Properties

Conductor 847
Order 330
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.fx

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[19]
 
pari: [g,chi] = znchar(Mod(19,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
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.fx
Orbit index = 154

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 ]
 

\(\chi_{7623}(19,\cdot)\) \(\chi_{7623}(73,\cdot)\) \(\chi_{7623}(145,\cdot)\) \(\chi_{7623}(271,\cdot)\) \(\chi_{7623}(325,\cdot)\) \(\chi_{7623}(514,\cdot)\) \(\chi_{7623}(523,\cdot)\) \(\chi_{7623}(640,\cdot)\) \(\chi_{7623}(712,\cdot)\) \(\chi_{7623}(964,\cdot)\) \(\chi_{7623}(1018,\cdot)\) \(\chi_{7623}(1216,\cdot)\) \(\chi_{7623}(1333,\cdot)\) \(\chi_{7623}(1405,\cdot)\) \(\chi_{7623}(1459,\cdot)\) \(\chi_{7623}(1531,\cdot)\) \(\chi_{7623}(1657,\cdot)\) \(\chi_{7623}(1711,\cdot)\) \(\chi_{7623}(1900,\cdot)\) \(\chi_{7623}(2026,\cdot)\) \(\chi_{7623}(2098,\cdot)\) \(\chi_{7623}(2152,\cdot)\) \(\chi_{7623}(2224,\cdot)\) \(\chi_{7623}(2350,\cdot)\) \(\chi_{7623}(2404,\cdot)\) \(\chi_{7623}(2593,\cdot)\) \(\chi_{7623}(2602,\cdot)\) \(\chi_{7623}(2719,\cdot)\) \(\chi_{7623}(2791,\cdot)\) \(\chi_{7623}(2845,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{83}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{139}{330}\right)\)\(e\left(\frac{139}{165}\right)\)\(e\left(\frac{1}{330}\right)\)\(e\left(\frac{29}{110}\right)\)\(e\left(\frac{14}{33}\right)\)\(e\left(\frac{39}{55}\right)\)\(e\left(\frac{113}{165}\right)\)\(e\left(\frac{133}{165}\right)\)\(e\left(\frac{131}{165}\right)\)\(e\left(\frac{93}{110}\right)\)
value at  e.g. 2

Related number fields

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