,\cdot)\) \(\chi_{4033}(2099,\cdot)\) \(\chi_{4033}(2173,\cdot)\) \(\chi_{4033}(2268,\cdot)\) \(\chi_{4033}(2284,\cdot)\) \(\chi_{4033}(2395,\cdot)\) \(\chi_{4033}(2601,\cdot)\) \(\chi_{4033}(2934,\cdot)\) \(\chi_{4033}(3135,\cdot)\) \(\chi_{4033}(3415,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{17}{54}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{19}{27}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{41}{54}\right)\)\(e\left(\frac{22}{27}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{47}{54}\right)\)\(e\left(\frac{7}{54}\right)\)
value at  e.g. 2

Related number fields

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