Properties

Conductor 675
Order 180
Real No
Primitive No
Parity Even
Orbit Label 9450.hb

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[113]
pari: [g,chi] = znchar(Mod(113,9450))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 675
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.hb
Orbit index = 184

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 ]

\(\chi_{9450}(113,\cdot)\) \(\chi_{9450}(533,\cdot)\) \(\chi_{9450}(617,\cdot)\) \(\chi_{9450}(1037,\cdot)\) \(\chi_{9450}(1163,\cdot)\) \(\chi_{9450}(1247,\cdot)\) \(\chi_{9450}(1373,\cdot)\) \(\chi_{9450}(1667,\cdot)\) \(\chi_{9450}(1877,\cdot)\) \(\chi_{9450}(2003,\cdot)\) \(\chi_{9450}(2297,\cdot)\) \(\chi_{9450}(2423,\cdot)\) \(\chi_{9450}(2633,\cdot)\) \(\chi_{9450}(2927,\cdot)\) \(\chi_{9450}(3053,\cdot)\) \(\chi_{9450}(3137,\cdot)\) \(\chi_{9450}(3263,\cdot)\) \(\chi_{9450}(3683,\cdot)\) \(\chi_{9450}(3767,\cdot)\) \(\chi_{9450}(4187,\cdot)\) \(\chi_{9450}(4313,\cdot)\) \(\chi_{9450}(4397,\cdot)\) \(\chi_{9450}(4523,\cdot)\) \(\chi_{9450}(4817,\cdot)\) \(\chi_{9450}(5027,\cdot)\) \(\chi_{9450}(5153,\cdot)\) \(\chi_{9450}(5447,\cdot)\) \(\chi_{9450}(5573,\cdot)\) \(\chi_{9450}(5783,\cdot)\) \(\chi_{9450}(6077,\cdot)\) ...

Inducing primitive character

\(\chi_{675}(113,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{19}{20}\right),1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{73}{90}\right)\)\(e\left(\frac{49}{180}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{91}{180}\right)\)\(e\left(\frac{8}{45}\right)\)\(e\left(\frac{7}{45}\right)\)\(e\left(\frac{13}{60}\right)\)\(e\left(\frac{47}{90}\right)\)\(e\left(\frac{13}{36}\right)\)
value at  e.g. 2

Related number fields

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