Properties

Modulus 4008
Conductor 501
Order 166
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 4008.ba

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4008)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,83,52]))
 
pari: [g,chi] = znchar(Mod(137,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 501
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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4008.ba
Orbit index = 27

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4008}(65,\cdot)\) \(\chi_{4008}(89,\cdot)\) \(\chi_{4008}(137,\cdot)\) \(\chi_{4008}(185,\cdot)\) \(\chi_{4008}(209,\cdot)\) \(\chi_{4008}(233,\cdot)\) \(\chi_{4008}(281,\cdot)\) \(\chi_{4008}(329,\cdot)\) \(\chi_{4008}(353,\cdot)\) \(\chi_{4008}(449,\cdot)\) \(\chi_{4008}(545,\cdot)\) \(\chi_{4008}(617,\cdot)\) \(\chi_{4008}(689,\cdot)\) \(\chi_{4008}(761,\cdot)\) \(\chi_{4008}(809,\cdot)\) \(\chi_{4008}(857,\cdot)\) \(\chi_{4008}(929,\cdot)\) \(\chi_{4008}(1049,\cdot)\) \(\chi_{4008}(1193,\cdot)\) \(\chi_{4008}(1217,\cdot)\) \(\chi_{4008}(1241,\cdot)\) \(\chi_{4008}(1265,\cdot)\) \(\chi_{4008}(1313,\cdot)\) \(\chi_{4008}(1361,\cdot)\) \(\chi_{4008}(1385,\cdot)\) \(\chi_{4008}(1433,\cdot)\) \(\chi_{4008}(1457,\cdot)\) \(\chi_{4008}(1505,\cdot)\) \(\chi_{4008}(1553,\cdot)\) \(\chi_{4008}(1601,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,1,-1,e\left(\frac{26}{83}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{135}{166}\right)\)\(e\left(\frac{80}{83}\right)\)\(e\left(\frac{45}{166}\right)\)\(e\left(\frac{22}{83}\right)\)\(e\left(\frac{17}{166}\right)\)\(e\left(\frac{14}{83}\right)\)\(e\left(\frac{85}{166}\right)\)\(e\left(\frac{52}{83}\right)\)\(e\left(\frac{81}{166}\right)\)\(e\left(\frac{16}{83}\right)\)
value at  e.g. 2

Related number fields

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