Properties

Modulus 4008
Conductor 4008
Order 166
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4008.y

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([0,83,83,109]))
 
pari: [g,chi] = znchar(Mod(53,4008))
 

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 = even
Orbit label = 4008.y
Orbit index = 25

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 ]
 

\(\chi_{4008}(5,\cdot)\) \(\chi_{4008}(53,\cdot)\) \(\chi_{4008}(101,\cdot)\) \(\chi_{4008}(125,\cdot)\) \(\chi_{4008}(149,\cdot)\) \(\chi_{4008}(197,\cdot)\) \(\chi_{4008}(245,\cdot)\) \(\chi_{4008}(269,\cdot)\) \(\chi_{4008}(389,\cdot)\) \(\chi_{4008}(413,\cdot)\) \(\chi_{4008}(437,\cdot)\) \(\chi_{4008}(485,\cdot)\) \(\chi_{4008}(581,\cdot)\) \(\chi_{4008}(605,\cdot)\) \(\chi_{4008}(773,\cdot)\) \(\chi_{4008}(797,\cdot)\) \(\chi_{4008}(821,\cdot)\) \(\chi_{4008}(845,\cdot)\) \(\chi_{4008}(869,\cdot)\) \(\chi_{4008}(917,\cdot)\) \(\chi_{4008}(941,\cdot)\) \(\chi_{4008}(1037,\cdot)\) \(\chi_{4008}(1061,\cdot)\) \(\chi_{4008}(1085,\cdot)\) \(\chi_{4008}(1133,\cdot)\) \(\chi_{4008}(1157,\cdot)\) \(\chi_{4008}(1229,\cdot)\) \(\chi_{4008}(1325,\cdot)\) \(\chi_{4008}(1349,\cdot)\) \(\chi_{4008}(1373,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,-1,e\left(\frac{109}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{109}{166}\right)\)\(e\left(\frac{40}{83}\right)\)\(e\left(\frac{32}{83}\right)\)\(e\left(\frac{11}{83}\right)\)\(e\left(\frac{25}{83}\right)\)\(e\left(\frac{97}{166}\right)\)\(e\left(\frac{42}{83}\right)\)\(e\left(\frac{26}{83}\right)\)\(e\left(\frac{41}{83}\right)\)\(e\left(\frac{8}{83}\right)\)
value at  e.g. 2

Related number fields

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