Properties

Conductor 3009
Order 8
Real No
Primitive No
Parity Even
Orbit Label 6018.o

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(6018)
sage: chi = H[2123]
pari: [g,chi] = znchar(Mod(2123,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 3009
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 8
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 = Even
Orbit label = 6018.o
Orbit index = 15

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 ]

\(\chi_{6018}(2123,\cdot)\) \(\chi_{6018}(2831,\cdot)\) \(\chi_{6018}(4955,\cdot)\) \(\chi_{6018}(5663,\cdot)\)

Inducing primitive character

\(\chi_{3009}(2123,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((-1,e\left(\frac{3}{8}\right),-1)\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{5}{8}\right)\)\(1\)\(i\)\(e\left(\frac{5}{8}\right)\)\(-i\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{8})\)