Properties

Modulus 3600
Conductor 3600
Order 60
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 3600.fh

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([30,45,20,48]))
 
pari: [g,chi] = znchar(Mod(211,3600))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 3600
Conductor = 3600
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 60
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 = odd
Orbit label = 3600.fh
Orbit index = 138

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 ]
 

\(\chi_{3600}(211,\cdot)\) \(\chi_{3600}(331,\cdot)\) \(\chi_{3600}(571,\cdot)\) \(\chi_{3600}(691,\cdot)\) \(\chi_{3600}(931,\cdot)\) \(\chi_{3600}(1291,\cdot)\) \(\chi_{3600}(1411,\cdot)\) \(\chi_{3600}(1771,\cdot)\) \(\chi_{3600}(2011,\cdot)\) \(\chi_{3600}(2131,\cdot)\) \(\chi_{3600}(2371,\cdot)\) \(\chi_{3600}(2491,\cdot)\) \(\chi_{3600}(2731,\cdot)\) \(\chi_{3600}(3091,\cdot)\) \(\chi_{3600}(3211,\cdot)\) \(\chi_{3600}(3571,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,-i,e\left(\frac{1}{3}\right),e\left(\frac{4}{5}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{11}{30}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)