Properties

Conductor 2365
Order 60
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.cq

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(4730)
 
sage: chi = H[37]
 
pari: [g,chi] = znchar(Mod(37,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2365
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 = 4730.cq
Orbit index = 69

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 ]
 

\(\chi_{4730}(37,\cdot)\) \(\chi_{4730}(93,\cdot)\) \(\chi_{4730}(467,\cdot)\) \(\chi_{4730}(553,\cdot)\) \(\chi_{4730}(867,\cdot)\) \(\chi_{4730}(983,\cdot)\) \(\chi_{4730}(1413,\cdot)\) \(\chi_{4730}(1813,\cdot)\) \(\chi_{4730}(2187,\cdot)\) \(\chi_{4730}(3017,\cdot)\) \(\chi_{4730}(3133,\cdot)\) \(\chi_{4730}(3447,\cdot)\) \(\chi_{4730}(3877,\cdot)\) \(\chi_{4730}(3963,\cdot)\) \(\chi_{4730}(4337,\cdot)\) \(\chi_{4730}(4393,\cdot)\)

Values on generators

\((947,431,1981)\) → \((i,e\left(\frac{1}{5}\right),e\left(\frac{1}{6}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{29}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{23}{60}\right)\)\(e\left(\frac{4}{15}\right)\)\(1\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{11}{15}\right)\)
value at  e.g. 2

Related number fields

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