Properties

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

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([0,83,83,146]))
 
pari: [g,chi] = znchar(Mod(77,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 4008
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4008.r
Orbit index = 18

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 ]
 

\(\chi_{4008}(29,\cdot)\) \(\chi_{4008}(77,\cdot)\) \(\chi_{4008}(173,\cdot)\) \(\chi_{4008}(221,\cdot)\) \(\chi_{4008}(293,\cdot)\) \(\chi_{4008}(317,\cdot)\) \(\chi_{4008}(341,\cdot)\) \(\chi_{4008}(365,\cdot)\) \(\chi_{4008}(461,\cdot)\) \(\chi_{4008}(509,\cdot)\) \(\chi_{4008}(533,\cdot)\) \(\chi_{4008}(557,\cdot)\) \(\chi_{4008}(629,\cdot)\) \(\chi_{4008}(653,\cdot)\) \(\chi_{4008}(677,\cdot)\) \(\chi_{4008}(701,\cdot)\) \(\chi_{4008}(725,\cdot)\) \(\chi_{4008}(749,\cdot)\) \(\chi_{4008}(893,\cdot)\) \(\chi_{4008}(965,\cdot)\) \(\chi_{4008}(989,\cdot)\) \(\chi_{4008}(1013,\cdot)\) \(\chi_{4008}(1109,\cdot)\) \(\chi_{4008}(1181,\cdot)\) \(\chi_{4008}(1205,\cdot)\) \(\chi_{4008}(1253,\cdot)\) \(\chi_{4008}(1277,\cdot)\) \(\chi_{4008}(1301,\cdot)\) \(\chi_{4008}(1397,\cdot)\) \(\chi_{4008}(1421,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,-1,e\left(\frac{73}{83}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{73}{83}\right)\)\(e\left(\frac{65}{83}\right)\)\(e\left(\frac{52}{83}\right)\)\(e\left(\frac{15}{166}\right)\)\(e\left(\frac{19}{166}\right)\)\(e\left(\frac{85}{166}\right)\)\(e\left(\frac{95}{166}\right)\)\(e\left(\frac{63}{83}\right)\)\(e\left(\frac{77}{83}\right)\)\(e\left(\frac{13}{83}\right)\)
value at  e.g. 2

Related number fields

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