Properties

Modulus 4008
Conductor 167
Order 83
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4008.q

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([0,0,0,35]))
 
pari: [g,chi] = znchar(Mod(49,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 167
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 83
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.q
Orbit index = 17

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 ]
 

\(\chi_{4008}(25,\cdot)\) \(\chi_{4008}(49,\cdot)\) \(\chi_{4008}(97,\cdot)\) \(\chi_{4008}(121,\cdot)\) \(\chi_{4008}(169,\cdot)\) \(\chi_{4008}(217,\cdot)\) \(\chi_{4008}(265,\cdot)\) \(\chi_{4008}(289,\cdot)\) \(\chi_{4008}(337,\cdot)\) \(\chi_{4008}(361,\cdot)\) \(\chi_{4008}(409,\cdot)\) \(\chi_{4008}(433,\cdot)\) \(\chi_{4008}(481,\cdot)\) \(\chi_{4008}(505,\cdot)\) \(\chi_{4008}(529,\cdot)\) \(\chi_{4008}(577,\cdot)\) \(\chi_{4008}(601,\cdot)\) \(\chi_{4008}(625,\cdot)\) \(\chi_{4008}(697,\cdot)\) \(\chi_{4008}(745,\cdot)\) \(\chi_{4008}(841,\cdot)\) \(\chi_{4008}(889,\cdot)\) \(\chi_{4008}(961,\cdot)\) \(\chi_{4008}(985,\cdot)\) \(\chi_{4008}(1009,\cdot)\) \(\chi_{4008}(1033,\cdot)\) \(\chi_{4008}(1129,\cdot)\) \(\chi_{4008}(1177,\cdot)\) \(\chi_{4008}(1201,\cdot)\) \(\chi_{4008}(1225,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,1,1,e\left(\frac{35}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{35}{83}\right)\)\(e\left(\frac{63}{83}\right)\)\(e\left(\frac{67}{83}\right)\)\(e\left(\frac{36}{83}\right)\)\(e\left(\frac{29}{83}\right)\)\(e\left(\frac{38}{83}\right)\)\(e\left(\frac{62}{83}\right)\)\(e\left(\frac{70}{83}\right)\)\(e\left(\frac{21}{83}\right)\)\(e\left(\frac{79}{83}\right)\)
value at  e.g. 2

Related number fields

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