Properties

Conductor 4033
Order 27
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.dz

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[618]
 
pari: [g,chi] = znchar(Mod(618,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 27
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.dz
Orbit index = 104

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 ]
 

\(\chi_{4033}(618,\cdot)\) \(\chi_{4033}(898,\cdot)\) \(\chi_{4033}(1099,\cdot)\) \(\chi_{4033}(1432,\cdot)\) \(\chi_{4033}(1638,\cdot)\) \(\chi_{4033}(1749,\cdot)\) \(\chi_{4033}(1765,\cdot)\) \(\chi_{4033}(1860,\cdot)\) \(\chi_{4033}(1934,\cdot)\) \(\chi_{4033}(1987,\cdot)\) \(\chi_{4033}(2119,\cdot)\) \(\chi_{4033}(2378,\cdot)\) \(\chi_{4033}(2542,\cdot)\) \(\chi_{4033}(2822,\cdot)\) \(\chi_{4033}(2912,\cdot)\) \(\chi_{4033}(3319,\cdot)\) \(\chi_{4033}(3837,\cdot)\) \(\chi_{4033}(3895,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{14}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{1}{27}\right)\)
value at  e.g. 2

Related number fields

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