Properties

Conductor 139
Order 23
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4031.r

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[175]
 
pari: [g,chi] = znchar(Mod(175,4031))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 139
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 23
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 = 4031.r
Orbit index = 18

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 ]
 

\(\chi_{4031}(175,\cdot)\) \(\chi_{4031}(204,\cdot)\) \(\chi_{4031}(378,\cdot)\) \(\chi_{4031}(407,\cdot)\) \(\chi_{4031}(494,\cdot)\) \(\chi_{4031}(523,\cdot)\) \(\chi_{4031}(668,\cdot)\) \(\chi_{4031}(1306,\cdot)\) \(\chi_{4031}(1654,\cdot)\) \(\chi_{4031}(1712,\cdot)\) \(\chi_{4031}(1799,\cdot)\) \(\chi_{4031}(1886,\cdot)\) \(\chi_{4031}(2176,\cdot)\) \(\chi_{4031}(2408,\cdot)\) \(\chi_{4031}(2582,\cdot)\) \(\chi_{4031}(2698,\cdot)\) \(\chi_{4031}(2814,\cdot)\) \(\chi_{4031}(2843,\cdot)\) \(\chi_{4031}(3249,\cdot)\) \(\chi_{4031}(3452,\cdot)\) \(\chi_{4031}(3481,\cdot)\) \(\chi_{4031}(3539,\cdot)\)

Values on generators

\((3337,697)\) → \((1,e\left(\frac{14}{23}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{14}{23}\right)\)\(e\left(\frac{22}{23}\right)\)\(e\left(\frac{5}{23}\right)\)\(e\left(\frac{8}{23}\right)\)\(e\left(\frac{13}{23}\right)\)\(e\left(\frac{10}{23}\right)\)\(e\left(\frac{19}{23}\right)\)\(e\left(\frac{21}{23}\right)\)\(e\left(\frac{22}{23}\right)\)\(e\left(\frac{6}{23}\right)\)
value at  e.g. 2

Related number fields

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