Properties

Conductor 4031
Order 28
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4031.s

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[416]
 
pari: [g,chi] = znchar(Mod(416,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4031
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 28
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.s
Orbit index = 19

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 ]
 

\(\chi_{4031}(416,\cdot)\) \(\chi_{4031}(694,\cdot)\) \(\chi_{4031}(833,\cdot)\) \(\chi_{4031}(972,\cdot)\) \(\chi_{4031}(1250,\cdot)\) \(\chi_{4031}(1389,\cdot)\) \(\chi_{4031}(1667,\cdot)\) \(\chi_{4031}(1806,\cdot)\) \(\chi_{4031}(1945,\cdot)\) \(\chi_{4031}(2223,\cdot)\) \(\chi_{4031}(2918,\cdot)\) \(\chi_{4031}(3752,\cdot)\)

Values on generators

\((3337,697)\) → \((e\left(\frac{23}{28}\right),-1)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{13}{14}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{11}{28}\right)\)\(e\left(\frac{15}{28}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{28})\)