Properties

Conductor 9900
Order 60
Real No
Primitive Yes
Parity Even
Orbit Label 9900.lp

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[103]
pari: [g,chi] = znchar(Mod(103,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 9900
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 = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 9900.lp
Orbit index = 302

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 ]

\(\chi_{9900}(103,\cdot)\) \(\chi_{9900}(427,\cdot)\) \(\chi_{9900}(823,\cdot)\) \(\chi_{9900}(2347,\cdot)\) \(\chi_{9900}(2887,\cdot)\) \(\chi_{9900}(4183,\cdot)\) \(\chi_{9900}(5263,\cdot)\) \(\chi_{9900}(5647,\cdot)\) \(\chi_{9900}(5767,\cdot)\) \(\chi_{9900}(6187,\cdot)\) \(\chi_{9900}(6703,\cdot)\) \(\chi_{9900}(7027,\cdot)\) \(\chi_{9900}(7423,\cdot)\) \(\chi_{9900}(7483,\cdot)\) \(\chi_{9900}(8563,\cdot)\) \(\chi_{9900}(9067,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{7}{20}\right),e\left(\frac{1}{5}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{59}{60}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{12}\right)\)
value at  e.g. 2

Related number fields

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