Conductor 825
Order 20
Real no
Primitive no
Minimal yes
Parity even
Orbit label 9900.gv

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(9900)
sage: chi = H[53]
pari: [g,chi] = znchar(Mod(53,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 825
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 20
Real = no
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = no
Minimal = yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = even
Orbit label = 9900.gv
Orbit index = 178

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 ]

\(\chi_{9900}(53,\cdot)\) \(\chi_{9900}(377,\cdot)\) \(\chi_{9900}(773,\cdot)\) \(\chi_{9900}(1313,\cdot)\) \(\chi_{9900}(3833,\cdot)\) \(\chi_{9900}(5417,\cdot)\) \(\chi_{9900}(5597,\cdot)\) \(\chi_{9900}(8837,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((1,-1,e\left(\frac{7}{20}\right),e\left(\frac{3}{5}\right))\)


value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)