Properties

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

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[317]
pari: [g,chi] = znchar(Mod(317,9450))

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.ha
Orbit index = 183

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 ]

\(\chi_{9450}(317,\cdot)\) \(\chi_{9450}(347,\cdot)\) \(\chi_{9450}(473,\cdot)\) \(\chi_{9450}(947,\cdot)\) \(\chi_{9450}(977,\cdot)\) \(\chi_{9450}(1073,\cdot)\) \(\chi_{9450}(1103,\cdot)\) \(\chi_{9450}(1577,\cdot)\) \(\chi_{9450}(1703,\cdot)\) \(\chi_{9450}(1733,\cdot)\) \(\chi_{9450}(2237,\cdot)\) \(\chi_{9450}(2333,\cdot)\) \(\chi_{9450}(2363,\cdot)\) \(\chi_{9450}(2837,\cdot)\) \(\chi_{9450}(2867,\cdot)\) \(\chi_{9450}(2963,\cdot)\) \(\chi_{9450}(3467,\cdot)\) \(\chi_{9450}(3497,\cdot)\) \(\chi_{9450}(3623,\cdot)\) \(\chi_{9450}(4097,\cdot)\) \(\chi_{9450}(4127,\cdot)\) \(\chi_{9450}(4223,\cdot)\) \(\chi_{9450}(4253,\cdot)\) \(\chi_{9450}(4727,\cdot)\) \(\chi_{9450}(4853,\cdot)\) \(\chi_{9450}(4883,\cdot)\) \(\chi_{9450}(5387,\cdot)\) \(\chi_{9450}(5483,\cdot)\) \(\chi_{9450}(5513,\cdot)\) \(\chi_{9450}(5987,\cdot)\) ...

Inducing primitive character

\(\chi_{4725}(317,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{13}{20}\right),e\left(\frac{1}{3}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{71}{90}\right)\)\(e\left(\frac{83}{180}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{17}{180}\right)\)\(e\left(\frac{31}{45}\right)\)\(e\left(\frac{14}{45}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{19}{90}\right)\)\(e\left(\frac{11}{36}\right)\)
value at  e.g. 2

Related number fields

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