Properties

Modulus 4000
Conductor 400
Order 20
Real no
Primitive no
Minimal no
Parity odd
Orbit label 4000.bk

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4000)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,15,9]))
 
pari: [g,chi] = znchar(Mod(457,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4000
Conductor = 400
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 20
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4000.bk
Orbit index = 37

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4000}(457,\cdot)\) \(\chi_{4000}(793,\cdot)\) \(\chi_{4000}(1257,\cdot)\) \(\chi_{4000}(1593,\cdot)\) \(\chi_{4000}(2393,\cdot)\) \(\chi_{4000}(2857,\cdot)\) \(\chi_{4000}(3657,\cdot)\) \(\chi_{4000}(3993,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((1,-i,e\left(\frac{9}{20}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{2}{5}\right)\)\(-i\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{1}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)