Properties

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

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[2798]
 
pari: [g,chi] = znchar(Mod(2798,7623))
 

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.fr
Orbit index = 148

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 ]
 

\(\chi_{7623}(26,\cdot)\) \(\chi_{7623}(80,\cdot)\) \(\chi_{7623}(152,\cdot)\) \(\chi_{7623}(278,\cdot)\) \(\chi_{7623}(467,\cdot)\) \(\chi_{7623}(521,\cdot)\) \(\chi_{7623}(647,\cdot)\) \(\chi_{7623}(719,\cdot)\) \(\chi_{7623}(773,\cdot)\) \(\chi_{7623}(845,\cdot)\) \(\chi_{7623}(962,\cdot)\) \(\chi_{7623}(1160,\cdot)\) \(\chi_{7623}(1214,\cdot)\) \(\chi_{7623}(1466,\cdot)\) \(\chi_{7623}(1538,\cdot)\) \(\chi_{7623}(1655,\cdot)\) \(\chi_{7623}(1664,\cdot)\) \(\chi_{7623}(1853,\cdot)\) \(\chi_{7623}(1907,\cdot)\) \(\chi_{7623}(2033,\cdot)\) \(\chi_{7623}(2105,\cdot)\) \(\chi_{7623}(2159,\cdot)\) \(\chi_{7623}(2231,\cdot)\) \(\chi_{7623}(2348,\cdot)\) \(\chi_{7623}(2357,\cdot)\) \(\chi_{7623}(2546,\cdot)\) \(\chi_{7623}(2600,\cdot)\) \(\chi_{7623}(2726,\cdot)\) \(\chi_{7623}(2798,\cdot)\) \(\chi_{7623}(2852,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{26}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{211}{330}\right)\)\(e\left(\frac{46}{165}\right)\)\(e\left(\frac{107}{165}\right)\)\(e\left(\frac{101}{110}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{27}{110}\right)\)\(e\left(\frac{92}{165}\right)\)\(e\left(\frac{82}{165}\right)\)\(e\left(\frac{133}{330}\right)\)\(e\left(\frac{51}{55}\right)\)
value at  e.g. 2

Related number fields

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