Properties

Conductor 660
Order 20
Real No
Primitive No
Parity Even
Orbit Label 9900.hk

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[107]
pari: [g,chi] = znchar(Mod(107,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 660
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 20
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.hk
Orbit index = 193

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 ]

\(\chi_{9900}(107,\cdot)\) \(\chi_{9900}(1007,\cdot)\) \(\chi_{9900}(1943,\cdot)\) \(\chi_{9900}(2807,\cdot)\) \(\chi_{9900}(5507,\cdot)\) \(\chi_{9900}(6443,\cdot)\) \(\chi_{9900}(7343,\cdot)\) \(\chi_{9900}(9143,\cdot)\)

Inducing primitive character

\(\chi_{660}(107,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,-1,i,e\left(\frac{3}{10}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{9}{10}\right)\)\(-i\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{2}{5}\right)\)\(-i\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)