Properties

Conductor 177
Order 58
Real No
Primitive No
Parity Even
Orbit Label 6018.y

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[443]
pari: [g,chi] = znchar(Mod(443,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 177
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 58
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.y
Orbit index = 25

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 ]

\(\chi_{6018}(443,\cdot)\) \(\chi_{6018}(545,\cdot)\) \(\chi_{6018}(1055,\cdot)\) \(\chi_{6018}(1463,\cdot)\) \(\chi_{6018}(1565,\cdot)\) \(\chi_{6018}(1871,\cdot)\) \(\chi_{6018}(2075,\cdot)\) \(\chi_{6018}(2279,\cdot)\) \(\chi_{6018}(2687,\cdot)\) \(\chi_{6018}(2993,\cdot)\) \(\chi_{6018}(3197,\cdot)\) \(\chi_{6018}(3299,\cdot)\) \(\chi_{6018}(3401,\cdot)\) \(\chi_{6018}(3605,\cdot)\) \(\chi_{6018}(3809,\cdot)\) \(\chi_{6018}(4115,\cdot)\) \(\chi_{6018}(4421,\cdot)\) \(\chi_{6018}(4523,\cdot)\) \(\chi_{6018}(4625,\cdot)\) \(\chi_{6018}(4829,\cdot)\) \(\chi_{6018}(4931,\cdot)\) \(\chi_{6018}(5033,\cdot)\) \(\chi_{6018}(5135,\cdot)\) \(\chi_{6018}(5441,\cdot)\) \(\chi_{6018}(5543,\cdot)\) \(\chi_{6018}(5645,\cdot)\) \(\chi_{6018}(5747,\cdot)\) \(\chi_{6018}(5849,\cdot)\)

Inducing primitive character

\(\chi_{177}(89,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((-1,1,e\left(\frac{57}{58}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{23}{58}\right)\)\(e\left(\frac{20}{29}\right)\)\(e\left(\frac{2}{29}\right)\)\(e\left(\frac{13}{58}\right)\)\(e\left(\frac{10}{29}\right)\)\(e\left(\frac{7}{29}\right)\)\(e\left(\frac{23}{29}\right)\)\(e\left(\frac{1}{58}\right)\)\(e\left(\frac{9}{58}\right)\)\(e\left(\frac{5}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{29})\)