Properties

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

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[13]
 
pari: [g,chi] = znchar(Mod(13,4033))
 

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.ia
Orbit index = 209

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 ]
 

\(\chi_{4033}(13,\cdot)\) \(\chi_{4033}(204,\cdot)\) \(\chi_{4033}(257,\cdot)\) \(\chi_{4033}(383,\cdot)\) \(\chi_{4033}(392,\cdot)\) \(\chi_{4033}(426,\cdot)\) \(\chi_{4033}(505,\cdot)\) \(\chi_{4033}(575,\cdot)\) \(\chi_{4033}(930,\cdot)\) \(\chi_{4033}(1053,\cdot)\) \(\chi_{4033}(1142,\cdot)\) \(\chi_{4033}(1241,\cdot)\) \(\chi_{4033}(1297,\cdot)\) \(\chi_{4033}(1367,\cdot)\) \(\chi_{4033}(1411,\cdot)\) \(\chi_{4033}(1720,\cdot)\) \(\chi_{4033}(1791,\cdot)\) \(\chi_{4033}(1835,\cdot)\) \(\chi_{4033}(2198,\cdot)\) \(\chi_{4033}(2242,\cdot)\) \(\chi_{4033}(2313,\cdot)\) \(\chi_{4033}(2622,\cdot)\) \(\chi_{4033}(2666,\cdot)\) \(\chi_{4033}(2736,\cdot)\) \(\chi_{4033}(2792,\cdot)\) \(\chi_{4033}(2891,\cdot)\) \(\chi_{4033}(2980,\cdot)\) \(\chi_{4033}(3103,\cdot)\) \(\chi_{4033}(3458,\cdot)\) \(\chi_{4033}(3528,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{11}{36}\right),e\left(\frac{67}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{11}{54}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{19}{108}\right)\)\(e\left(\frac{47}{54}\right)\)\(e\left(\frac{16}{27}\right)\)\(1\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{91}{108}\right)\)\(e\left(\frac{71}{108}\right)\)
value at  e.g. 2

Related number fields

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