Properties

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

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([0,83,166,2]))
 
pari: [g,chi] = znchar(Mod(5,8016))
 

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.bt
Orbit index = 46

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 ]
 

\(\chi_{8016}(5,\cdot)\) \(\chi_{8016}(53,\cdot)\) \(\chi_{8016}(101,\cdot)\) \(\chi_{8016}(125,\cdot)\) \(\chi_{8016}(149,\cdot)\) \(\chi_{8016}(197,\cdot)\) \(\chi_{8016}(245,\cdot)\) \(\chi_{8016}(269,\cdot)\) \(\chi_{8016}(389,\cdot)\) \(\chi_{8016}(413,\cdot)\) \(\chi_{8016}(437,\cdot)\) \(\chi_{8016}(485,\cdot)\) \(\chi_{8016}(581,\cdot)\) \(\chi_{8016}(605,\cdot)\) \(\chi_{8016}(773,\cdot)\) \(\chi_{8016}(797,\cdot)\) \(\chi_{8016}(821,\cdot)\) \(\chi_{8016}(845,\cdot)\) \(\chi_{8016}(869,\cdot)\) \(\chi_{8016}(917,\cdot)\) \(\chi_{8016}(941,\cdot)\) \(\chi_{8016}(1037,\cdot)\) \(\chi_{8016}(1061,\cdot)\) \(\chi_{8016}(1085,\cdot)\) \(\chi_{8016}(1133,\cdot)\) \(\chi_{8016}(1157,\cdot)\) \(\chi_{8016}(1229,\cdot)\) \(\chi_{8016}(1325,\cdot)\) \(\chi_{8016}(1349,\cdot)\) \(\chi_{8016}(1373,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((1,i,-1,e\left(\frac{1}{166}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{251}{332}\right)\)\(e\left(\frac{35}{166}\right)\)\(e\left(\frac{305}{332}\right)\)\(e\left(\frac{123}{332}\right)\)\(e\left(\frac{68}{83}\right)\)\(e\left(\frac{33}{332}\right)\)\(e\left(\frac{99}{166}\right)\)\(e\left(\frac{85}{166}\right)\)\(e\left(\frac{51}{332}\right)\)\(e\left(\frac{45}{83}\right)\)
value at  e.g. 2

Related number fields

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