Properties

Modulus 9900
Conductor 2475
Order 60
Real no
Primitive no
Minimal yes
Parity even
Orbit label 9900.lx

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([0,40,51,18]))
 
pari: [g,chi] = znchar(Mod(5497,9900))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 9900
Conductor = 2475
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 = 9900.lx
Orbit index = 310

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 ]
 

\(\chi_{9900}(13,\cdot)\) \(\chi_{9900}(733,\cdot)\) \(\chi_{9900}(1777,\cdot)\) \(\chi_{9900}(2173,\cdot)\) \(\chi_{9900}(2317,\cdot)\) \(\chi_{9900}(3253,\cdot)\) \(\chi_{9900}(4237,\cdot)\) \(\chi_{9900}(5497,\cdot)\) \(\chi_{9900}(6613,\cdot)\) \(\chi_{9900}(7333,\cdot)\) \(\chi_{9900}(7537,\cdot)\) \(\chi_{9900}(8377,\cdot)\) \(\chi_{9900}(8773,\cdot)\) \(\chi_{9900}(8797,\cdot)\) \(\chi_{9900}(8917,\cdot)\) \(\chi_{9900}(9853,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{3}{10}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{47}{60}\right)\)\(-i\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(i\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{11}{12}\right)\)
value at  e.g. 2

Related number fields

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