Properties

Conductor 121
Order 55
Real no
Primitive no
Minimal yes
Parity even
Orbit label 7623.do

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[3529]
 
pari: [g,chi] = znchar(Mod(3529,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 121
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 55
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.do
Orbit index = 93

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 ]
 

\(\chi_{7623}(64,\cdot)\) \(\chi_{7623}(190,\cdot)\) \(\chi_{7623}(379,\cdot)\) \(\chi_{7623}(631,\cdot)\) \(\chi_{7623}(757,\cdot)\) \(\chi_{7623}(883,\cdot)\) \(\chi_{7623}(1072,\cdot)\) \(\chi_{7623}(1324,\cdot)\) \(\chi_{7623}(1450,\cdot)\) \(\chi_{7623}(1765,\cdot)\) \(\chi_{7623}(2143,\cdot)\) \(\chi_{7623}(2269,\cdot)\) \(\chi_{7623}(2458,\cdot)\) \(\chi_{7623}(2710,\cdot)\) \(\chi_{7623}(2836,\cdot)\) \(\chi_{7623}(2962,\cdot)\) \(\chi_{7623}(3151,\cdot)\) \(\chi_{7623}(3403,\cdot)\) \(\chi_{7623}(3529,\cdot)\) \(\chi_{7623}(3655,\cdot)\) \(\chi_{7623}(3844,\cdot)\) \(\chi_{7623}(4096,\cdot)\) \(\chi_{7623}(4222,\cdot)\) \(\chi_{7623}(4348,\cdot)\) \(\chi_{7623}(4537,\cdot)\) \(\chi_{7623}(4789,\cdot)\) \(\chi_{7623}(4915,\cdot)\) \(\chi_{7623}(5041,\cdot)\) \(\chi_{7623}(5482,\cdot)\) \(\chi_{7623}(5608,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((1,1,e\left(\frac{38}{55}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{38}{55}\right)\)\(e\left(\frac{21}{55}\right)\)\(e\left(\frac{7}{55}\right)\)\(e\left(\frac{4}{55}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{43}{55}\right)\)\(e\left(\frac{42}{55}\right)\)\(e\left(\frac{47}{55}\right)\)\(e\left(\frac{19}{55}\right)\)\(e\left(\frac{28}{55}\right)\)
value at  e.g. 2

Related number fields

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