Properties

Conductor 7623
Order 330
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 7623.fp

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[61]
 
pari: [g,chi] = znchar(Mod(61,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
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.fp
Orbit index = 146

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 ]
 

\(\chi_{7623}(61,\cdot)\) \(\chi_{7623}(250,\cdot)\) \(\chi_{7623}(283,\cdot)\) \(\chi_{7623}(376,\cdot)\) \(\chi_{7623}(409,\cdot)\) \(\chi_{7623}(502,\cdot)\) \(\chi_{7623}(535,\cdot)\) \(\chi_{7623}(754,\cdot)\) \(\chi_{7623}(787,\cdot)\) \(\chi_{7623}(943,\cdot)\) \(\chi_{7623}(976,\cdot)\) \(\chi_{7623}(1069,\cdot)\) \(\chi_{7623}(1102,\cdot)\) \(\chi_{7623}(1195,\cdot)\) \(\chi_{7623}(1228,\cdot)\) \(\chi_{7623}(1447,\cdot)\) \(\chi_{7623}(1480,\cdot)\) \(\chi_{7623}(1636,\cdot)\) \(\chi_{7623}(1669,\cdot)\) \(\chi_{7623}(1762,\cdot)\) \(\chi_{7623}(1795,\cdot)\) \(\chi_{7623}(1888,\cdot)\) \(\chi_{7623}(1921,\cdot)\) \(\chi_{7623}(2140,\cdot)\) \(\chi_{7623}(2173,\cdot)\) \(\chi_{7623}(2329,\cdot)\) \(\chi_{7623}(2362,\cdot)\) \(\chi_{7623}(2455,\cdot)\) \(\chi_{7623}(2488,\cdot)\) \(\chi_{7623}(2614,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{5}{6}\right),e\left(\frac{109}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{107}{330}\right)\)\(e\left(\frac{107}{165}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{107}{110}\right)\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{151}{165}\right)\)\(e\left(\frac{49}{165}\right)\)\(e\left(\frac{64}{165}\right)\)\(e\left(\frac{68}{165}\right)\)\(e\left(\frac{157}{330}\right)\)
value at  e.g. 2

Related number fields

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