Properties

Modulus 4008
Conductor 501
Order 166
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4008.t

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([0,0,83,53]))
 
pari: [g,chi] = znchar(Mod(17,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 501
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.t
Orbit index = 20

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 ]
 

\(\chi_{4008}(17,\cdot)\) \(\chi_{4008}(41,\cdot)\) \(\chi_{4008}(113,\cdot)\) \(\chi_{4008}(161,\cdot)\) \(\chi_{4008}(257,\cdot)\) \(\chi_{4008}(305,\cdot)\) \(\chi_{4008}(377,\cdot)\) \(\chi_{4008}(401,\cdot)\) \(\chi_{4008}(425,\cdot)\) \(\chi_{4008}(473,\cdot)\) \(\chi_{4008}(497,\cdot)\) \(\chi_{4008}(521,\cdot)\) \(\chi_{4008}(569,\cdot)\) \(\chi_{4008}(593,\cdot)\) \(\chi_{4008}(641,\cdot)\) \(\chi_{4008}(665,\cdot)\) \(\chi_{4008}(713,\cdot)\) \(\chi_{4008}(737,\cdot)\) \(\chi_{4008}(785,\cdot)\) \(\chi_{4008}(833,\cdot)\) \(\chi_{4008}(881,\cdot)\) \(\chi_{4008}(905,\cdot)\) \(\chi_{4008}(953,\cdot)\) \(\chi_{4008}(977,\cdot)\) \(\chi_{4008}(1025,\cdot)\) \(\chi_{4008}(1073,\cdot)\) \(\chi_{4008}(1097,\cdot)\) \(\chi_{4008}(1121,\cdot)\) \(\chi_{4008}(1145,\cdot)\) \(\chi_{4008}(1289,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,1,-1,e\left(\frac{53}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{68}{83}\right)\)\(e\left(\frac{56}{83}\right)\)\(e\left(\frac{73}{166}\right)\)\(e\left(\frac{147}{166}\right)\)\(e\left(\frac{35}{83}\right)\)\(e\left(\frac{43}{83}\right)\)\(e\left(\frac{9}{83}\right)\)\(e\left(\frac{53}{83}\right)\)\(e\left(\frac{65}{166}\right)\)\(e\left(\frac{61}{83}\right)\)
value at  e.g. 2

Related number fields

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