Properties

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

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[331]
pari: [g,chi] = znchar(Mod(331,9450))

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.fl
Orbit index = 142

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 ]

\(\chi_{9450}(331,\cdot)\) \(\chi_{9450}(571,\cdot)\) \(\chi_{9450}(961,\cdot)\) \(\chi_{9450}(1591,\cdot)\) \(\chi_{9450}(1831,\cdot)\) \(\chi_{9450}(2221,\cdot)\) \(\chi_{9450}(2461,\cdot)\) \(\chi_{9450}(3091,\cdot)\) \(\chi_{9450}(3481,\cdot)\) \(\chi_{9450}(3721,\cdot)\) \(\chi_{9450}(4111,\cdot)\) \(\chi_{9450}(4741,\cdot)\) \(\chi_{9450}(4981,\cdot)\) \(\chi_{9450}(5371,\cdot)\) \(\chi_{9450}(5611,\cdot)\) \(\chi_{9450}(6241,\cdot)\) \(\chi_{9450}(6631,\cdot)\) \(\chi_{9450}(6871,\cdot)\) \(\chi_{9450}(7261,\cdot)\) \(\chi_{9450}(7891,\cdot)\) \(\chi_{9450}(8131,\cdot)\) \(\chi_{9450}(8521,\cdot)\) \(\chi_{9450}(8761,\cdot)\) \(\chi_{9450}(9391,\cdot)\)

Inducing primitive character

\(\chi_{4725}(331,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{13}{45}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{38}{45}\right)\)\(e\left(\frac{31}{45}\right)\)\(e\left(\frac{14}{45}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{5}{9}\right)\)
value at  e.g. 2

Related number fields

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