Properties

Conductor 4725
Order 90
Real No
Primitive No
Parity Even
Orbit Label 9450.gw

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[479]
pari: [g,chi] = znchar(Mod(479,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4725
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.gw
Orbit index = 179

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 ]

\(\chi_{9450}(479,\cdot)\) \(\chi_{9450}(509,\cdot)\) \(\chi_{9450}(1109,\cdot)\) \(\chi_{9450}(1139,\cdot)\) \(\chi_{9450}(1739,\cdot)\) \(\chi_{9450}(1769,\cdot)\) \(\chi_{9450}(2369,\cdot)\) \(\chi_{9450}(3029,\cdot)\) \(\chi_{9450}(3629,\cdot)\) \(\chi_{9450}(3659,\cdot)\) \(\chi_{9450}(4259,\cdot)\) \(\chi_{9450}(4289,\cdot)\) \(\chi_{9450}(4889,\cdot)\) \(\chi_{9450}(4919,\cdot)\) \(\chi_{9450}(5519,\cdot)\) \(\chi_{9450}(6179,\cdot)\) \(\chi_{9450}(6779,\cdot)\) \(\chi_{9450}(6809,\cdot)\) \(\chi_{9450}(7409,\cdot)\) \(\chi_{9450}(7439,\cdot)\) \(\chi_{9450}(8039,\cdot)\) \(\chi_{9450}(8069,\cdot)\) \(\chi_{9450}(8669,\cdot)\) \(\chi_{9450}(9329,\cdot)\)

Inducing primitive character

\(\chi_{4725}(479,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{1}{10}\right),e\left(\frac{1}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{29}{90}\right)\)\(e\left(\frac{23}{45}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{53}{90}\right)\)\(e\left(\frac{67}{90}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{23}{45}\right)\)\(e\left(\frac{1}{18}\right)\)
value at  e.g. 2

Related number fields

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