Properties

Conductor 847
Order 110
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.es

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[244]
 
pari: [g,chi] = znchar(Mod(244,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 110
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.es
Orbit index = 123

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 ]
 

\(\chi_{7623}(244,\cdot)\) \(\chi_{7623}(370,\cdot)\) \(\chi_{7623}(622,\cdot)\) \(\chi_{7623}(811,\cdot)\) \(\chi_{7623}(937,\cdot)\) \(\chi_{7623}(1063,\cdot)\) \(\chi_{7623}(1315,\cdot)\) \(\chi_{7623}(1504,\cdot)\) \(\chi_{7623}(1630,\cdot)\) \(\chi_{7623}(1756,\cdot)\) \(\chi_{7623}(2008,\cdot)\) \(\chi_{7623}(2197,\cdot)\) \(\chi_{7623}(2323,\cdot)\) \(\chi_{7623}(2449,\cdot)\) \(\chi_{7623}(2701,\cdot)\) \(\chi_{7623}(2890,\cdot)\) \(\chi_{7623}(3142,\cdot)\) \(\chi_{7623}(3394,\cdot)\) \(\chi_{7623}(3583,\cdot)\) \(\chi_{7623}(3709,\cdot)\) \(\chi_{7623}(3835,\cdot)\) \(\chi_{7623}(4276,\cdot)\) \(\chi_{7623}(4402,\cdot)\) \(\chi_{7623}(4528,\cdot)\) \(\chi_{7623}(4780,\cdot)\) \(\chi_{7623}(4969,\cdot)\) \(\chi_{7623}(5095,\cdot)\) \(\chi_{7623}(5221,\cdot)\) \(\chi_{7623}(5473,\cdot)\) \(\chi_{7623}(5662,\cdot)\) ...

Values on generators

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

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{1}{110}\right)\)\(e\left(\frac{1}{55}\right)\)\(e\left(\frac{19}{110}\right)\)\(e\left(\frac{3}{110}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{23}{55}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{52}{55}\right)\)\(e\left(\frac{14}{55}\right)\)\(e\left(\frac{21}{110}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{55})\)