Properties

Conductor 4031
Order 966
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.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(4031)
 
sage: chi = H[4]
 
pari: [g,chi] = znchar(Mod(4,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 966
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 = 4031.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 ]
 

\(\chi_{4031}(4,\cdot)\) \(\chi_{4031}(5,\cdot)\) \(\chi_{4031}(9,\cdot)\) \(\chi_{4031}(13,\cdot)\) \(\chi_{4031}(35,\cdot)\) \(\chi_{4031}(38,\cdot)\) \(\chi_{4031}(51,\cdot)\) \(\chi_{4031}(67,\cdot)\) \(\chi_{4031}(71,\cdot)\) \(\chi_{4031}(120,\cdot)\) \(\chi_{4031}(121,\cdot)\) \(\chi_{4031}(122,\cdot)\) \(\chi_{4031}(150,\cdot)\) \(\chi_{4031}(167,\cdot)\) \(\chi_{4031}(180,\cdot)\) \(\chi_{4031}(208,\cdot)\) \(\chi_{4031}(225,\cdot)\) \(\chi_{4031}(238,\cdot)\) \(\chi_{4031}(266,\cdot)\) \(\chi_{4031}(283,\cdot)\) \(\chi_{4031}(294,\cdot)\) \(\chi_{4031}(303,\cdot)\) \(\chi_{4031}(324,\cdot)\) \(\chi_{4031}(325,\cdot)\) \(\chi_{4031}(332,\cdot)\) \(\chi_{4031}(361,\cdot)\) \(\chi_{4031}(399,\cdot)\) \(\chi_{4031}(415,\cdot)\) \(\chi_{4031}(428,\cdot)\) \(\chi_{4031}(441,\cdot)\) ...

Values on generators

\((3337,697)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{1}{69}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{83}{966}\right)\)\(e\left(\frac{919}{966}\right)\)\(e\left(\frac{83}{483}\right)\)\(e\left(\frac{395}{483}\right)\)\(e\left(\frac{6}{161}\right)\)\(e\left(\frac{281}{483}\right)\)\(e\left(\frac{83}{322}\right)\)\(e\left(\frac{436}{483}\right)\)\(e\left(\frac{291}{322}\right)\)\(e\left(\frac{857}{966}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{483})\)