Properties

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

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[131]
pari: [g,chi] = znchar(Mod(131,9450))

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.gf
Orbit index = 162

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 ]

\(\chi_{9450}(131,\cdot)\) \(\chi_{9450}(731,\cdot)\) \(\chi_{9450}(761,\cdot)\) \(\chi_{9450}(1361,\cdot)\) \(\chi_{9450}(1391,\cdot)\) \(\chi_{9450}(1991,\cdot)\) \(\chi_{9450}(2021,\cdot)\) \(\chi_{9450}(2621,\cdot)\) \(\chi_{9450}(3281,\cdot)\) \(\chi_{9450}(3881,\cdot)\) \(\chi_{9450}(3911,\cdot)\) \(\chi_{9450}(4511,\cdot)\) \(\chi_{9450}(4541,\cdot)\) \(\chi_{9450}(5141,\cdot)\) \(\chi_{9450}(5171,\cdot)\) \(\chi_{9450}(5771,\cdot)\) \(\chi_{9450}(6431,\cdot)\) \(\chi_{9450}(7031,\cdot)\) \(\chi_{9450}(7061,\cdot)\) \(\chi_{9450}(7661,\cdot)\) \(\chi_{9450}(7691,\cdot)\) \(\chi_{9450}(8291,\cdot)\) \(\chi_{9450}(8321,\cdot)\) \(\chi_{9450}(8921,\cdot)\)

Inducing primitive character

\(\chi_{4725}(131,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{61}{90}\right)\)\(e\left(\frac{89}{90}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{71}{90}\right)\)\(e\left(\frac{37}{90}\right)\)\(e\left(\frac{23}{90}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{22}{45}\right)\)\(e\left(\frac{4}{9}\right)\)
value at  e.g. 2

Related number fields

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