Properties

Conductor 403
Order 60
Real No
Primitive No
Parity Even
Orbit Label 4030.hq

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[11]
pari: [g,chi] = znchar(Mod(11,4030))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 403
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.hq
Orbit index = 199

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 ]

\(\chi_{4030}(11,\cdot)\) \(\chi_{4030}(241,\cdot)\) \(\chi_{4030}(301,\cdot)\) \(\chi_{4030}(761,\cdot)\) \(\chi_{4030}(921,\cdot)\) \(\chi_{4030}(951,\cdot)\) \(\chi_{4030}(1571,\cdot)\) \(\chi_{4030}(1801,\cdot)\) \(\chi_{4030}(2121,\cdot)\) \(\chi_{4030}(2151,\cdot)\) \(\chi_{4030}(2411,\cdot)\) \(\chi_{4030}(2741,\cdot)\) \(\chi_{4030}(2931,\cdot)\) \(\chi_{4030}(3421,\cdot)\) \(\chi_{4030}(3971,\cdot)\) \(\chi_{4030}(4011,\cdot)\)

Inducing primitive character

\(\chi_{403}(11,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((1,e\left(\frac{7}{12}\right),e\left(\frac{23}{30}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{43}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{7}{30}\right)\)
value at  e.g. 2

Related number fields

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