Properties

Modulus 4008
Conductor 167
Order 166
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 4008.z

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([0,0,0,141]))
 
pari: [g,chi] = znchar(Mod(649,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 167
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.z
Orbit index = 26

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 ]
 

\(\chi_{4008}(73,\cdot)\) \(\chi_{4008}(145,\cdot)\) \(\chi_{4008}(193,\cdot)\) \(\chi_{4008}(241,\cdot)\) \(\chi_{4008}(313,\cdot)\) \(\chi_{4008}(385,\cdot)\) \(\chi_{4008}(457,\cdot)\) \(\chi_{4008}(553,\cdot)\) \(\chi_{4008}(649,\cdot)\) \(\chi_{4008}(673,\cdot)\) \(\chi_{4008}(721,\cdot)\) \(\chi_{4008}(769,\cdot)\) \(\chi_{4008}(793,\cdot)\) \(\chi_{4008}(817,\cdot)\) \(\chi_{4008}(865,\cdot)\) \(\chi_{4008}(913,\cdot)\) \(\chi_{4008}(937,\cdot)\) \(\chi_{4008}(1057,\cdot)\) \(\chi_{4008}(1081,\cdot)\) \(\chi_{4008}(1105,\cdot)\) \(\chi_{4008}(1153,\cdot)\) \(\chi_{4008}(1249,\cdot)\) \(\chi_{4008}(1273,\cdot)\) \(\chi_{4008}(1441,\cdot)\) \(\chi_{4008}(1465,\cdot)\) \(\chi_{4008}(1489,\cdot)\) \(\chi_{4008}(1513,\cdot)\) \(\chi_{4008}(1537,\cdot)\) \(\chi_{4008}(1585,\cdot)\) \(\chi_{4008}(1609,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,1,1,e\left(\frac{141}{166}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{141}{166}\right)\)\(e\left(\frac{19}{83}\right)\)\(e\left(\frac{65}{83}\right)\)\(e\left(\frac{81}{166}\right)\)\(e\left(\frac{3}{166}\right)\)\(e\left(\frac{22}{83}\right)\)\(e\left(\frac{15}{166}\right)\)\(e\left(\frac{58}{83}\right)\)\(e\left(\frac{34}{83}\right)\)\(e\left(\frac{37}{83}\right)\)
value at  e.g. 2

Related number fields

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