Properties

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

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[961]
 
pari: [g,chi] = znchar(Mod(961,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.fa
Orbit index = 131

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 ]
 

\(\chi_{7623}(4,\cdot)\) \(\chi_{7623}(16,\cdot)\) \(\chi_{7623}(256,\cdot)\) \(\chi_{7623}(268,\cdot)\) \(\chi_{7623}(394,\cdot)\) \(\chi_{7623}(445,\cdot)\) \(\chi_{7623}(520,\cdot)\) \(\chi_{7623}(697,\cdot)\) \(\chi_{7623}(709,\cdot)\) \(\chi_{7623}(823,\cdot)\) \(\chi_{7623}(949,\cdot)\) \(\chi_{7623}(961,\cdot)\) \(\chi_{7623}(1087,\cdot)\) \(\chi_{7623}(1138,\cdot)\) \(\chi_{7623}(1390,\cdot)\) \(\chi_{7623}(1402,\cdot)\) \(\chi_{7623}(1516,\cdot)\) \(\chi_{7623}(1642,\cdot)\) \(\chi_{7623}(1780,\cdot)\) \(\chi_{7623}(1831,\cdot)\) \(\chi_{7623}(1906,\cdot)\) \(\chi_{7623}(2083,\cdot)\) \(\chi_{7623}(2095,\cdot)\) \(\chi_{7623}(2209,\cdot)\) \(\chi_{7623}(2335,\cdot)\) \(\chi_{7623}(2347,\cdot)\) \(\chi_{7623}(2473,\cdot)\) \(\chi_{7623}(2524,\cdot)\) \(\chi_{7623}(2599,\cdot)\) \(\chi_{7623}(2776,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{3}\right),e\left(\frac{31}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{148}{165}\right)\)\(e\left(\frac{131}{165}\right)\)\(e\left(\frac{39}{55}\right)\)\(e\left(\frac{38}{55}\right)\)\(e\left(\frac{20}{33}\right)\)\(e\left(\frac{43}{165}\right)\)\(e\left(\frac{97}{165}\right)\)\(e\left(\frac{157}{165}\right)\)\(e\left(\frac{74}{165}\right)\)\(e\left(\frac{83}{165}\right)\)
value at  e.g. 2

Related number fields

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