Properties

Conductor 1800
Order 30
Real No
Primitive No
Parity Odd
Orbit Label 3600.fe

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[329]
pari: [g,chi] = znchar(Mod(329,3600))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1800
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 30
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.fe
Orbit index = 135

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 ]

\(\chi_{3600}(329,\cdot)\) \(\chi_{3600}(569,\cdot)\) \(\chi_{3600}(1289,\cdot)\) \(\chi_{3600}(1769,\cdot)\) \(\chi_{3600}(2009,\cdot)\) \(\chi_{3600}(2489,\cdot)\) \(\chi_{3600}(2729,\cdot)\) \(\chi_{3600}(3209,\cdot)\)

Inducing primitive character

\(\chi_{1800}(1229,\cdot)\)

Values on generators

\((3151,901,2801,577)\) → \((1,-1,e\left(\frac{5}{6}\right),e\left(\frac{1}{10}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{17}{30}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)