Properties

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

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[83]
pari: [g,chi] = znchar(Mod(83,3600))

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.fp
Orbit index = 146

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 ]

\(\chi_{3600}(83,\cdot)\) \(\chi_{3600}(347,\cdot)\) \(\chi_{3600}(563,\cdot)\) \(\chi_{3600}(587,\cdot)\) \(\chi_{3600}(803,\cdot)\) \(\chi_{3600}(1067,\cdot)\) \(\chi_{3600}(1283,\cdot)\) \(\chi_{3600}(1523,\cdot)\) \(\chi_{3600}(1787,\cdot)\) \(\chi_{3600}(2003,\cdot)\) \(\chi_{3600}(2027,\cdot)\) \(\chi_{3600}(2723,\cdot)\) \(\chi_{3600}(2747,\cdot)\) \(\chi_{3600}(2963,\cdot)\) \(\chi_{3600}(3227,\cdot)\) \(\chi_{3600}(3467,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((-1,-i,e\left(\frac{1}{6}\right),e\left(\frac{3}{20}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{14}{15}\right)\)
value at  e.g. 2

Related number fields

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