Properties

Conductor 27
Order 9
Real no
Primitive no
Minimal yes
Parity even
Orbit label 1350.l

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(1350)
 
sage: chi = H[151]
 
pari: [g,chi] = znchar(Mod(151,1350))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 27
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 9
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 1350.l
Orbit index = 12

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 ]
 

\(\chi_{1350}(151,\cdot)\) \(\chi_{1350}(301,\cdot)\) \(\chi_{1350}(601,\cdot)\) \(\chi_{1350}(751,\cdot)\) \(\chi_{1350}(1051,\cdot)\) \(\chi_{1350}(1201,\cdot)\)

Values on generators

\((1001,1027)\) → \((e\left(\frac{2}{9}\right),1)\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{9}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{9})\)