Properties

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

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[203]
pari: [g,chi] = znchar(Mod(203,3600))

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.ft
Orbit index = 150

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 ]

\(\chi_{3600}(203,\cdot)\) \(\chi_{3600}(227,\cdot)\) \(\chi_{3600}(923,\cdot)\) \(\chi_{3600}(947,\cdot)\) \(\chi_{3600}(1163,\cdot)\) \(\chi_{3600}(1427,\cdot)\) \(\chi_{3600}(1667,\cdot)\) \(\chi_{3600}(1883,\cdot)\) \(\chi_{3600}(2147,\cdot)\) \(\chi_{3600}(2363,\cdot)\) \(\chi_{3600}(2387,\cdot)\) \(\chi_{3600}(2603,\cdot)\) \(\chi_{3600}(2867,\cdot)\) \(\chi_{3600}(3083,\cdot)\) \(\chi_{3600}(3323,\cdot)\) \(\chi_{3600}(3587,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,i,e\left(\frac{5}{6}\right),e\left(\frac{7}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{15}\right)\)
value at  e.g. 2

Related number fields

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