Properties

Conductor 155
Order 60
Real No
Primitive No
Parity Even
Orbit Label 4030.go

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(4030)
 
sage: chi = H[53]
 
pari: [g,chi] = znchar(Mod(53,4030))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 155
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 = 4030.go
Orbit index = 171

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 ]
 

\(\chi_{4030}(53,\cdot)\) \(\chi_{4030}(313,\cdot)\) \(\chi_{4030}(703,\cdot)\) \(\chi_{4030}(1067,\cdot)\) \(\chi_{4030}(1717,\cdot)\) \(\chi_{4030}(1873,\cdot)\) \(\chi_{4030}(1977,\cdot)\) \(\chi_{4030}(2367,\cdot)\) \(\chi_{4030}(2497,\cdot)\) \(\chi_{4030}(2523,\cdot)\) \(\chi_{4030}(2783,\cdot)\) \(\chi_{4030}(3173,\cdot)\) \(\chi_{4030}(3277,\cdot)\) \(\chi_{4030}(3303,\cdot)\) \(\chi_{4030}(3537,\cdot)\) \(\chi_{4030}(3927,\cdot)\)

Inducing primitive character

\(\chi_{155}(53,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((-i,1,e\left(\frac{17}{30}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{3}{5}\right)\)
value at  e.g. 2

Related number fields

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