Properties

Conductor 2011
Order 30
Real No
Primitive Yes
Parity Odd
Orbit Label 2011.h

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[72]
pari: [g,chi] = znchar(Mod(72,2011))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2011
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 = Odd
Orbit label = 2011.h
Orbit index = 8

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 ]

\(\chi_{2011}(72,\cdot)\) \(\chi_{2011}(810,\cdot)\) \(\chi_{2011}(849,\cdot)\) \(\chi_{2011}(1099,\cdot)\) \(\chi_{2011}(1148,\cdot)\) \(\chi_{2011}(1256,\cdot)\) \(\chi_{2011}(1312,\cdot)\) \(\chi_{2011}(1497,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{11}{30}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{17}{30}\right)\)\(-1\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{7}{30}\right)\)
value at  e.g. 2

Related number fields

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