Properties

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

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[2081]
 
pari: [g,chi] = znchar(Mod(2081,7623))
 

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.fg
Orbit index = 137

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 ]
 

\(\chi_{7623}(2,\cdot)\) \(\chi_{7623}(95,\cdot)\) \(\chi_{7623}(128,\cdot)\) \(\chi_{7623}(347,\cdot)\) \(\chi_{7623}(380,\cdot)\) \(\chi_{7623}(536,\cdot)\) \(\chi_{7623}(569,\cdot)\) \(\chi_{7623}(662,\cdot)\) \(\chi_{7623}(695,\cdot)\) \(\chi_{7623}(788,\cdot)\) \(\chi_{7623}(821,\cdot)\) \(\chi_{7623}(1040,\cdot)\) \(\chi_{7623}(1073,\cdot)\) \(\chi_{7623}(1229,\cdot)\) \(\chi_{7623}(1262,\cdot)\) \(\chi_{7623}(1355,\cdot)\) \(\chi_{7623}(1388,\cdot)\) \(\chi_{7623}(1481,\cdot)\) \(\chi_{7623}(1514,\cdot)\) \(\chi_{7623}(1733,\cdot)\) \(\chi_{7623}(1766,\cdot)\) \(\chi_{7623}(1922,\cdot)\) \(\chi_{7623}(1955,\cdot)\) \(\chi_{7623}(2081,\cdot)\) \(\chi_{7623}(2174,\cdot)\) \(\chi_{7623}(2207,\cdot)\) \(\chi_{7623}(2426,\cdot)\) \(\chi_{7623}(2459,\cdot)\) \(\chi_{7623}(2615,\cdot)\) \(\chi_{7623}(2648,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{91}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{109}{165}\right)\)\(e\left(\frac{53}{165}\right)\)\(e\left(\frac{79}{110}\right)\)\(e\left(\frac{54}{55}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{293}{330}\right)\)\(e\left(\frac{106}{165}\right)\)\(e\left(\frac{61}{165}\right)\)\(e\left(\frac{109}{330}\right)\)\(e\left(\frac{13}{330}\right)\)
value at  e.g. 2

Related number fields

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