Properties

Conductor 2011
Order 134
Real No
Primitive Yes
Parity Odd
Orbit Label 2011.j

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(2011)
sage: chi = H[8]
pari: [g,chi] = znchar(Mod(8,2011))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2011
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 134
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 = Odd
Orbit label = 2011.j
Orbit index = 10

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 ]

\(\chi_{2011}(8,\cdot)\) \(\chi_{2011}(60,\cdot)\) \(\chi_{2011}(97,\cdot)\) \(\chi_{2011}(147,\cdot)\) \(\chi_{2011}(175,\cdot)\) \(\chi_{2011}(213,\cdot)\) \(\chi_{2011}(233,\cdot)\) \(\chi_{2011}(268,\cdot)\) \(\chi_{2011}(307,\cdot)\) \(\chi_{2011}(378,\cdot)\) \(\chi_{2011}(386,\cdot)\) \(\chi_{2011}(410,\cdot)\) \(\chi_{2011}(418,\cdot)\) \(\chi_{2011}(422,\cdot)\) \(\chi_{2011}(450,\cdot)\) \(\chi_{2011}(512,\cdot)\) \(\chi_{2011}(557,\cdot)\) \(\chi_{2011}(572,\cdot)\) \(\chi_{2011}(592,\cdot)\) \(\chi_{2011}(597,\cdot)\) \(\chi_{2011}(609,\cdot)\) \(\chi_{2011}(611,\cdot)\) \(\chi_{2011}(646,\cdot)\) \(\chi_{2011}(678,\cdot)\) \(\chi_{2011}(725,\cdot)\) \(\chi_{2011}(742,\cdot)\) \(\chi_{2011}(767,\cdot)\) \(\chi_{2011}(823,\cdot)\) \(\chi_{2011}(824,\cdot)\) \(\chi_{2011}(835,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{49}{134}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{79}{134}\right)\)\(e\left(\frac{49}{134}\right)\)\(e\left(\frac{12}{67}\right)\)\(e\left(\frac{30}{67}\right)\)\(e\left(\frac{64}{67}\right)\)\(e\left(\frac{103}{134}\right)\)\(e\left(\frac{103}{134}\right)\)\(e\left(\frac{49}{67}\right)\)\(e\left(\frac{5}{134}\right)\)\(e\left(\frac{27}{134}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{67})\)