Properties

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

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[103]
pari: [g,chi] = znchar(Mod(103,9450))

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.gz
Orbit index = 182

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 ]

\(\chi_{9450}(103,\cdot)\) \(\chi_{9450}(367,\cdot)\) \(\chi_{9450}(733,\cdot)\) \(\chi_{9450}(997,\cdot)\) \(\chi_{9450}(1123,\cdot)\) \(\chi_{9450}(1237,\cdot)\) \(\chi_{9450}(1363,\cdot)\) \(\chi_{9450}(1627,\cdot)\) \(\chi_{9450}(1753,\cdot)\) \(\chi_{9450}(1867,\cdot)\) \(\chi_{9450}(2383,\cdot)\) \(\chi_{9450}(2497,\cdot)\) \(\chi_{9450}(2623,\cdot)\) \(\chi_{9450}(2887,\cdot)\) \(\chi_{9450}(3013,\cdot)\) \(\chi_{9450}(3127,\cdot)\) \(\chi_{9450}(3253,\cdot)\) \(\chi_{9450}(3517,\cdot)\) \(\chi_{9450}(3883,\cdot)\) \(\chi_{9450}(4147,\cdot)\) \(\chi_{9450}(4273,\cdot)\) \(\chi_{9450}(4387,\cdot)\) \(\chi_{9450}(4513,\cdot)\) \(\chi_{9450}(4777,\cdot)\) \(\chi_{9450}(4903,\cdot)\) \(\chi_{9450}(5017,\cdot)\) \(\chi_{9450}(5533,\cdot)\) \(\chi_{9450}(5647,\cdot)\) \(\chi_{9450}(5773,\cdot)\) \(\chi_{9450}(6037,\cdot)\) ...

Inducing primitive character

\(\chi_{4725}(103,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{7}{20}\right),e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{2}{45}\right)\)\(e\left(\frac{67}{180}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{13}{180}\right)\)\(e\left(\frac{43}{90}\right)\)\(e\left(\frac{17}{90}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{11}{90}\right)\)\(e\left(\frac{13}{36}\right)\)
value at  e.g. 2

Related number fields

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