Properties

Conductor 2009
Order 28
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 2009.bd

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(2009)
 
sage: chi = H[1485]
 
pari: [g,chi] = znchar(Mod(1485,2009))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 28
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 = 2009.bd
Orbit index = 30

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 ]
 

\(\chi_{2009}(155,\cdot)\) \(\chi_{2009}(337,\cdot)\) \(\chi_{2009}(624,\cdot)\) \(\chi_{2009}(729,\cdot)\) \(\chi_{2009}(911,\cdot)\) \(\chi_{2009}(1016,\cdot)\) \(\chi_{2009}(1198,\cdot)\) \(\chi_{2009}(1303,\cdot)\) \(\chi_{2009}(1485,\cdot)\) \(\chi_{2009}(1590,\cdot)\) \(\chi_{2009}(1772,\cdot)\) \(\chi_{2009}(1877,\cdot)\)

Values on generators

\((493,785)\) → \((e\left(\frac{5}{7}\right),-i)\)

Values

-112345689101112
\(1\)\(1\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{1}{28}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{23}{28}\right)\)\(e\left(\frac{3}{28}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{28})\)