Properties

Conductor 2015
Order 60
Real No
Primitive No
Parity Even
Orbit Label 4030.hk

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[89]
pari: [g,chi] = znchar(Mod(89,4030))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2015
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.hk
Orbit index = 193

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 ]

\(\chi_{4030}(89,\cdot)\) \(\chi_{4030}(449,\cdot)\) \(\chi_{4030}(709,\cdot)\) \(\chi_{4030}(1449,\cdot)\) \(\chi_{4030}(1579,\cdot)\) \(\chi_{4030}(2069,\cdot)\) \(\chi_{4030}(2199,\cdot)\) \(\chi_{4030}(2619,\cdot)\) \(\chi_{4030}(2689,\cdot)\) \(\chi_{4030}(2819,\cdot)\) \(\chi_{4030}(2879,\cdot)\) \(\chi_{4030}(3239,\cdot)\) \(\chi_{4030}(3309,\cdot)\) \(\chi_{4030}(3439,\cdot)\) \(\chi_{4030}(3499,\cdot)\) \(\chi_{4030}(3859,\cdot)\)

Inducing primitive character

\(\chi_{2015}(89,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((-1,e\left(\frac{7}{12}\right),e\left(\frac{1}{10}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{7}{30}\right)\)
value at  e.g. 2

Related number fields

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