Properties

Conductor 668
Order 166
Real No
Primitive No
Parity Even
Orbit Label 4008.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(4008)
sage: chi = H[55]
pari: [g,chi] = znchar(Mod(55,4008))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 668
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.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 ]

\(\chi_{4008}(55,\cdot)\) \(\chi_{4008}(79,\cdot)\) \(\chi_{4008}(103,\cdot)\) \(\chi_{4008}(151,\cdot)\) \(\chi_{4008}(247,\cdot)\) \(\chi_{4008}(271,\cdot)\) \(\chi_{4008}(439,\cdot)\) \(\chi_{4008}(463,\cdot)\) \(\chi_{4008}(487,\cdot)\) \(\chi_{4008}(511,\cdot)\) \(\chi_{4008}(535,\cdot)\) \(\chi_{4008}(583,\cdot)\) \(\chi_{4008}(607,\cdot)\) \(\chi_{4008}(703,\cdot)\) \(\chi_{4008}(727,\cdot)\) \(\chi_{4008}(751,\cdot)\) \(\chi_{4008}(799,\cdot)\) \(\chi_{4008}(823,\cdot)\) \(\chi_{4008}(895,\cdot)\) \(\chi_{4008}(991,\cdot)\) \(\chi_{4008}(1015,\cdot)\) \(\chi_{4008}(1039,\cdot)\) \(\chi_{4008}(1111,\cdot)\) \(\chi_{4008}(1255,\cdot)\) \(\chi_{4008}(1279,\cdot)\) \(\chi_{4008}(1303,\cdot)\) \(\chi_{4008}(1327,\cdot)\) \(\chi_{4008}(1351,\cdot)\) \(\chi_{4008}(1375,\cdot)\) \(\chi_{4008}(1447,\cdot)\) ...

Inducing primitive character

\(\chi_{668}(55,\cdot)\)

Values on generators

\((3007,2005,1337,673)\) → \((-1,1,1,e\left(\frac{29}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{29}{166}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{65}{166}\right)\)\(e\left(\frac{165}{166}\right)\)\(e\left(\frac{43}{166}\right)\)\(e\left(\frac{105}{166}\right)\)\(e\left(\frac{66}{83}\right)\)\(e\left(\frac{29}{83}\right)\)\(e\left(\frac{17}{83}\right)\)\(e\left(\frac{37}{166}\right)\)
value at  e.g. 2

Related number fields

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