Properties

Modulus 4008
Conductor 668
Order 166
Real no
Primitive no
Minimal no
Parity odd
Orbit label 4008.w

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([83,0,0,118]))
 
pari: [g,chi] = znchar(Mod(7,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
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
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4008.w
Orbit index = 23

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 ]
 

\(\chi_{4008}(7,\cdot)\) \(\chi_{4008}(31,\cdot)\) \(\chi_{4008}(127,\cdot)\) \(\chi_{4008}(175,\cdot)\) \(\chi_{4008}(199,\cdot)\) \(\chi_{4008}(223,\cdot)\) \(\chi_{4008}(295,\cdot)\) \(\chi_{4008}(319,\cdot)\) \(\chi_{4008}(343,\cdot)\) \(\chi_{4008}(367,\cdot)\) \(\chi_{4008}(391,\cdot)\) \(\chi_{4008}(415,\cdot)\) \(\chi_{4008}(559,\cdot)\) \(\chi_{4008}(631,\cdot)\) \(\chi_{4008}(655,\cdot)\) \(\chi_{4008}(679,\cdot)\) \(\chi_{4008}(775,\cdot)\) \(\chi_{4008}(847,\cdot)\) \(\chi_{4008}(871,\cdot)\) \(\chi_{4008}(919,\cdot)\) \(\chi_{4008}(943,\cdot)\) \(\chi_{4008}(967,\cdot)\) \(\chi_{4008}(1063,\cdot)\) \(\chi_{4008}(1087,\cdot)\) \(\chi_{4008}(1135,\cdot)\) \(\chi_{4008}(1159,\cdot)\) \(\chi_{4008}(1183,\cdot)\) \(\chi_{4008}(1207,\cdot)\) \(\chi_{4008}(1231,\cdot)\) \(\chi_{4008}(1399,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,1,1,e\left(\frac{59}{83}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{59}{83}\right)\)\(e\left(\frac{63}{166}\right)\)\(e\left(\frac{67}{166}\right)\)\(e\left(\frac{18}{83}\right)\)\(e\left(\frac{56}{83}\right)\)\(e\left(\frac{121}{166}\right)\)\(e\left(\frac{145}{166}\right)\)\(e\left(\frac{35}{83}\right)\)\(e\left(\frac{52}{83}\right)\)\(e\left(\frac{79}{166}\right)\)
value at  e.g. 2

Related number fields

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