Properties

Conductor 675
Order 45
Real No
Primitive No
Parity Even
Orbit Label 9450.fm

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[9031]
pari: [g,chi] = znchar(Mod(9031,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 675
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.fm
Orbit index = 143

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 ]

\(\chi_{9450}(211,\cdot)\) \(\chi_{9450}(421,\cdot)\) \(\chi_{9450}(841,\cdot)\) \(\chi_{9450}(1471,\cdot)\) \(\chi_{9450}(1681,\cdot)\) \(\chi_{9450}(2311,\cdot)\) \(\chi_{9450}(2731,\cdot)\) \(\chi_{9450}(2941,\cdot)\) \(\chi_{9450}(3361,\cdot)\) \(\chi_{9450}(3571,\cdot)\) \(\chi_{9450}(3991,\cdot)\) \(\chi_{9450}(4621,\cdot)\) \(\chi_{9450}(4831,\cdot)\) \(\chi_{9450}(5461,\cdot)\) \(\chi_{9450}(5881,\cdot)\) \(\chi_{9450}(6091,\cdot)\) \(\chi_{9450}(6511,\cdot)\) \(\chi_{9450}(6721,\cdot)\) \(\chi_{9450}(7141,\cdot)\) \(\chi_{9450}(7771,\cdot)\) \(\chi_{9450}(7981,\cdot)\) \(\chi_{9450}(8611,\cdot)\) \(\chi_{9450}(9031,\cdot)\) \(\chi_{9450}(9241,\cdot)\)

Inducing primitive character

\(\chi_{675}(256,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{2}{5}\right),1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{8}{45}\right)\)\(e\left(\frac{7}{45}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{13}{45}\right)\)\(e\left(\frac{11}{45}\right)\)\(e\left(\frac{4}{45}\right)\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{7}{45}\right)\)\(e\left(\frac{7}{9}\right)\)
value at  e.g. 2

Related number fields

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