Properties

Modulus 9900
Conductor 1100
Order 20
Real no
Primitive no
Minimal yes
Parity odd
Orbit label 9900.ha

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(9900)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([10,0,1,18]))
 
pari: [g,chi] = znchar(Mod(127,9900))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 9900
Conductor = 1100
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 9900.ha
Orbit index = 183

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 ]
 

\(\chi_{9900}(127,\cdot)\) \(\chi_{9900}(523,\cdot)\) \(\chi_{9900}(667,\cdot)\) \(\chi_{9900}(1603,\cdot)\) \(\chi_{9900}(5887,\cdot)\) \(\chi_{9900}(7147,\cdot)\) \(\chi_{9900}(8263,\cdot)\) \(\chi_{9900}(8983,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,1,e\left(\frac{1}{20}\right),e\left(\frac{9}{10}\right))\)

Values

-117131719232931374143
\(-1\)\(1\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{17}{20}\right)\)\(-i\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{10}\right)\)\(i\)\(e\left(\frac{9}{10}\right)\)\(-i\)
value at  e.g. 2

Related number fields

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