Properties

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

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[187]
pari: [g,chi] = znchar(Mod(187,9450))

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.hg
Orbit index = 189

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 ]

\(\chi_{9450}(187,\cdot)\) \(\chi_{9450}(283,\cdot)\) \(\chi_{9450}(313,\cdot)\) \(\chi_{9450}(787,\cdot)\) \(\chi_{9450}(817,\cdot)\) \(\chi_{9450}(913,\cdot)\) \(\chi_{9450}(1417,\cdot)\) \(\chi_{9450}(1447,\cdot)\) \(\chi_{9450}(1573,\cdot)\) \(\chi_{9450}(2047,\cdot)\) \(\chi_{9450}(2077,\cdot)\) \(\chi_{9450}(2173,\cdot)\) \(\chi_{9450}(2203,\cdot)\) \(\chi_{9450}(2677,\cdot)\) \(\chi_{9450}(2803,\cdot)\) \(\chi_{9450}(2833,\cdot)\) \(\chi_{9450}(3337,\cdot)\) \(\chi_{9450}(3433,\cdot)\) \(\chi_{9450}(3463,\cdot)\) \(\chi_{9450}(3937,\cdot)\) \(\chi_{9450}(3967,\cdot)\) \(\chi_{9450}(4063,\cdot)\) \(\chi_{9450}(4567,\cdot)\) \(\chi_{9450}(4597,\cdot)\) \(\chi_{9450}(4723,\cdot)\) \(\chi_{9450}(5197,\cdot)\) \(\chi_{9450}(5227,\cdot)\) \(\chi_{9450}(5323,\cdot)\) \(\chi_{9450}(5353,\cdot)\) \(\chi_{9450}(5827,\cdot)\) ...

Inducing primitive character

\(\chi_{4725}(187,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{9}{20}\right),e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{34}{45}\right)\)\(e\left(\frac{89}{180}\right)\)\(e\left(\frac{1}{60}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{131}{180}\right)\)\(e\left(\frac{41}{90}\right)\)\(e\left(\frac{49}{90}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{67}{90}\right)\)\(e\left(\frac{35}{36}\right)\)
value at  e.g. 2

Related number fields

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