Properties

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

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[21]
pari: [g,chi] = znchar(Mod(21,4030))

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.gb
Orbit index = 158

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 ]

\(\chi_{4030}(21,\cdot)\) \(\chi_{4030}(291,\cdot)\) \(\chi_{4030}(551,\cdot)\) \(\chi_{4030}(941,\cdot)\) \(\chi_{4030}(1071,\cdot)\) \(\chi_{4030}(1191,\cdot)\) \(\chi_{4030}(1841,\cdot)\) \(\chi_{4030}(1851,\cdot)\) \(\chi_{4030}(2101,\cdot)\) \(\chi_{4030}(2111,\cdot)\) \(\chi_{4030}(2491,\cdot)\) \(\chi_{4030}(2501,\cdot)\) \(\chi_{4030}(2621,\cdot)\) \(\chi_{4030}(3401,\cdot)\) \(\chi_{4030}(3661,\cdot)\) \(\chi_{4030}(3671,\cdot)\)

Inducing primitive character

\(\chi_{403}(21,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((1,i,e\left(\frac{29}{30}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{49}{60}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{7}{10}\right)\)
value at  e.g. 2

Related number fields

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