Properties

Modulus 8016
Conductor 8016
Order 332
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 8016.bq

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8016)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([166,83,166,56]))
 
pari: [g,chi] = znchar(Mod(11,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
Conductor = 8016
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 332
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 8016.bq
Orbit index = 43

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 ]
 

\(\chi_{8016}(11,\cdot)\) \(\chi_{8016}(107,\cdot)\) \(\chi_{8016}(179,\cdot)\) \(\chi_{8016}(203,\cdot)\) \(\chi_{8016}(251,\cdot)\) \(\chi_{8016}(275,\cdot)\) \(\chi_{8016}(299,\cdot)\) \(\chi_{8016}(395,\cdot)\) \(\chi_{8016}(419,\cdot)\) \(\chi_{8016}(467,\cdot)\) \(\chi_{8016}(491,\cdot)\) \(\chi_{8016}(515,\cdot)\) \(\chi_{8016}(539,\cdot)\) \(\chi_{8016}(563,\cdot)\) \(\chi_{8016}(731,\cdot)\) \(\chi_{8016}(755,\cdot)\) \(\chi_{8016}(851,\cdot)\) \(\chi_{8016}(899,\cdot)\) \(\chi_{8016}(923,\cdot)\) \(\chi_{8016}(947,\cdot)\) \(\chi_{8016}(1067,\cdot)\) \(\chi_{8016}(1091,\cdot)\) \(\chi_{8016}(1139,\cdot)\) \(\chi_{8016}(1187,\cdot)\) \(\chi_{8016}(1211,\cdot)\) \(\chi_{8016}(1235,\cdot)\) \(\chi_{8016}(1283,\cdot)\) \(\chi_{8016}(1331,\cdot)\) \(\chi_{8016}(1355,\cdot)\) \(\chi_{8016}(1451,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((-1,i,-1,e\left(\frac{14}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{305}{332}\right)\)\(e\left(\frac{75}{83}\right)\)\(e\left(\frac{323}{332}\right)\)\(e\left(\frac{41}{332}\right)\)\(e\left(\frac{73}{166}\right)\)\(e\left(\frac{11}{332}\right)\)\(e\left(\frac{33}{166}\right)\)\(e\left(\frac{139}{166}\right)\)\(e\left(\frac{183}{332}\right)\)\(e\left(\frac{113}{166}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{332})\)