Properties

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

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[171]
 
pari: [g,chi] = znchar(Mod(171,4033))
 

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.ii
Orbit index = 217

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 ]
 

\(\chi_{4033}(171,\cdot)\) \(\chi_{4033}(236,\cdot)\) \(\chi_{4033}(643,\cdot)\) \(\chi_{4033}(711,\cdot)\) \(\chi_{4033}(726,\cdot)\) \(\chi_{4033}(769,\cdot)\) \(\chi_{4033}(896,\cdot)\) \(\chi_{4033}(902,\cdot)\) \(\chi_{4033}(911,\cdot)\) \(\chi_{4033}(991,\cdot)\) \(\chi_{4033}(1213,\cdot)\) \(\chi_{4033}(1250,\cdot)\) \(\chi_{4033}(1361,\cdot)\) \(\chi_{4033}(1568,\cdot)\) \(\chi_{4033}(1679,\cdot)\) \(\chi_{4033}(1731,\cdot)\) \(\chi_{4033}(1784,\cdot)\) \(\chi_{4033}(2012,\cdot)\) \(\chi_{4033}(2021,\cdot)\) \(\chi_{4033}(2249,\cdot)\) \(\chi_{4033}(2302,\cdot)\) \(\chi_{4033}(2354,\cdot)\) \(\chi_{4033}(2465,\cdot)\) \(\chi_{4033}(2672,\cdot)\) \(\chi_{4033}(2783,\cdot)\) \(\chi_{4033}(2820,\cdot)\) \(\chi_{4033}(3042,\cdot)\) \(\chi_{4033}(3122,\cdot)\) \(\chi_{4033}(3131,\cdot)\) \(\chi_{4033}(3137,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{5}{12}\right),e\left(\frac{71}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{1}{54}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{59}{108}\right)\)\(e\left(\frac{49}{54}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{27}\right)\)\(e\left(\frac{47}{108}\right)\)\(e\left(\frac{7}{108}\right)\)
value at  e.g. 2

Related number fields

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