Properties

Conductor 1575
Order 60
Real No
Primitive No
Parity Even
Orbit Label 9450.fo

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(9450)
sage: chi = H[397]
pari: [g,chi] = znchar(Mod(397,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1575
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 = 9450.fo
Orbit index = 145

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 ]

\(\chi_{9450}(397,\cdot)\) \(\chi_{9450}(577,\cdot)\) \(\chi_{9450}(1153,\cdot)\) \(\chi_{9450}(1333,\cdot)\) \(\chi_{9450}(2287,\cdot)\) \(\chi_{9450}(2467,\cdot)\) \(\chi_{9450}(3223,\cdot)\) \(\chi_{9450}(4177,\cdot)\) \(\chi_{9450}(4933,\cdot)\) \(\chi_{9450}(5113,\cdot)\) \(\chi_{9450}(6067,\cdot)\) \(\chi_{9450}(6247,\cdot)\) \(\chi_{9450}(6823,\cdot)\) \(\chi_{9450}(7003,\cdot)\) \(\chi_{9450}(8137,\cdot)\) \(\chi_{9450}(8713,\cdot)\)

Inducing primitive character

\(\chi_{1575}(1447,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{5}{12}\right)\)
value at  e.g. 2

Related number fields

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