Properties

Conductor 1575
Order 30
Real No
Primitive Yes
Parity Even
Orbit Label 1575.dv

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(1575)
sage: chi = H[614]
pari: [g,chi] = znchar(Mod(614,1575))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1575
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 30
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 1575.dv
Orbit index = 100

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 ]

\(\chi_{1575}(59,\cdot)\) \(\chi_{1575}(614,\cdot)\) \(\chi_{1575}(689,\cdot)\) \(\chi_{1575}(929,\cdot)\) \(\chi_{1575}(1004,\cdot)\) \(\chi_{1575}(1244,\cdot)\) \(\chi_{1575}(1319,\cdot)\) \(\chi_{1575}(1559,\cdot)\)

Values on generators

\((1226,127,451)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{10}\right),e\left(\frac{5}{6}\right))\)

Values

-1124811131617192223
\(1\)\(1\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{4}{5}\right)\)
value at  e.g. 2

Related number fields

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