Properties

Conductor 525
Order 60
Real no
Primitive no
Minimal yes
Parity even
Orbit label 9450.fq

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(9450)
 
sage: chi = H[3887]
 
pari: [g,chi] = znchar(Mod(3887,9450))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
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 = 9450.fq
Orbit index = 147

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{9450}(53,\cdot)\) \(\chi_{9450}(863,\cdot)\) \(\chi_{9450}(1187,\cdot)\) \(\chi_{9450}(1997,\cdot)\) \(\chi_{9450}(2753,\cdot)\) \(\chi_{9450}(3077,\cdot)\) \(\chi_{9450}(3833,\cdot)\) \(\chi_{9450}(3887,\cdot)\) \(\chi_{9450}(4967,\cdot)\) \(\chi_{9450}(5723,\cdot)\) \(\chi_{9450}(5777,\cdot)\) \(\chi_{9450}(6533,\cdot)\) \(\chi_{9450}(7613,\cdot)\) \(\chi_{9450}(7667,\cdot)\) \(\chi_{9450}(8423,\cdot)\) \(\chi_{9450}(8747,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((-1,e\left(\frac{9}{20}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{41}{60}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(-i\)
value at  e.g. 2

Related number fields

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