Properties

Conductor 1336
Order 166
Real No
Primitive No
Parity Even
Orbit Label 4008.u

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(4008)
sage: chi = H[43]
pari: [g,chi] = znchar(Mod(43,4008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1336
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 166
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 = 4008.u
Orbit index = 21

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 ]

\(\chi_{4008}(43,\cdot)\) \(\chi_{4008}(67,\cdot)\) \(\chi_{4008}(91,\cdot)\) \(\chi_{4008}(139,\cdot)\) \(\chi_{4008}(163,\cdot)\) \(\chi_{4008}(187,\cdot)\) \(\chi_{4008}(235,\cdot)\) \(\chi_{4008}(259,\cdot)\) \(\chi_{4008}(307,\cdot)\) \(\chi_{4008}(331,\cdot)\) \(\chi_{4008}(379,\cdot)\) \(\chi_{4008}(403,\cdot)\) \(\chi_{4008}(451,\cdot)\) \(\chi_{4008}(499,\cdot)\) \(\chi_{4008}(547,\cdot)\) \(\chi_{4008}(571,\cdot)\) \(\chi_{4008}(619,\cdot)\) \(\chi_{4008}(643,\cdot)\) \(\chi_{4008}(691,\cdot)\) \(\chi_{4008}(739,\cdot)\) \(\chi_{4008}(763,\cdot)\) \(\chi_{4008}(787,\cdot)\) \(\chi_{4008}(811,\cdot)\) \(\chi_{4008}(955,\cdot)\) \(\chi_{4008}(1075,\cdot)\) \(\chi_{4008}(1147,\cdot)\) \(\chi_{4008}(1195,\cdot)\) \(\chi_{4008}(1243,\cdot)\) \(\chi_{4008}(1315,\cdot)\) \(\chi_{4008}(1387,\cdot)\) ...

Inducing primitive character

\(\chi_{1336}(43,\cdot)\)

Values on generators

\((3007,2005,1337,673)\) → \((-1,-1,1,e\left(\frac{87}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{2}{83}\right)\)\(e\left(\frac{57}{166}\right)\)\(e\left(\frac{56}{83}\right)\)\(e\left(\frac{40}{83}\right)\)\(e\left(\frac{129}{166}\right)\)\(e\left(\frac{33}{83}\right)\)\(e\left(\frac{32}{83}\right)\)\(e\left(\frac{4}{83}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{111}{166}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{83})\)