Properties

Modulus 2100
Conductor 2100
Order 20
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 2100.cp

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2100)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([10,10,3,10]))
 
pari: [g,chi] = znchar(Mod(83,2100))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 2100
Conductor = 2100
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 20
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 = 2100.cp
Orbit index = 68

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 ]
 

\(\chi_{2100}(83,\cdot)\) \(\chi_{2100}(167,\cdot)\) \(\chi_{2100}(503,\cdot)\) \(\chi_{2100}(587,\cdot)\) \(\chi_{2100}(923,\cdot)\) \(\chi_{2100}(1427,\cdot)\) \(\chi_{2100}(1763,\cdot)\) \(\chi_{2100}(1847,\cdot)\)

Values on generators

\((1051,701,1177,1501)\) → \((-1,-1,e\left(\frac{3}{20}\right),-1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{19}{20}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{3}{5}\right)\)\(-i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)