Properties

Conductor 4033
Order 108
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.jy

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4033)
 
sage: chi = H[146]
 
pari: [g,chi] = znchar(Mod(146,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 108
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4033.jy
Orbit index = 259

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 ]
 

\(\chi_{4033}(146,\cdot)\) \(\chi_{4033}(161,\cdot)\) \(\chi_{4033}(207,\cdot)\) \(\chi_{4033}(412,\cdot)\) \(\chi_{4033}(501,\cdot)\) \(\chi_{4033}(1239,\cdot)\) \(\chi_{4033}(1347,\cdot)\) \(\chi_{4033}(1512,\cdot)\) \(\chi_{4033}(1576,\cdot)\) \(\chi_{4033}(1593,\cdot)\) \(\chi_{4033}(1641,\cdot)\) \(\chi_{4033}(1682,\cdot)\) \(\chi_{4033}(1734,\cdot)\) \(\chi_{4033}(1757,\cdot)\) \(\chi_{4033}(1774,\cdot)\) \(\chi_{4033}(1906,\cdot)\) \(\chi_{4033}(1911,\cdot)\) \(\chi_{4033}(1944,\cdot)\) \(\chi_{4033}(2089,\cdot)\) \(\chi_{4033}(2122,\cdot)\) \(\chi_{4033}(2127,\cdot)\) \(\chi_{4033}(2259,\cdot)\) \(\chi_{4033}(2276,\cdot)\) \(\chi_{4033}(2299,\cdot)\) \(\chi_{4033}(2351,\cdot)\) \(\chi_{4033}(2392,\cdot)\) \(\chi_{4033}(2440,\cdot)\) \(\chi_{4033}(2457,\cdot)\) \(\chi_{4033}(2521,\cdot)\) \(\chi_{4033}(2686,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{19}{36}\right),e\left(\frac{5}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{71}{108}\right)\)\(e\left(\frac{8}{27}\right)\)\(e\left(\frac{20}{27}\right)\)\(-1\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{89}{108}\right)\)\(e\left(\frac{73}{108}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{108})\)