Properties

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

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([83,83,83,95]))
 
pari: [g,chi] = znchar(Mod(683,4008))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4008
Conductor = 4008
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 4008.be
Orbit index = 31

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 ]
 

\(\chi_{4008}(35,\cdot)\) \(\chi_{4008}(59,\cdot)\) \(\chi_{4008}(83,\cdot)\) \(\chi_{4008}(131,\cdot)\) \(\chi_{4008}(155,\cdot)\) \(\chi_{4008}(227,\cdot)\) \(\chi_{4008}(323,\cdot)\) \(\chi_{4008}(347,\cdot)\) \(\chi_{4008}(371,\cdot)\) \(\chi_{4008}(443,\cdot)\) \(\chi_{4008}(587,\cdot)\) \(\chi_{4008}(611,\cdot)\) \(\chi_{4008}(635,\cdot)\) \(\chi_{4008}(659,\cdot)\) \(\chi_{4008}(683,\cdot)\) \(\chi_{4008}(707,\cdot)\) \(\chi_{4008}(779,\cdot)\) \(\chi_{4008}(803,\cdot)\) \(\chi_{4008}(827,\cdot)\) \(\chi_{4008}(875,\cdot)\) \(\chi_{4008}(971,\cdot)\) \(\chi_{4008}(995,\cdot)\) \(\chi_{4008}(1019,\cdot)\) \(\chi_{4008}(1043,\cdot)\) \(\chi_{4008}(1115,\cdot)\) \(\chi_{4008}(1163,\cdot)\) \(\chi_{4008}(1259,\cdot)\) \(\chi_{4008}(1307,\cdot)\) \(\chi_{4008}(1379,\cdot)\) \(\chi_{4008}(1403,\cdot)\) ...

Values on generators

\((3007,2005,1337,673)\) → \((-1,-1,-1,e\left(\frac{95}{166}\right))\)

Values

-11571113171923252931
\(-1\)\(1\)\(e\left(\frac{95}{166}\right)\)\(e\left(\frac{5}{166}\right)\)\(e\left(\frac{87}{166}\right)\)\(e\left(\frac{37}{83}\right)\)\(e\left(\frac{69}{83}\right)\)\(e\left(\frac{16}{83}\right)\)\(e\left(\frac{109}{166}\right)\)\(e\left(\frac{12}{83}\right)\)\(e\left(\frac{70}{83}\right)\)\(e\left(\frac{1}{166}\right)\)
value at  e.g. 2

Related number fields

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