Properties

Conductor 3009
Order 116
Real No
Primitive No
Parity Even
Orbit Label 6018.bf

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[47]
pari: [g,chi] = znchar(Mod(47,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 3009
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 116
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.bf
Orbit index = 32

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 ]

\(\chi_{6018}(47,\cdot)\) \(\chi_{6018}(89,\cdot)\) \(\chi_{6018}(149,\cdot)\) \(\chi_{6018}(191,\cdot)\) \(\chi_{6018}(455,\cdot)\) \(\chi_{6018}(659,\cdot)\) \(\chi_{6018}(701,\cdot)\) \(\chi_{6018}(863,\cdot)\) \(\chi_{6018}(1109,\cdot)\) \(\chi_{6018}(1211,\cdot)\) \(\chi_{6018}(1271,\cdot)\) \(\chi_{6018}(1517,\cdot)\) \(\chi_{6018}(1577,\cdot)\) \(\chi_{6018}(1721,\cdot)\) \(\chi_{6018}(1781,\cdot)\) \(\chi_{6018}(1883,\cdot)\) \(\chi_{6018}(1925,\cdot)\) \(\chi_{6018}(1985,\cdot)\) \(\chi_{6018}(2189,\cdot)\) \(\chi_{6018}(2333,\cdot)\) \(\chi_{6018}(2393,\cdot)\) \(\chi_{6018}(2639,\cdot)\) \(\chi_{6018}(2699,\cdot)\) \(\chi_{6018}(2843,\cdot)\) \(\chi_{6018}(2945,\cdot)\) \(\chi_{6018}(3005,\cdot)\) \(\chi_{6018}(3047,\cdot)\) \(\chi_{6018}(3107,\cdot)\) \(\chi_{6018}(3209,\cdot)\) \(\chi_{6018}(3251,\cdot)\) ...

Inducing primitive character

\(\chi_{3009}(47,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((-1,i,e\left(\frac{23}{58}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{15}{116}\right)\)\(e\left(\frac{103}{116}\right)\)\(e\left(\frac{19}{116}\right)\)\(e\left(\frac{49}{58}\right)\)\(e\left(\frac{33}{58}\right)\)\(e\left(\frac{23}{116}\right)\)\(e\left(\frac{15}{58}\right)\)\(e\left(\frac{99}{116}\right)\)\(e\left(\frac{79}{116}\right)\)\(e\left(\frac{1}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{116})\)