Properties

Conductor 847
Order 165
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.ez

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[37]
 
pari: [g,chi] = znchar(Mod(37,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 165
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 = 7623.ez
Orbit index = 130

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 ]
 

\(\chi_{7623}(37,\cdot)\) \(\chi_{7623}(163,\cdot)\) \(\chi_{7623}(235,\cdot)\) \(\chi_{7623}(289,\cdot)\) \(\chi_{7623}(361,\cdot)\) \(\chi_{7623}(478,\cdot)\) \(\chi_{7623}(676,\cdot)\) \(\chi_{7623}(730,\cdot)\) \(\chi_{7623}(982,\cdot)\) \(\chi_{7623}(1054,\cdot)\) \(\chi_{7623}(1171,\cdot)\) \(\chi_{7623}(1180,\cdot)\) \(\chi_{7623}(1369,\cdot)\) \(\chi_{7623}(1423,\cdot)\) \(\chi_{7623}(1549,\cdot)\) \(\chi_{7623}(1621,\cdot)\) \(\chi_{7623}(1675,\cdot)\) \(\chi_{7623}(1747,\cdot)\) \(\chi_{7623}(1864,\cdot)\) \(\chi_{7623}(1873,\cdot)\) \(\chi_{7623}(2062,\cdot)\) \(\chi_{7623}(2116,\cdot)\) \(\chi_{7623}(2242,\cdot)\) \(\chi_{7623}(2314,\cdot)\) \(\chi_{7623}(2368,\cdot)\) \(\chi_{7623}(2440,\cdot)\) \(\chi_{7623}(2557,\cdot)\) \(\chi_{7623}(2566,\cdot)\) \(\chi_{7623}(2755,\cdot)\) \(\chi_{7623}(2809,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{21}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{8}{165}\right)\)\(e\left(\frac{16}{165}\right)\)\(e\left(\frac{152}{165}\right)\)\(e\left(\frac{8}{55}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{31}{55}\right)\)\(e\left(\frac{32}{165}\right)\)\(e\left(\frac{7}{165}\right)\)\(e\left(\frac{59}{165}\right)\)\(e\left(\frac{1}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)