Properties

Conductor 1089
Order 165
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.ey

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[1534]
 
pari: [g,chi] = znchar(Mod(1534,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1089
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 165
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.ey
Orbit index = 129

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 ]
 

\(\chi_{7623}(169,\cdot)\) \(\chi_{7623}(295,\cdot)\) \(\chi_{7623}(400,\cdot)\) \(\chi_{7623}(421,\cdot)\) \(\chi_{7623}(526,\cdot)\) \(\chi_{7623}(610,\cdot)\) \(\chi_{7623}(652,\cdot)\) \(\chi_{7623}(841,\cdot)\) \(\chi_{7623}(862,\cdot)\) \(\chi_{7623}(988,\cdot)\) \(\chi_{7623}(1093,\cdot)\) \(\chi_{7623}(1114,\cdot)\) \(\chi_{7623}(1303,\cdot)\) \(\chi_{7623}(1345,\cdot)\) \(\chi_{7623}(1534,\cdot)\) \(\chi_{7623}(1555,\cdot)\) \(\chi_{7623}(1681,\cdot)\) \(\chi_{7623}(1786,\cdot)\) \(\chi_{7623}(1807,\cdot)\) \(\chi_{7623}(1912,\cdot)\) \(\chi_{7623}(1996,\cdot)\) \(\chi_{7623}(2038,\cdot)\) \(\chi_{7623}(2227,\cdot)\) \(\chi_{7623}(2248,\cdot)\) \(\chi_{7623}(2374,\cdot)\) \(\chi_{7623}(2479,\cdot)\) \(\chi_{7623}(2500,\cdot)\) \(\chi_{7623}(2605,\cdot)\) \(\chi_{7623}(2731,\cdot)\) \(\chi_{7623}(2920,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{12}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{91}{165}\right)\)\(e\left(\frac{17}{165}\right)\)\(e\left(\frac{134}{165}\right)\)\(e\left(\frac{36}{55}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{116}{165}\right)\)\(e\left(\frac{34}{165}\right)\)\(e\left(\frac{38}{55}\right)\)\(e\left(\frac{6}{55}\right)\)\(e\left(\frac{151}{165}\right)\)
value at  e.g. 2

Related number fields

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