Properties

Conductor 4011
Order 38
Real No
Primitive Yes
Parity Odd
Orbit Label 4011.bk

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4011)
 
sage: chi = H[41]
 
pari: [g,chi] = znchar(Mod(41,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4011
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 38
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4011.bk
Orbit index = 37

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 ]
 

\(\chi_{4011}(41,\cdot)\) \(\chi_{4011}(377,\cdot)\) \(\chi_{4011}(419,\cdot)\) \(\chi_{4011}(587,\cdot)\) \(\chi_{4011}(734,\cdot)\) \(\chi_{4011}(923,\cdot)\) \(\chi_{4011}(986,\cdot)\) \(\chi_{4011}(1301,\cdot)\) \(\chi_{4011}(1994,\cdot)\) \(\chi_{4011}(2267,\cdot)\) \(\chi_{4011}(2330,\cdot)\) \(\chi_{4011}(2414,\cdot)\) \(\chi_{4011}(2477,\cdot)\) \(\chi_{4011}(2729,\cdot)\) \(\chi_{4011}(2813,\cdot)\) \(\chi_{4011}(2876,\cdot)\) \(\chi_{4011}(3317,\cdot)\) \(\chi_{4011}(3695,\cdot)\)

Values on generators

\((2675,2866,2311)\) → \((-1,-1,e\left(\frac{33}{38}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{27}{38}\right)\)\(e\left(\frac{8}{19}\right)\)\(e\left(\frac{8}{19}\right)\)\(e\left(\frac{5}{38}\right)\)\(e\left(\frac{5}{38}\right)\)\(e\left(\frac{6}{19}\right)\)\(e\left(\frac{29}{38}\right)\)\(e\left(\frac{16}{19}\right)\)\(e\left(\frac{2}{19}\right)\)\(e\left(\frac{7}{19}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{19})\)