Properties

Conductor 900
Order 60
Real No
Primitive No
Parity Even
Orbit Label 9900.lk

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(9900)
sage: chi = H[67]
pari: [g,chi] = znchar(Mod(67,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 900
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 = 9900.lk
Orbit index = 297

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 ]

\(\chi_{9900}(67,\cdot)\) \(\chi_{9900}(463,\cdot)\) \(\chi_{9900}(727,\cdot)\) \(\chi_{9900}(1123,\cdot)\) \(\chi_{9900}(2047,\cdot)\) \(\chi_{9900}(3103,\cdot)\) \(\chi_{9900}(4027,\cdot)\) \(\chi_{9900}(4423,\cdot)\) \(\chi_{9900}(4687,\cdot)\) \(\chi_{9900}(5083,\cdot)\) \(\chi_{9900}(6403,\cdot)\) \(\chi_{9900}(6667,\cdot)\) \(\chi_{9900}(7063,\cdot)\) \(\chi_{9900}(7987,\cdot)\) \(\chi_{9900}(8383,\cdot)\) \(\chi_{9900}(8647,\cdot)\)

Inducing primitive character

\(\chi_{900}(67,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{13}{20}\right),1)\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{19}{60}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{7}{12}\right)\)
value at  e.g. 2

Related number fields

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