Properties

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

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[2113]
 
pari: [g,chi] = znchar(Mod(2113,3150))
 

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.ei
Orbit index = 113

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 ]
 

\(\chi_{3150}(13,\cdot)\) \(\chi_{3150}(97,\cdot)\) \(\chi_{3150}(223,\cdot)\) \(\chi_{3150}(517,\cdot)\) \(\chi_{3150}(727,\cdot)\) \(\chi_{3150}(853,\cdot)\) \(\chi_{3150}(1147,\cdot)\) \(\chi_{3150}(1273,\cdot)\) \(\chi_{3150}(1483,\cdot)\) \(\chi_{3150}(1777,\cdot)\) \(\chi_{3150}(1903,\cdot)\) \(\chi_{3150}(1987,\cdot)\) \(\chi_{3150}(2113,\cdot)\) \(\chi_{3150}(2533,\cdot)\) \(\chi_{3150}(2617,\cdot)\) \(\chi_{3150}(3037,\cdot)\)

Values on generators

\((2801,127,451)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{19}{20}\right),-1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{47}{60}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{13}{30}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{11}{12}\right)\)
value at  e.g. 2

Related number fields

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