Properties

Conductor 693
Order 30
Real no
Primitive no
Minimal no
Parity even
Orbit label 7623.df

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(7623)
 
sage: chi = H[2048]
 
pari: [g,chi] = znchar(Mod(2048,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 693
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 = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.df
Orbit index = 84

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 ]
 

\(\chi_{7623}(2048,\cdot)\) \(\chi_{7623}(2774,\cdot)\) \(\chi_{7623}(3119,\cdot)\) \(\chi_{7623}(3845,\cdot)\) \(\chi_{7623}(6332,\cdot)\) \(\chi_{7623}(6773,\cdot)\) \(\chi_{7623}(7058,\cdot)\) \(\chi_{7623}(7499,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{1}{10}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{4}{15}\right)\)\(e\left(\frac{8}{15}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{23}{30}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{13}{30}\right)\)
value at  e.g. 2

Related number fields

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