Properties

Conductor 900
Order 60
Real No
Primitive No
Parity Odd
Orbit Label 3600.fx

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(3600)
 
sage: chi = H[47]
 
pari: [g,chi] = znchar(Mod(47,3600))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 900
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 3600.fx
Orbit index = 154

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 ]
 

\(\chi_{3600}(47,\cdot)\) \(\chi_{3600}(383,\cdot)\) \(\chi_{3600}(527,\cdot)\) \(\chi_{3600}(623,\cdot)\) \(\chi_{3600}(767,\cdot)\) \(\chi_{3600}(1103,\cdot)\) \(\chi_{3600}(1247,\cdot)\) \(\chi_{3600}(1487,\cdot)\) \(\chi_{3600}(1823,\cdot)\) \(\chi_{3600}(1967,\cdot)\) \(\chi_{3600}(2063,\cdot)\) \(\chi_{3600}(2687,\cdot)\) \(\chi_{3600}(2783,\cdot)\) \(\chi_{3600}(2927,\cdot)\) \(\chi_{3600}(3263,\cdot)\) \(\chi_{3600}(3503,\cdot)\)

Inducing primitive character

\(\chi_{900}(47,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,1,e\left(\frac{1}{6}\right),e\left(\frac{17}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{7}{30}\right)\)
value at  e.g. 2

Related number fields

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