Properties

Conductor 49
Order 21
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3234.bh

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[331]
 
pari: [g,chi] = znchar(Mod(331,3234))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 49
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 21
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.bh
Orbit index = 34

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 ]
 

\(\chi_{3234}(331,\cdot)\) \(\chi_{3234}(529,\cdot)\) \(\chi_{3234}(793,\cdot)\) \(\chi_{3234}(991,\cdot)\) \(\chi_{3234}(1453,\cdot)\) \(\chi_{3234}(1717,\cdot)\) \(\chi_{3234}(1915,\cdot)\) \(\chi_{3234}(2179,\cdot)\) \(\chi_{3234}(2377,\cdot)\) \(\chi_{3234}(2641,\cdot)\) \(\chi_{3234}(2839,\cdot)\) \(\chi_{3234}(3103,\cdot)\)

Values on generators

\((1079,199,2059)\) → \((1,e\left(\frac{16}{21}\right),1)\)

Values

-115131719232529313741
\(1\)\(1\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{3}{7}\right)\)
value at  e.g. 2

Related number fields

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