Properties

Conductor 1089
Order 330
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.fn

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[29]
 
pari: [g,chi] = znchar(Mod(29,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1089
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.fn
Orbit index = 144

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 ]
 

\(\chi_{7623}(29,\cdot)\) \(\chi_{7623}(50,\cdot)\) \(\chi_{7623}(281,\cdot)\) \(\chi_{7623}(365,\cdot)\) \(\chi_{7623}(470,\cdot)\) \(\chi_{7623}(491,\cdot)\) \(\chi_{7623}(722,\cdot)\) \(\chi_{7623}(743,\cdot)\) \(\chi_{7623}(932,\cdot)\) \(\chi_{7623}(974,\cdot)\) \(\chi_{7623}(1058,\cdot)\) \(\chi_{7623}(1163,\cdot)\) \(\chi_{7623}(1184,\cdot)\) \(\chi_{7623}(1289,\cdot)\) \(\chi_{7623}(1415,\cdot)\) \(\chi_{7623}(1436,\cdot)\) \(\chi_{7623}(1625,\cdot)\) \(\chi_{7623}(1751,\cdot)\) \(\chi_{7623}(1856,\cdot)\) \(\chi_{7623}(1877,\cdot)\) \(\chi_{7623}(1982,\cdot)\) \(\chi_{7623}(2108,\cdot)\) \(\chi_{7623}(2129,\cdot)\) \(\chi_{7623}(2318,\cdot)\) \(\chi_{7623}(2360,\cdot)\) \(\chi_{7623}(2444,\cdot)\) \(\chi_{7623}(2549,\cdot)\) \(\chi_{7623}(2570,\cdot)\) \(\chi_{7623}(2675,\cdot)\) \(\chi_{7623}(2801,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),1,e\left(\frac{17}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{53}{165}\right)\)\(e\left(\frac{106}{165}\right)\)\(e\left(\frac{89}{330}\right)\)\(e\left(\frac{53}{55}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{311}{330}\right)\)\(e\left(\frac{47}{165}\right)\)\(e\left(\frac{4}{55}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{301}{330}\right)\)
value at  e.g. 2

Related number fields

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