Properties

Modulus 3600
Conductor 1200
Order 20
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 3600.ed

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3600)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([10,15,10,13]))
 
pari: [g,chi] = znchar(Mod(467,3600))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 3600
Conductor = 1200
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 = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 3600.ed
Orbit index = 108

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 ]
 

\(\chi_{3600}(467,\cdot)\) \(\chi_{3600}(683,\cdot)\) \(\chi_{3600}(1187,\cdot)\) \(\chi_{3600}(1403,\cdot)\) \(\chi_{3600}(2123,\cdot)\) \(\chi_{3600}(2627,\cdot)\) \(\chi_{3600}(3347,\cdot)\) \(\chi_{3600}(3563,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,-i,-1,e\left(\frac{13}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(i\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{3}{5}\right)\)
value at  e.g. 2

Related number fields

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