Properties

Conductor 175
Order 60
Real No
Primitive No
Parity Even
Orbit Label 9450.fz

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[5563]
pari: [g,chi] = znchar(Mod(5563,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 175
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.fz
Orbit index = 156

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 ]

\(\chi_{9450}(703,\cdot)\) \(\chi_{9450}(1027,\cdot)\) \(\chi_{9450}(1783,\cdot)\) \(\chi_{9450}(1837,\cdot)\) \(\chi_{9450}(2917,\cdot)\) \(\chi_{9450}(3673,\cdot)\) \(\chi_{9450}(3727,\cdot)\) \(\chi_{9450}(4483,\cdot)\) \(\chi_{9450}(5563,\cdot)\) \(\chi_{9450}(5617,\cdot)\) \(\chi_{9450}(6373,\cdot)\) \(\chi_{9450}(6697,\cdot)\) \(\chi_{9450}(7453,\cdot)\) \(\chi_{9450}(8263,\cdot)\) \(\chi_{9450}(8587,\cdot)\) \(\chi_{9450}(9397,\cdot)\)

Inducing primitive character

\(\chi_{175}(138,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((1,e\left(\frac{19}{20}\right),e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{3}{10}\right)\)\(i\)
value at  e.g. 2

Related number fields

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