Properties

Conductor 9900
Order 30
Real No
Primitive Yes
Parity Even
Orbit Label 9900.kr

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[59]
pari: [g,chi] = znchar(Mod(59,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 9900
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 = Even
Orbit label = 9900.kr
Orbit index = 278

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 ]

\(\chi_{9900}(59,\cdot)\) \(\chi_{9900}(779,\cdot)\) \(\chi_{9900}(839,\cdot)\) \(\chi_{9900}(1919,\cdot)\) \(\chi_{9900}(3359,\cdot)\) \(\chi_{9900}(4079,\cdot)\) \(\chi_{9900}(7439,\cdot)\) \(\chi_{9900}(8519,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{7}{10}\right),e\left(\frac{1}{5}\right))\)

Values

-117131719232931374143
\(1\)\(1\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{1}{3}\right)\)
value at  e.g. 2

Related number fields

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