Properties

Conductor 4031
Order 46
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.z

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[57]
 
pari: [g,chi] = znchar(Mod(57,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 46
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.z
Orbit index = 26

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 ]
 

\(\chi_{4031}(57,\cdot)\) \(\chi_{4031}(173,\cdot)\) \(\chi_{4031}(202,\cdot)\) \(\chi_{4031}(608,\cdot)\) \(\chi_{4031}(811,\cdot)\) \(\chi_{4031}(840,\cdot)\) \(\chi_{4031}(898,\cdot)\) \(\chi_{4031}(1565,\cdot)\) \(\chi_{4031}(1594,\cdot)\) \(\chi_{4031}(1768,\cdot)\) \(\chi_{4031}(1797,\cdot)\) \(\chi_{4031}(1884,\cdot)\) \(\chi_{4031}(1913,\cdot)\) \(\chi_{4031}(2058,\cdot)\) \(\chi_{4031}(2696,\cdot)\) \(\chi_{4031}(3044,\cdot)\) \(\chi_{4031}(3102,\cdot)\) \(\chi_{4031}(3189,\cdot)\) \(\chi_{4031}(3276,\cdot)\) \(\chi_{4031}(3566,\cdot)\) \(\chi_{4031}(3798,\cdot)\) \(\chi_{4031}(3972,\cdot)\)

Values on generators

\((3337,697)\) → \((-1,e\left(\frac{17}{23}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{11}{46}\right)\)\(e\left(\frac{37}{46}\right)\)\(e\left(\frac{11}{23}\right)\)\(e\left(\frac{13}{23}\right)\)\(e\left(\frac{1}{23}\right)\)\(e\left(\frac{22}{23}\right)\)\(e\left(\frac{33}{46}\right)\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{37}{46}\right)\)\(e\left(\frac{31}{46}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{23})\)