Properties

Conductor 675
Order 90
Real No
Primitive No
Parity Even
Orbit Label 9450.gl

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[169]
pari: [g,chi] = znchar(Mod(169,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 675
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 90
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.gl
Orbit index = 168

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 ]

\(\chi_{9450}(169,\cdot)\) \(\chi_{9450}(589,\cdot)\) \(\chi_{9450}(1219,\cdot)\) \(\chi_{9450}(1429,\cdot)\) \(\chi_{9450}(2059,\cdot)\) \(\chi_{9450}(2479,\cdot)\) \(\chi_{9450}(2689,\cdot)\) \(\chi_{9450}(3109,\cdot)\) \(\chi_{9450}(3319,\cdot)\) \(\chi_{9450}(3739,\cdot)\) \(\chi_{9450}(4369,\cdot)\) \(\chi_{9450}(4579,\cdot)\) \(\chi_{9450}(5209,\cdot)\) \(\chi_{9450}(5629,\cdot)\) \(\chi_{9450}(5839,\cdot)\) \(\chi_{9450}(6259,\cdot)\) \(\chi_{9450}(6469,\cdot)\) \(\chi_{9450}(6889,\cdot)\) \(\chi_{9450}(7519,\cdot)\) \(\chi_{9450}(7729,\cdot)\) \(\chi_{9450}(8359,\cdot)\) \(\chi_{9450}(8779,\cdot)\) \(\chi_{9450}(8989,\cdot)\) \(\chi_{9450}(9409,\cdot)\)

Inducing primitive character

\(\chi_{675}(169,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{9}{10}\right),1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{43}{45}\right)\)\(e\left(\frac{19}{90}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{61}{90}\right)\)\(e\left(\frac{31}{45}\right)\)\(e\left(\frac{44}{45}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{1}{18}\right)\)
value at  e.g. 2

Related number fields

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