Properties

Conductor 2009
Order 28
Real No
Primitive No
Parity Even
Orbit Label 6027.cf

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(6027)
 
sage: chi = H[337]
 
pari: [g,chi] = znchar(Mod(337,6027))
 

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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.cf
Orbit index = 58

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 ]
 

\(\chi_{6027}(337,\cdot)\) \(\chi_{6027}(1198,\cdot)\) \(\chi_{6027}(1303,\cdot)\) \(\chi_{6027}(2164,\cdot)\) \(\chi_{6027}(2920,\cdot)\) \(\chi_{6027}(3025,\cdot)\) \(\chi_{6027}(3781,\cdot)\) \(\chi_{6027}(3886,\cdot)\) \(\chi_{6027}(4642,\cdot)\) \(\chi_{6027}(4747,\cdot)\) \(\chi_{6027}(5503,\cdot)\) \(\chi_{6027}(5608,\cdot)\)

Inducing primitive character

\(\chi_{2009}(337,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{1}{7}\right),-i)\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{9}{28}\right)\)\(-i\)
value at  e.g. 2

Related number fields

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