Properties

Conductor 2004
Order 166
Real No
Primitive No
Parity Even
Orbit Label 4008.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(4008)
sage: chi = H[47]
pari: [g,chi] = znchar(Mod(47,4008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2004
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.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 ]

\(\chi_{4008}(47,\cdot)\) \(\chi_{4008}(191,\cdot)\) \(\chi_{4008}(215,\cdot)\) \(\chi_{4008}(239,\cdot)\) \(\chi_{4008}(263,\cdot)\) \(\chi_{4008}(311,\cdot)\) \(\chi_{4008}(359,\cdot)\) \(\chi_{4008}(383,\cdot)\) \(\chi_{4008}(431,\cdot)\) \(\chi_{4008}(455,\cdot)\) \(\chi_{4008}(503,\cdot)\) \(\chi_{4008}(551,\cdot)\) \(\chi_{4008}(599,\cdot)\) \(\chi_{4008}(623,\cdot)\) \(\chi_{4008}(671,\cdot)\) \(\chi_{4008}(695,\cdot)\) \(\chi_{4008}(743,\cdot)\) \(\chi_{4008}(767,\cdot)\) \(\chi_{4008}(815,\cdot)\) \(\chi_{4008}(839,\cdot)\) \(\chi_{4008}(863,\cdot)\) \(\chi_{4008}(911,\cdot)\) \(\chi_{4008}(935,\cdot)\) \(\chi_{4008}(959,\cdot)\) \(\chi_{4008}(1031,\cdot)\) \(\chi_{4008}(1079,\cdot)\) \(\chi_{4008}(1175,\cdot)\) \(\chi_{4008}(1223,\cdot)\) \(\chi_{4008}(1295,\cdot)\) \(\chi_{4008}(1319,\cdot)\) ...

Inducing primitive character

\(\chi_{2004}(47,\cdot)\)

Values on generators

\((3007,2005,1337,673)\) → \((-1,1,-1,e\left(\frac{66}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{49}{166}\right)\)\(e\left(\frac{55}{166}\right)\)\(e\left(\frac{22}{83}\right)\)\(e\left(\frac{75}{83}\right)\)\(e\left(\frac{107}{166}\right)\)\(e\left(\frac{103}{166}\right)\)\(e\left(\frac{60}{83}\right)\)\(e\left(\frac{49}{83}\right)\)\(e\left(\frac{129}{166}\right)\)\(e\left(\frac{11}{166}\right)\)
value at  e.g. 2

Related number fields

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