Properties

Conductor 72
Order 6
Real No
Primitive No
Parity Odd
Orbit Label 1800.bb

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(1800)
sage: chi = H[101]
pari: [g,chi] = znchar(Mod(101,1800))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 72
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 6
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 = 1800.bb
Orbit index = 28

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 ]

\(\chi_{1800}(101,\cdot)\) \(\chi_{1800}(1301,\cdot)\)

Inducing primitive character

\(\chi_{72}(29,\cdot)\)

Values on generators

\((1351,901,1001,577)\) → \((1,-1,e\left(\frac{1}{6}\right),1)\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)\(-1\)\(-1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{3}\right)\)\(-1\)\(e\left(\frac{5}{6}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3})\)