Properties

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

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[29]
pari: [g,chi] = znchar(Mod(29,3600))

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.fg
Orbit index = 137

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 ]

\(\chi_{3600}(29,\cdot)\) \(\chi_{3600}(389,\cdot)\) \(\chi_{3600}(509,\cdot)\) \(\chi_{3600}(869,\cdot)\) \(\chi_{3600}(1109,\cdot)\) \(\chi_{3600}(1229,\cdot)\) \(\chi_{3600}(1469,\cdot)\) \(\chi_{3600}(1589,\cdot)\) \(\chi_{3600}(1829,\cdot)\) \(\chi_{3600}(2189,\cdot)\) \(\chi_{3600}(2309,\cdot)\) \(\chi_{3600}(2669,\cdot)\) \(\chi_{3600}(2909,\cdot)\) \(\chi_{3600}(3029,\cdot)\) \(\chi_{3600}(3269,\cdot)\) \(\chi_{3600}(3389,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((1,-i,e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{11}{15}\right)\)
value at  e.g. 2

Related number fields

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