Properties

Conductor 8027
Order 44
Real No
Primitive Yes
Parity Even
Orbit Label 8027.s

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(8027)
 
sage: chi = H[136]
 
pari: [g,chi] = znchar(Mod(136,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 44
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8027.s
Orbit index = 19

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 ]
 

\(\chi_{8027}(136,\cdot)\) \(\chi_{8027}(562,\cdot)\) \(\chi_{8027}(911,\cdot)\) \(\chi_{8027}(1183,\cdot)\) \(\chi_{8027}(1532,\cdot)\) \(\chi_{8027}(2307,\cdot)\) \(\chi_{8027}(2656,\cdot)\) \(\chi_{8027}(2928,\cdot)\) \(\chi_{8027}(3005,\cdot)\) \(\chi_{8027}(3277,\cdot)\) \(\chi_{8027}(3354,\cdot)\) \(\chi_{8027}(3626,\cdot)\) \(\chi_{8027}(3975,\cdot)\) \(\chi_{8027}(5448,\cdot)\) \(\chi_{8027}(6069,\cdot)\) \(\chi_{8027}(6146,\cdot)\) \(\chi_{8027}(6767,\cdot)\) \(\chi_{8027}(7193,\cdot)\) \(\chi_{8027}(7542,\cdot)\) \(\chi_{8027}(7814,\cdot)\)

Values on generators

\((350,5935)\) → \((e\left(\frac{13}{22}\right),-i)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{3}{44}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{44})\)