Properties

Modulus 4008
Conductor 1336
Order 166
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 4008.bd

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([83,83,0,58]))
 
pari: [g,chi] = znchar(Mod(19,4008))
 

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 = odd
Orbit label = 4008.bd
Orbit index = 30

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 ]
 

\(\chi_{4008}(19,\cdot)\) \(\chi_{4008}(115,\cdot)\) \(\chi_{4008}(211,\cdot)\) \(\chi_{4008}(283,\cdot)\) \(\chi_{4008}(355,\cdot)\) \(\chi_{4008}(427,\cdot)\) \(\chi_{4008}(475,\cdot)\) \(\chi_{4008}(523,\cdot)\) \(\chi_{4008}(595,\cdot)\) \(\chi_{4008}(715,\cdot)\) \(\chi_{4008}(859,\cdot)\) \(\chi_{4008}(883,\cdot)\) \(\chi_{4008}(907,\cdot)\) \(\chi_{4008}(931,\cdot)\) \(\chi_{4008}(979,\cdot)\) \(\chi_{4008}(1027,\cdot)\) \(\chi_{4008}(1051,\cdot)\) \(\chi_{4008}(1099,\cdot)\) \(\chi_{4008}(1123,\cdot)\) \(\chi_{4008}(1171,\cdot)\) \(\chi_{4008}(1219,\cdot)\) \(\chi_{4008}(1267,\cdot)\) \(\chi_{4008}(1291,\cdot)\) \(\chi_{4008}(1339,\cdot)\) \(\chi_{4008}(1363,\cdot)\) \(\chi_{4008}(1411,\cdot)\) \(\chi_{4008}(1435,\cdot)\) \(\chi_{4008}(1483,\cdot)\) \(\chi_{4008}(1507,\cdot)\) \(\chi_{4008}(1531,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,-1,1,e\left(\frac{29}{83}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{141}{166}\right)\)\(e\left(\frac{121}{166}\right)\)\(e\left(\frac{65}{83}\right)\)\(e\left(\frac{81}{166}\right)\)\(e\left(\frac{43}{83}\right)\)\(e\left(\frac{22}{83}\right)\)\(e\left(\frac{15}{166}\right)\)\(e\left(\frac{58}{83}\right)\)\(e\left(\frac{151}{166}\right)\)\(e\left(\frac{157}{166}\right)\)
value at  e.g. 2

Related number fields

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