Properties

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

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([0,83,0,103]))
 
pari: [g,chi] = znchar(Mod(13,4008))
 

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.s
Orbit index = 19

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 ]
 

\(\chi_{4008}(13,\cdot)\) \(\chi_{4008}(37,\cdot)\) \(\chi_{4008}(109,\cdot)\) \(\chi_{4008}(253,\cdot)\) \(\chi_{4008}(277,\cdot)\) \(\chi_{4008}(301,\cdot)\) \(\chi_{4008}(325,\cdot)\) \(\chi_{4008}(349,\cdot)\) \(\chi_{4008}(373,\cdot)\) \(\chi_{4008}(445,\cdot)\) \(\chi_{4008}(469,\cdot)\) \(\chi_{4008}(493,\cdot)\) \(\chi_{4008}(541,\cdot)\) \(\chi_{4008}(637,\cdot)\) \(\chi_{4008}(661,\cdot)\) \(\chi_{4008}(685,\cdot)\) \(\chi_{4008}(709,\cdot)\) \(\chi_{4008}(781,\cdot)\) \(\chi_{4008}(829,\cdot)\) \(\chi_{4008}(925,\cdot)\) \(\chi_{4008}(973,\cdot)\) \(\chi_{4008}(1045,\cdot)\) \(\chi_{4008}(1069,\cdot)\) \(\chi_{4008}(1093,\cdot)\) \(\chi_{4008}(1141,\cdot)\) \(\chi_{4008}(1165,\cdot)\) \(\chi_{4008}(1189,\cdot)\) \(\chi_{4008}(1237,\cdot)\) \(\chi_{4008}(1261,\cdot)\) \(\chi_{4008}(1309,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((1,-1,1,e\left(\frac{103}{166}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{10}{83}\right)\)\(e\left(\frac{18}{83}\right)\)\(e\left(\frac{145}{166}\right)\)\(e\left(\frac{34}{83}\right)\)\(e\left(\frac{147}{166}\right)\)\(e\left(\frac{81}{166}\right)\)\(e\left(\frac{71}{166}\right)\)\(e\left(\frac{20}{83}\right)\)\(e\left(\frac{95}{166}\right)\)\(e\left(\frac{70}{83}\right)\)
value at  e.g. 2

Related number fields

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