Properties

Conductor 1575
Order 60
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3150.eb

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(3150)
 
sage: chi = H[817]
 
pari: [g,chi] = znchar(Mod(817,3150))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 60
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 3150.eb
Orbit index = 106

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 ]
 

\(\chi_{3150}(187,\cdot)\) \(\chi_{3150}(283,\cdot)\) \(\chi_{3150}(313,\cdot)\) \(\chi_{3150}(787,\cdot)\) \(\chi_{3150}(817,\cdot)\) \(\chi_{3150}(913,\cdot)\) \(\chi_{3150}(1417,\cdot)\) \(\chi_{3150}(1447,\cdot)\) \(\chi_{3150}(1573,\cdot)\) \(\chi_{3150}(2047,\cdot)\) \(\chi_{3150}(2077,\cdot)\) \(\chi_{3150}(2173,\cdot)\) \(\chi_{3150}(2203,\cdot)\) \(\chi_{3150}(2677,\cdot)\) \(\chi_{3150}(2803,\cdot)\) \(\chi_{3150}(2833,\cdot)\)

Values on generators

\((2801,127,451)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{13}{20}\right),e\left(\frac{5}{6}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{29}{30}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{5}{12}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)