Properties

Conductor 7623
Order 33
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 7623.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(7623)
 
sage: chi = H[529]
 
pari: [g,chi] = znchar(Mod(529,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 33
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.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 ]
 

\(\chi_{7623}(529,\cdot)\) \(\chi_{7623}(562,\cdot)\) \(\chi_{7623}(1222,\cdot)\) \(\chi_{7623}(1255,\cdot)\) \(\chi_{7623}(1915,\cdot)\) \(\chi_{7623}(1948,\cdot)\) \(\chi_{7623}(2608,\cdot)\) \(\chi_{7623}(2641,\cdot)\) \(\chi_{7623}(3301,\cdot)\) \(\chi_{7623}(3334,\cdot)\) \(\chi_{7623}(4027,\cdot)\) \(\chi_{7623}(4687,\cdot)\) \(\chi_{7623}(5380,\cdot)\) \(\chi_{7623}(5413,\cdot)\) \(\chi_{7623}(6073,\cdot)\) \(\chi_{7623}(6106,\cdot)\) \(\chi_{7623}(6766,\cdot)\) \(\chi_{7623}(6799,\cdot)\) \(\chi_{7623}(7459,\cdot)\) \(\chi_{7623}(7492,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{11}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{13}{33}\right)\)
value at  e.g. 2

Related number fields

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