Properties

Conductor 1617
Order 42
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.bt

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(3234)
 
sage: chi = H[65]
 
pari: [g,chi] = znchar(Mod(65,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1617
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 42
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 = 3234.bt
Orbit index = 46

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 ]
 

\(\chi_{3234}(65,\cdot)\) \(\chi_{3234}(527,\cdot)\) \(\chi_{3234}(725,\cdot)\) \(\chi_{3234}(989,\cdot)\) \(\chi_{3234}(1187,\cdot)\) \(\chi_{3234}(1649,\cdot)\) \(\chi_{3234}(1913,\cdot)\) \(\chi_{3234}(2111,\cdot)\) \(\chi_{3234}(2375,\cdot)\) \(\chi_{3234}(2573,\cdot)\) \(\chi_{3234}(2837,\cdot)\) \(\chi_{3234}(3035,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((-1,e\left(\frac{10}{21}\right),-1)\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{19}{21}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{25}{42}\right)\)\(e\left(\frac{13}{21}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{5}{21}\right)\)\(e\left(\frac{1}{7}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)