Properties

Conductor 403
Order 15
Real No
Primitive No
Parity Even
Orbit Label 4030.ef

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[81]
pari: [g,chi] = znchar(Mod(81,4030))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 403
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 15
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.ef
Orbit index = 110

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 ]

\(\chi_{4030}(81,\cdot)\) \(\chi_{4030}(971,\cdot)\) \(\chi_{4030}(1621,\cdot)\) \(\chi_{4030}(2291,\cdot)\) \(\chi_{4030}(2531,\cdot)\) \(\chi_{4030}(3331,\cdot)\) \(\chi_{4030}(3831,\cdot)\) \(\chi_{4030}(3851,\cdot)\)

Inducing primitive character

\(\chi_{403}(81,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{2}{15}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{8}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)