Properties

Conductor 2541
Order 330
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.fk

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[557]
 
pari: [g,chi] = znchar(Mod(557,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2541
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.fk
Orbit index = 141

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 ]
 

\(\chi_{7623}(107,\cdot)\) \(\chi_{7623}(116,\cdot)\) \(\chi_{7623}(305,\cdot)\) \(\chi_{7623}(359,\cdot)\) \(\chi_{7623}(431,\cdot)\) \(\chi_{7623}(557,\cdot)\) \(\chi_{7623}(611,\cdot)\) \(\chi_{7623}(800,\cdot)\) \(\chi_{7623}(809,\cdot)\) \(\chi_{7623}(926,\cdot)\) \(\chi_{7623}(998,\cdot)\) \(\chi_{7623}(1052,\cdot)\) \(\chi_{7623}(1124,\cdot)\) \(\chi_{7623}(1493,\cdot)\) \(\chi_{7623}(1502,\cdot)\) \(\chi_{7623}(1619,\cdot)\) \(\chi_{7623}(1745,\cdot)\) \(\chi_{7623}(1817,\cdot)\) \(\chi_{7623}(1943,\cdot)\) \(\chi_{7623}(1997,\cdot)\) \(\chi_{7623}(2186,\cdot)\) \(\chi_{7623}(2195,\cdot)\) \(\chi_{7623}(2312,\cdot)\) \(\chi_{7623}(2384,\cdot)\) \(\chi_{7623}(2438,\cdot)\) \(\chi_{7623}(2510,\cdot)\) \(\chi_{7623}(2636,\cdot)\) \(\chi_{7623}(2690,\cdot)\) \(\chi_{7623}(2879,\cdot)\) \(\chi_{7623}(2888,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{37}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{28}{165}\right)\)\(e\left(\frac{56}{165}\right)\)\(e\left(\frac{239}{330}\right)\)\(e\left(\frac{28}{55}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{107}{110}\right)\)\(e\left(\frac{112}{165}\right)\)\(e\left(\frac{107}{165}\right)\)\(e\left(\frac{83}{330}\right)\)\(e\left(\frac{7}{110}\right)\)
value at  e.g. 2

Related number fields

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