Properties

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

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[579]
pari: [g,chi] = znchar(Mod(579,4030))

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.ho
Orbit index = 197

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 ]

\(\chi_{4030}(579,\cdot)\) \(\chi_{4030}(1159,\cdot)\) \(\chi_{4030}(1189,\cdot)\) \(\chi_{4030}(1419,\cdot)\) \(\chi_{4030}(1749,\cdot)\) \(\chi_{4030}(1779,\cdot)\) \(\chi_{4030}(1939,\cdot)\) \(\chi_{4030}(2039,\cdot)\) \(\chi_{4030}(2099,\cdot)\) \(\chi_{4030}(2559,\cdot)\) \(\chi_{4030}(2749,\cdot)\) \(\chi_{4030}(2979,\cdot)\) \(\chi_{4030}(3049,\cdot)\) \(\chi_{4030}(3599,\cdot)\) \(\chi_{4030}(3919,\cdot)\) \(\chi_{4030}(3959,\cdot)\)

Inducing primitive character

\(\chi_{2015}(579,\cdot)\)

Values on generators

\((807,1861,2731)\) → \((-1,e\left(\frac{11}{12}\right),e\left(\frac{29}{30}\right))\)

Values

-1137911171921232729
\(1\)\(1\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{11}{30}\right)\)
value at  e.g. 2

Related number fields

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