Properties

Conductor 1003
Order 16
Real No
Primitive No
Parity Even
Orbit Label 6018.t

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[235]
pari: [g,chi] = znchar(Mod(235,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 16
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.t
Orbit index = 20

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 ]

\(\chi_{6018}(235,\cdot)\) \(\chi_{6018}(589,\cdot)\) \(\chi_{6018}(1297,\cdot)\) \(\chi_{6018}(2713,\cdot)\) \(\chi_{6018}(3067,\cdot)\) \(\chi_{6018}(4483,\cdot)\) \(\chi_{6018}(5191,\cdot)\) \(\chi_{6018}(5545,\cdot)\)

Inducing primitive character

\(\chi_{1003}(235,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((1,e\left(\frac{9}{16}\right),-1)\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{7}{16}\right)\)\(-i\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{16})\)