Properties

Conductor 1003
Order 116
Real No
Primitive No
Parity Even
Orbit Label 6018.bc

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[361]
pari: [g,chi] = znchar(Mod(361,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1003
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.bc
Orbit index = 29

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 ]

\(\chi_{6018}(361,\cdot)\) \(\chi_{6018}(523,\cdot)\) \(\chi_{6018}(625,\cdot)\) \(\chi_{6018}(727,\cdot)\) \(\chi_{6018}(829,\cdot)\) \(\chi_{6018}(871,\cdot)\) \(\chi_{6018}(931,\cdot)\) \(\chi_{6018}(973,\cdot)\) \(\chi_{6018}(1237,\cdot)\) \(\chi_{6018}(1339,\cdot)\) \(\chi_{6018}(1441,\cdot)\) \(\chi_{6018}(1543,\cdot)\) \(\chi_{6018}(1585,\cdot)\) \(\chi_{6018}(1687,\cdot)\) \(\chi_{6018}(1747,\cdot)\) \(\chi_{6018}(1789,\cdot)\) \(\chi_{6018}(1849,\cdot)\) \(\chi_{6018}(1891,\cdot)\) \(\chi_{6018}(1951,\cdot)\) \(\chi_{6018}(1993,\cdot)\) \(\chi_{6018}(2257,\cdot)\) \(\chi_{6018}(2299,\cdot)\) \(\chi_{6018}(2401,\cdot)\) \(\chi_{6018}(2503,\cdot)\) \(\chi_{6018}(2563,\cdot)\) \(\chi_{6018}(2605,\cdot)\) \(\chi_{6018}(2767,\cdot)\) \(\chi_{6018}(2809,\cdot)\) \(\chi_{6018}(2911,\cdot)\) \(\chi_{6018}(2971,\cdot)\) ...

Inducing primitive character

\(\chi_{1003}(361,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((1,-i,e\left(\frac{9}{29}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{71}{116}\right)\)\(e\left(\frac{97}{116}\right)\)\(e\left(\frac{1}{116}\right)\)\(e\left(\frac{28}{29}\right)\)\(e\left(\frac{17}{58}\right)\)\(e\left(\frac{105}{116}\right)\)\(e\left(\frac{13}{58}\right)\)\(e\left(\frac{51}{116}\right)\)\(e\left(\frac{111}{116}\right)\)\(e\left(\frac{13}{29}\right)\)
value at  e.g. 2

Related number fields

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