Properties

Conductor 4725
Order 180
Real No
Primitive No
Parity Even
Orbit Label 9450.hi

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[23]
pari: [g,chi] = znchar(Mod(23,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4725
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 180
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.hi
Orbit index = 191

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 ]

\(\chi_{9450}(23,\cdot)\) \(\chi_{9450}(137,\cdot)\) \(\chi_{9450}(263,\cdot)\) \(\chi_{9450}(527,\cdot)\) \(\chi_{9450}(653,\cdot)\) \(\chi_{9450}(767,\cdot)\) \(\chi_{9450}(1283,\cdot)\) \(\chi_{9450}(1397,\cdot)\) \(\chi_{9450}(1523,\cdot)\) \(\chi_{9450}(1787,\cdot)\) \(\chi_{9450}(1913,\cdot)\) \(\chi_{9450}(2027,\cdot)\) \(\chi_{9450}(2153,\cdot)\) \(\chi_{9450}(2417,\cdot)\) \(\chi_{9450}(2783,\cdot)\) \(\chi_{9450}(3047,\cdot)\) \(\chi_{9450}(3173,\cdot)\) \(\chi_{9450}(3287,\cdot)\) \(\chi_{9450}(3413,\cdot)\) \(\chi_{9450}(3677,\cdot)\) \(\chi_{9450}(3803,\cdot)\) \(\chi_{9450}(3917,\cdot)\) \(\chi_{9450}(4433,\cdot)\) \(\chi_{9450}(4547,\cdot)\) \(\chi_{9450}(4673,\cdot)\) \(\chi_{9450}(4937,\cdot)\) \(\chi_{9450}(5063,\cdot)\) \(\chi_{9450}(5177,\cdot)\) \(\chi_{9450}(5303,\cdot)\) \(\chi_{9450}(5567,\cdot)\) ...

Inducing primitive character

\(\chi_{4725}(23,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{11}{20}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{7}{90}\right)\)\(e\left(\frac{61}{180}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{79}{180}\right)\)\(e\left(\frac{32}{45}\right)\)\(e\left(\frac{43}{45}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{53}{90}\right)\)\(e\left(\frac{25}{36}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{180})\)