Properties

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

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[1805]
 
pari: [g,chi] = znchar(Mod(1805,7623))
 

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.ea
Orbit index = 105

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 ]
 

\(\chi_{7623}(419,\cdot)\) \(\chi_{7623}(650,\cdot)\) \(\chi_{7623}(1112,\cdot)\) \(\chi_{7623}(1343,\cdot)\) \(\chi_{7623}(1805,\cdot)\) \(\chi_{7623}(2036,\cdot)\) \(\chi_{7623}(2498,\cdot)\) \(\chi_{7623}(2729,\cdot)\) \(\chi_{7623}(3191,\cdot)\) \(\chi_{7623}(3422,\cdot)\) \(\chi_{7623}(3884,\cdot)\) \(\chi_{7623}(4577,\cdot)\) \(\chi_{7623}(4808,\cdot)\) \(\chi_{7623}(5270,\cdot)\) \(\chi_{7623}(5501,\cdot)\) \(\chi_{7623}(5963,\cdot)\) \(\chi_{7623}(6194,\cdot)\) \(\chi_{7623}(6887,\cdot)\) \(\chi_{7623}(7349,\cdot)\) \(\chi_{7623}(7580,\cdot)\)

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),-1,e\left(\frac{2}{11}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{5}{33}\right)\)
value at  e.g. 2

Related number fields

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