Properties

Modulus 2100
Conductor 700
Order 30
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2100.da

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([15,0,12,5]))
 
pari: [g,chi] = znchar(Mod(31,2100))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 2100
Conductor = 700
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 30
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 = 2100.da
Orbit index = 79

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 ]
 

\(\chi_{2100}(31,\cdot)\) \(\chi_{2100}(271,\cdot)\) \(\chi_{2100}(691,\cdot)\) \(\chi_{2100}(871,\cdot)\) \(\chi_{2100}(1111,\cdot)\) \(\chi_{2100}(1291,\cdot)\) \(\chi_{2100}(1531,\cdot)\) \(\chi_{2100}(1711,\cdot)\)

Values on generators

\((1051,701,1177,1501)\) → \((-1,1,e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{1}{10}\right)\)\(-1\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)