Properties

Conductor 3600
Order 60
Real No
Primitive Yes
Parity Odd
Orbit Label 3600.fu

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[133]
 
pari: [g,chi] = znchar(Mod(133,3600))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 3600.fu
Orbit index = 151

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 ]
 

\(\chi_{3600}(133,\cdot)\) \(\chi_{3600}(373,\cdot)\) \(\chi_{3600}(637,\cdot)\) \(\chi_{3600}(853,\cdot)\) \(\chi_{3600}(877,\cdot)\) \(\chi_{3600}(1573,\cdot)\) \(\chi_{3600}(1597,\cdot)\) \(\chi_{3600}(1813,\cdot)\) \(\chi_{3600}(2077,\cdot)\) \(\chi_{3600}(2317,\cdot)\) \(\chi_{3600}(2533,\cdot)\) \(\chi_{3600}(2797,\cdot)\) \(\chi_{3600}(3013,\cdot)\) \(\chi_{3600}(3037,\cdot)\) \(\chi_{3600}(3253,\cdot)\) \(\chi_{3600}(3517,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((1,i,e\left(\frac{2}{3}\right),e\left(\frac{3}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{13}{30}\right)\)
value at  e.g. 2

Related number fields

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