Properties

Conductor 2475
Order 30
Real No
Primitive No
Parity Odd
Orbit Label 9900.ic

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[61]
pari: [g,chi] = znchar(Mod(61,9900))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2475
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 = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Odd
Orbit label = 9900.ic
Orbit index = 211

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 ]

\(\chi_{9900}(61,\cdot)\) \(\chi_{9900}(2581,\cdot)\) \(\chi_{9900}(3121,\cdot)\) \(\chi_{9900}(3361,\cdot)\) \(\chi_{9900}(3841,\cdot)\) \(\chi_{9900}(5881,\cdot)\) \(\chi_{9900}(6421,\cdot)\) \(\chi_{9900}(7141,\cdot)\)

Inducing primitive character

\(\chi_{2475}(61,\cdot)\)

Values on generators

\((4951,5501,2377,4501)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{9}{10}\right))\)

Values

-117131719232931374143
\(-1\)\(1\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(-1\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(1\)\(e\left(\frac{7}{30}\right)\)\(e\left(\frac{1}{6}\right)\)
value at  e.g. 2

Related number fields

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