Properties

Conductor 287
Order 60
Real No
Primitive No
Parity Even
Orbit Label 6027.dd

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6027)
 
sage: chi = H[226]
 
pari: [g,chi] = znchar(Mod(226,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 287
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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.dd
Orbit index = 82

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 ]
 

\(\chi_{6027}(226,\cdot)\) \(\chi_{6027}(361,\cdot)\) \(\chi_{6027}(1402,\cdot)\) \(\chi_{6027}(1537,\cdot)\) \(\chi_{6027}(1843,\cdot)\) \(\chi_{6027}(2137,\cdot)\) \(\chi_{6027}(2578,\cdot)\) \(\chi_{6027}(2872,\cdot)\) \(\chi_{6027}(3301,\cdot)\) \(\chi_{6027}(3313,\cdot)\) \(\chi_{6027}(4477,\cdot)\) \(\chi_{6027}(4489,\cdot)\) \(\chi_{6027}(4918,\cdot)\) \(\chi_{6027}(5212,\cdot)\) \(\chi_{6027}(5653,\cdot)\) \(\chi_{6027}(5947,\cdot)\)

Inducing primitive character

\(\chi_{287}(226,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{7}{20}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{49}{60}\right)\)
value at  e.g. 2

Related number fields

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