Properties

Conductor 4033
Order 108
Real No
Primitive Yes
Parity Even
Orbit Label 4033.ih

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(4033)
 
sage: chi = H[1842]
 
pari: [g,chi] = znchar(Mod(1842,4033))
 

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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4033.ih
Orbit index = 216

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 ]
 

\(\chi_{4033}(14,\cdot)\) \(\chi_{4033}(51,\cdot)\) \(\chi_{4033}(162,\cdot)\) \(\chi_{4033}(208,\cdot)\) \(\chi_{4033}(288,\cdot)\) \(\chi_{4033}(430,\cdot)\) \(\chi_{4033}(473,\cdot)\) \(\chi_{4033}(532,\cdot)\) \(\chi_{4033}(822,\cdot)\) \(\chi_{4033}(1028,\cdot)\) \(\chi_{4033}(1050,\cdot)\) \(\chi_{4033}(1155,\cdot)\) \(\chi_{4033}(1266,\cdot)\) \(\chi_{4033}(1435,\cdot)\) \(\chi_{4033}(1842,\cdot)\) \(\chi_{4033}(1910,\cdot)\) \(\chi_{4033}(1932,\cdot)\) \(\chi_{4033}(1938,\cdot)\) \(\chi_{4033}(2095,\cdot)\) \(\chi_{4033}(2101,\cdot)\) \(\chi_{4033}(2123,\cdot)\) \(\chi_{4033}(2191,\cdot)\) \(\chi_{4033}(2598,\cdot)\) \(\chi_{4033}(2767,\cdot)\) \(\chi_{4033}(2878,\cdot)\) \(\chi_{4033}(2983,\cdot)\) \(\chi_{4033}(3005,\cdot)\) \(\chi_{4033}(3211,\cdot)\) \(\chi_{4033}(3501,\cdot)\) \(\chi_{4033}(3560,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{29}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{89}{108}\right)\)\(e\left(\frac{1}{54}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{77}{108}\right)\)\(e\left(\frac{85}{108}\right)\)
value at  e.g. 2

Related number fields

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