Properties

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

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[698]
 
pari: [g,chi] = znchar(Mod(698,7623))
 

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.fc
Orbit index = 133

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 ]
 

\(\chi_{7623}(5,\cdot)\) \(\chi_{7623}(38,\cdot)\) \(\chi_{7623}(257,\cdot)\) \(\chi_{7623}(290,\cdot)\) \(\chi_{7623}(383,\cdot)\) \(\chi_{7623}(416,\cdot)\) \(\chi_{7623}(509,\cdot)\) \(\chi_{7623}(542,\cdot)\) \(\chi_{7623}(698,\cdot)\) \(\chi_{7623}(731,\cdot)\) \(\chi_{7623}(950,\cdot)\) \(\chi_{7623}(983,\cdot)\) \(\chi_{7623}(1076,\cdot)\) \(\chi_{7623}(1109,\cdot)\) \(\chi_{7623}(1202,\cdot)\) \(\chi_{7623}(1235,\cdot)\) \(\chi_{7623}(1391,\cdot)\) \(\chi_{7623}(1424,\cdot)\) \(\chi_{7623}(1643,\cdot)\) \(\chi_{7623}(1676,\cdot)\) \(\chi_{7623}(1769,\cdot)\) \(\chi_{7623}(1802,\cdot)\) \(\chi_{7623}(1895,\cdot)\) \(\chi_{7623}(1928,\cdot)\) \(\chi_{7623}(2117,\cdot)\) \(\chi_{7623}(2336,\cdot)\) \(\chi_{7623}(2369,\cdot)\) \(\chi_{7623}(2462,\cdot)\) \(\chi_{7623}(2495,\cdot)\) \(\chi_{7623}(2588,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{5}{6}\right),e\left(\frac{32}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{9}{110}\right)\)\(e\left(\frac{9}{55}\right)\)\(e\left(\frac{64}{165}\right)\)\(e\left(\frac{27}{110}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{307}{330}\right)\)\(e\left(\frac{18}{55}\right)\)\(e\left(\frac{139}{165}\right)\)\(e\left(\frac{151}{330}\right)\)\(e\left(\frac{91}{165}\right)\)
value at  e.g. 2

Related number fields

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