Properties

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

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[20]
 
pari: [g,chi] = znchar(Mod(20,7623))
 

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.fu
Orbit index = 151

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 ]
 

\(\chi_{7623}(20,\cdot)\) \(\chi_{7623}(104,\cdot)\) \(\chi_{7623}(146,\cdot)\) \(\chi_{7623}(335,\cdot)\) \(\chi_{7623}(356,\cdot)\) \(\chi_{7623}(482,\cdot)\) \(\chi_{7623}(587,\cdot)\) \(\chi_{7623}(713,\cdot)\) \(\chi_{7623}(797,\cdot)\) \(\chi_{7623}(839,\cdot)\) \(\chi_{7623}(1028,\cdot)\) \(\chi_{7623}(1175,\cdot)\) \(\chi_{7623}(1280,\cdot)\) \(\chi_{7623}(1301,\cdot)\) \(\chi_{7623}(1406,\cdot)\) \(\chi_{7623}(1490,\cdot)\) \(\chi_{7623}(1532,\cdot)\) \(\chi_{7623}(1742,\cdot)\) \(\chi_{7623}(1868,\cdot)\) \(\chi_{7623}(1973,\cdot)\) \(\chi_{7623}(1994,\cdot)\) \(\chi_{7623}(2099,\cdot)\) \(\chi_{7623}(2183,\cdot)\) \(\chi_{7623}(2225,\cdot)\) \(\chi_{7623}(2414,\cdot)\) \(\chi_{7623}(2435,\cdot)\) \(\chi_{7623}(2561,\cdot)\) \(\chi_{7623}(2666,\cdot)\) \(\chi_{7623}(2687,\cdot)\) \(\chi_{7623}(2876,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),-1,e\left(\frac{38}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{283}{330}\right)\)\(e\left(\frac{118}{165}\right)\)\(e\left(\frac{76}{165}\right)\)\(e\left(\frac{63}{110}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{203}{330}\right)\)\(e\left(\frac{71}{165}\right)\)\(e\left(\frac{47}{55}\right)\)\(e\left(\frac{93}{110}\right)\)\(e\left(\frac{29}{165}\right)\)
value at  e.g. 2

Related number fields

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