Properties

Conductor 4031
Order 1932
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.bu

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[2]
 
pari: [g,chi] = znchar(Mod(2,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1932
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.bu
Orbit index = 47

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 ]
 

\(\chi_{4031}(2,\cdot)\) \(\chi_{4031}(3,\cdot)\) \(\chi_{4031}(15,\cdot)\) \(\chi_{4031}(18,\cdot)\) \(\chi_{4031}(19,\cdot)\) \(\chi_{4031}(21,\cdot)\) \(\chi_{4031}(26,\cdot)\) \(\chi_{4031}(32,\cdot)\) \(\chi_{4031}(40,\cdot)\) \(\chi_{4031}(50,\cdot)\) \(\chi_{4031}(56,\cdot)\) \(\chi_{4031}(61,\cdot)\) \(\chi_{4031}(68,\cdot)\) \(\chi_{4031}(72,\cdot)\) \(\chi_{4031}(73,\cdot)\) \(\chi_{4031}(85,\cdot)\) \(\chi_{4031}(90,\cdot)\) \(\chi_{4031}(98,\cdot)\) \(\chi_{4031}(101,\cdot)\) \(\chi_{4031}(102,\cdot)\) \(\chi_{4031}(108,\cdot)\) \(\chi_{4031}(114,\cdot)\) \(\chi_{4031}(119,\cdot)\) \(\chi_{4031}(126,\cdot)\) \(\chi_{4031}(130,\cdot)\) \(\chi_{4031}(134,\cdot)\) \(\chi_{4031}(135,\cdot)\) \(\chi_{4031}(142,\cdot)\) \(\chi_{4031}(156,\cdot)\) \(\chi_{4031}(160,\cdot)\) ...

Values on generators

\((3337,697)\) → \((e\left(\frac{1}{28}\right),e\left(\frac{1}{138}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{83}{1932}\right)\)\(e\left(\frac{919}{1932}\right)\)\(e\left(\frac{83}{966}\right)\)\(e\left(\frac{395}{966}\right)\)\(e\left(\frac{167}{322}\right)\)\(e\left(\frac{382}{483}\right)\)\(e\left(\frac{83}{644}\right)\)\(e\left(\frac{919}{966}\right)\)\(e\left(\frac{291}{644}\right)\)\(e\left(\frac{857}{1932}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{1932})\)