Properties

Conductor 7623
Order 66
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 7623.ed

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[3244]
 
pari: [g,chi] = znchar(Mod(3244,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 66
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.ed
Orbit index = 108

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 ]
 

\(\chi_{7623}(439,\cdot)\) \(\chi_{7623}(472,\cdot)\) \(\chi_{7623}(1132,\cdot)\) \(\chi_{7623}(1165,\cdot)\) \(\chi_{7623}(1825,\cdot)\) \(\chi_{7623}(1858,\cdot)\) \(\chi_{7623}(2518,\cdot)\) \(\chi_{7623}(2551,\cdot)\) \(\chi_{7623}(3211,\cdot)\) \(\chi_{7623}(3244,\cdot)\) \(\chi_{7623}(3904,\cdot)\) \(\chi_{7623}(3937,\cdot)\) \(\chi_{7623}(4630,\cdot)\) \(\chi_{7623}(5290,\cdot)\) \(\chi_{7623}(5983,\cdot)\) \(\chi_{7623}(6016,\cdot)\) \(\chi_{7623}(6676,\cdot)\) \(\chi_{7623}(6709,\cdot)\) \(\chi_{7623}(7369,\cdot)\) \(\chi_{7623}(7402,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{3}{22}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{53}{66}\right)\)\(e\left(\frac{20}{33}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{31}{33}\right)\)\(e\left(\frac{7}{33}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{13}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)