Properties

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

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[25]
 
pari: [g,chi] = znchar(Mod(25,7623))
 

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.fb
Orbit index = 132

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 ]
 

\(\chi_{7623}(25,\cdot)\) \(\chi_{7623}(58,\cdot)\) \(\chi_{7623}(214,\cdot)\) \(\chi_{7623}(247,\cdot)\) \(\chi_{7623}(466,\cdot)\) \(\chi_{7623}(499,\cdot)\) \(\chi_{7623}(592,\cdot)\) \(\chi_{7623}(625,\cdot)\) \(\chi_{7623}(718,\cdot)\) \(\chi_{7623}(751,\cdot)\) \(\chi_{7623}(907,\cdot)\) \(\chi_{7623}(940,\cdot)\) \(\chi_{7623}(1159,\cdot)\) \(\chi_{7623}(1192,\cdot)\) \(\chi_{7623}(1285,\cdot)\) \(\chi_{7623}(1318,\cdot)\) \(\chi_{7623}(1411,\cdot)\) \(\chi_{7623}(1444,\cdot)\) \(\chi_{7623}(1633,\cdot)\) \(\chi_{7623}(1852,\cdot)\) \(\chi_{7623}(1885,\cdot)\) \(\chi_{7623}(1978,\cdot)\) \(\chi_{7623}(2011,\cdot)\) \(\chi_{7623}(2104,\cdot)\) \(\chi_{7623}(2137,\cdot)\) \(\chi_{7623}(2293,\cdot)\) \(\chi_{7623}(2545,\cdot)\) \(\chi_{7623}(2578,\cdot)\) \(\chi_{7623}(2704,\cdot)\) \(\chi_{7623}(2797,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{19}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{19}{55}\right)\)\(e\left(\frac{38}{55}\right)\)\(e\left(\frac{38}{165}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{37}{165}\right)\)\(e\left(\frac{21}{55}\right)\)\(e\left(\frac{98}{165}\right)\)\(e\left(\frac{1}{165}\right)\)\(e\left(\frac{152}{165}\right)\)
value at  e.g. 2

Related number fields

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