Properties

Modulus 8016
Conductor 2004
Order 166
Real no
Primitive no
Minimal yes
Parity even
Orbit label 8016.bk

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([83,0,83,132]))
 
pari: [g,chi] = znchar(Mod(47,8016))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 8016
Conductor = 2004
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 = even
Orbit label = 8016.bk
Orbit index = 37

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 ]
 

\(\chi_{8016}(47,\cdot)\) \(\chi_{8016}(191,\cdot)\) \(\chi_{8016}(239,\cdot)\) \(\chi_{8016}(383,\cdot)\) \(\chi_{8016}(431,\cdot)\) \(\chi_{8016}(623,\cdot)\) \(\chi_{8016}(671,\cdot)\) \(\chi_{8016}(767,\cdot)\) \(\chi_{8016}(815,\cdot)\) \(\chi_{8016}(863,\cdot)\) \(\chi_{8016}(911,\cdot)\) \(\chi_{8016}(959,\cdot)\) \(\chi_{8016}(1295,\cdot)\) \(\chi_{8016}(1343,\cdot)\) \(\chi_{8016}(1535,\cdot)\) \(\chi_{8016}(1631,\cdot)\) \(\chi_{8016}(1679,\cdot)\) \(\chi_{8016}(1727,\cdot)\) \(\chi_{8016}(1967,\cdot)\) \(\chi_{8016}(2015,\cdot)\) \(\chi_{8016}(2111,\cdot)\) \(\chi_{8016}(2207,\cdot)\) \(\chi_{8016}(2255,\cdot)\) \(\chi_{8016}(2303,\cdot)\) \(\chi_{8016}(2399,\cdot)\) \(\chi_{8016}(2495,\cdot)\) \(\chi_{8016}(2543,\cdot)\) \(\chi_{8016}(2735,\cdot)\) \(\chi_{8016}(2927,\cdot)\) \(\chi_{8016}(3071,\cdot)\) ...

Values on generators

\((3007,2005,5345,673)\) → \((-1,1,-1,e\left(\frac{66}{83}\right))\)

Values

-11571113171923252931
\(1\)\(1\)\(e\left(\frac{49}{166}\right)\)\(e\left(\frac{55}{166}\right)\)\(e\left(\frac{22}{83}\right)\)\(e\left(\frac{75}{83}\right)\)\(e\left(\frac{107}{166}\right)\)\(e\left(\frac{103}{166}\right)\)\(e\left(\frac{60}{83}\right)\)\(e\left(\frac{49}{83}\right)\)\(e\left(\frac{129}{166}\right)\)\(e\left(\frac{11}{166}\right)\)
value at  e.g. 2

Related number fields

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