Properties

Conductor 4725
Order 45
Real No
Primitive No
Parity Even
Orbit Label 9450.fk

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(9450)
sage: chi = H[121]
pari: [g,chi] = znchar(Mod(121,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4725
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 45
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 = 9450.fk
Orbit index = 141

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 ]

\(\chi_{9450}(121,\cdot)\) \(\chi_{9450}(781,\cdot)\) \(\chi_{9450}(1381,\cdot)\) \(\chi_{9450}(1411,\cdot)\) \(\chi_{9450}(2011,\cdot)\) \(\chi_{9450}(2041,\cdot)\) \(\chi_{9450}(2641,\cdot)\) \(\chi_{9450}(2671,\cdot)\) \(\chi_{9450}(3271,\cdot)\) \(\chi_{9450}(3931,\cdot)\) \(\chi_{9450}(4531,\cdot)\) \(\chi_{9450}(4561,\cdot)\) \(\chi_{9450}(5161,\cdot)\) \(\chi_{9450}(5191,\cdot)\) \(\chi_{9450}(5791,\cdot)\) \(\chi_{9450}(5821,\cdot)\) \(\chi_{9450}(6421,\cdot)\) \(\chi_{9450}(7081,\cdot)\) \(\chi_{9450}(7681,\cdot)\) \(\chi_{9450}(7711,\cdot)\) \(\chi_{9450}(8311,\cdot)\) \(\chi_{9450}(8341,\cdot)\) \(\chi_{9450}(8941,\cdot)\) \(\chi_{9450}(8971,\cdot)\)

Inducing primitive character

\(\chi_{4725}(121,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{3}{5}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{43}{45}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{7}{45}\right)\)\(e\left(\frac{29}{45}\right)\)\(e\left(\frac{1}{45}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{43}{45}\right)\)\(e\left(\frac{7}{9}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{45})\)