Properties

Modulus 2100
Conductor 525
Order 60
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2100.dk

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([0,30,21,40]))
 
pari: [g,chi] = znchar(Mod(53,2100))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 2100
Conductor = 525
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 60
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.dk
Orbit index = 89

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 ]
 

\(\chi_{2100}(53,\cdot)\) \(\chi_{2100}(137,\cdot)\) \(\chi_{2100}(233,\cdot)\) \(\chi_{2100}(317,\cdot)\) \(\chi_{2100}(473,\cdot)\) \(\chi_{2100}(653,\cdot)\) \(\chi_{2100}(737,\cdot)\) \(\chi_{2100}(977,\cdot)\) \(\chi_{2100}(1073,\cdot)\) \(\chi_{2100}(1313,\cdot)\) \(\chi_{2100}(1397,\cdot)\) \(\chi_{2100}(1577,\cdot)\) \(\chi_{2100}(1733,\cdot)\) \(\chi_{2100}(1817,\cdot)\) \(\chi_{2100}(1913,\cdot)\) \(\chi_{2100}(1997,\cdot)\)

Values on generators

\((1051,701,1177,1501)\) → \((1,-1,e\left(\frac{7}{20}\right),e\left(\frac{2}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{9}{10}\right)\)\(i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)