Properties

Conductor 1575
Order 30
Real no
Primitive no
Minimal yes
Parity even
Orbit label 3150.dk

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[209]
 
pari: [g,chi] = znchar(Mod(209,3150))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 30
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.dk
Orbit index = 89

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 ]
 

\(\chi_{3150}(209,\cdot)\) \(\chi_{3150}(419,\cdot)\) \(\chi_{3150}(839,\cdot)\) \(\chi_{3150}(1469,\cdot)\) \(\chi_{3150}(1679,\cdot)\) \(\chi_{3150}(2309,\cdot)\) \(\chi_{3150}(2729,\cdot)\) \(\chi_{3150}(2939,\cdot)\)

Values on generators

\((2801,127,451)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{7}{10}\right),-1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{2}{15}\right)\)\(e\left(\frac{1}{6}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{15})\)