Properties

Conductor 363
Order 110
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.ew

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[5111]
 
pari: [g,chi] = znchar(Mod(5111,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 363
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.ew
Orbit index = 127

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 ]
 

\(\chi_{7623}(8,\cdot)\) \(\chi_{7623}(134,\cdot)\) \(\chi_{7623}(260,\cdot)\) \(\chi_{7623}(512,\cdot)\) \(\chi_{7623}(701,\cdot)\) \(\chi_{7623}(827,\cdot)\) \(\chi_{7623}(953,\cdot)\) \(\chi_{7623}(1205,\cdot)\) \(\chi_{7623}(1394,\cdot)\) \(\chi_{7623}(1520,\cdot)\) \(\chi_{7623}(1646,\cdot)\) \(\chi_{7623}(1898,\cdot)\) \(\chi_{7623}(2087,\cdot)\) \(\chi_{7623}(2213,\cdot)\) \(\chi_{7623}(2591,\cdot)\) \(\chi_{7623}(2906,\cdot)\) \(\chi_{7623}(3032,\cdot)\) \(\chi_{7623}(3284,\cdot)\) \(\chi_{7623}(3473,\cdot)\) \(\chi_{7623}(3599,\cdot)\) \(\chi_{7623}(3725,\cdot)\) \(\chi_{7623}(3977,\cdot)\) \(\chi_{7623}(4166,\cdot)\) \(\chi_{7623}(4292,\cdot)\) \(\chi_{7623}(4418,\cdot)\) \(\chi_{7623}(4670,\cdot)\) \(\chi_{7623}(4859,\cdot)\) \(\chi_{7623}(4985,\cdot)\) \(\chi_{7623}(5111,\cdot)\) \(\chi_{7623}(5363,\cdot)\) ...

Values on generators

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

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{36}{55}\right)\)\(e\left(\frac{17}{55}\right)\)\(e\left(\frac{103}{110}\right)\)\(e\left(\frac{53}{55}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{67}{110}\right)\)\(e\left(\frac{34}{55}\right)\)\(e\left(\frac{4}{55}\right)\)\(e\left(\frac{91}{110}\right)\)\(e\left(\frac{27}{110}\right)\)
value at  e.g. 2

Related number fields

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