Properties

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

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[133]
 
pari: [g,chi] = znchar(Mod(133,4033))
 

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.ik
Orbit index = 219

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 ]
 

\(\chi_{4033}(133,\cdot)\) \(\chi_{4033}(276,\cdot)\) \(\chi_{4033}(309,\cdot)\) \(\chi_{4033}(338,\cdot)\) \(\chi_{4033}(684,\cdot)\) \(\chi_{4033}(716,\cdot)\) \(\chi_{4033}(757,\cdot)\) \(\chi_{4033}(816,\cdot)\) \(\chi_{4033}(944,\cdot)\) \(\chi_{4033}(1031,\cdot)\) \(\chi_{4033}(1134,\cdot)\) \(\chi_{4033}(1186,\cdot)\) \(\chi_{4033}(1350,\cdot)\) \(\chi_{4033}(1704,\cdot)\) \(\chi_{4033}(1754,\cdot)\) \(\chi_{4033}(1796,\cdot)\) \(\chi_{4033}(1892,\cdot)\) \(\chi_{4033}(1976,\cdot)\) \(\chi_{4033}(2057,\cdot)\) \(\chi_{4033}(2141,\cdot)\) \(\chi_{4033}(2237,\cdot)\) \(\chi_{4033}(2279,\cdot)\) \(\chi_{4033}(2329,\cdot)\) \(\chi_{4033}(2683,\cdot)\) \(\chi_{4033}(2847,\cdot)\) \(\chi_{4033}(2899,\cdot)\) \(\chi_{4033}(3002,\cdot)\) \(\chi_{4033}(3089,\cdot)\) \(\chi_{4033}(3217,\cdot)\) \(\chi_{4033}(3276,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{31}{36}\right),e\left(\frac{7}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{41}{54}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{79}{108}\right)\)\(e\left(\frac{17}{54}\right)\)\(e\left(\frac{4}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{31}{108}\right)\)\(e\left(\frac{23}{108}\right)\)
value at  e.g. 2

Related number fields

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