Properties

Modulus 4008
Conductor 1336
Order 166
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4008.bb

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([0,83,0,54]))
 
pari: [g,chi] = znchar(Mod(85,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 1336
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 = even
Orbit label = 4008.bb
Orbit index = 28

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 ]
 

\(\chi_{4008}(61,\cdot)\) \(\chi_{4008}(85,\cdot)\) \(\chi_{4008}(133,\cdot)\) \(\chi_{4008}(157,\cdot)\) \(\chi_{4008}(181,\cdot)\) \(\chi_{4008}(205,\cdot)\) \(\chi_{4008}(229,\cdot)\) \(\chi_{4008}(397,\cdot)\) \(\chi_{4008}(421,\cdot)\) \(\chi_{4008}(517,\cdot)\) \(\chi_{4008}(565,\cdot)\) \(\chi_{4008}(589,\cdot)\) \(\chi_{4008}(613,\cdot)\) \(\chi_{4008}(733,\cdot)\) \(\chi_{4008}(757,\cdot)\) \(\chi_{4008}(805,\cdot)\) \(\chi_{4008}(853,\cdot)\) \(\chi_{4008}(877,\cdot)\) \(\chi_{4008}(901,\cdot)\) \(\chi_{4008}(949,\cdot)\) \(\chi_{4008}(997,\cdot)\) \(\chi_{4008}(1021,\cdot)\) \(\chi_{4008}(1117,\cdot)\) \(\chi_{4008}(1213,\cdot)\) \(\chi_{4008}(1285,\cdot)\) \(\chi_{4008}(1357,\cdot)\) \(\chi_{4008}(1429,\cdot)\) \(\chi_{4008}(1477,\cdot)\) \(\chi_{4008}(1525,\cdot)\) \(\chi_{4008}(1597,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,1,e\left(\frac{27}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{137}{166}\right)\)\(e\left(\frac{32}{83}\right)\)\(e\left(\frac{101}{166}\right)\)\(e\left(\frac{1}{166}\right)\)\(e\left(\frac{20}{83}\right)\)\(e\left(\frac{61}{166}\right)\)\(e\left(\frac{17}{83}\right)\)\(e\left(\frac{54}{83}\right)\)\(e\left(\frac{49}{166}\right)\)\(e\left(\frac{23}{83}\right)\)
value at  e.g. 2

Related number fields

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