Properties

Conductor 4033
Order 54
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.gz

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[169]
 
pari: [g,chi] = znchar(Mod(169,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 54
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.gz
Orbit index = 182

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 ]
 

\(\chi_{4033}(169,\cdot)\) \(\chi_{4033}(410,\cdot)\) \(\chi_{4033}(448,\cdot)\) \(\chi_{4033}(946,\cdot)\) \(\chi_{4033}(1286,\cdot)\) \(\chi_{4033}(1410,\cdot)\) \(\chi_{4033}(1446,\cdot)\) \(\chi_{4033}(1501,\cdot)\) \(\chi_{4033}(1505,\cdot)\) \(\chi_{4033}(1521,\cdot)\) \(\chi_{4033}(1838,\cdot)\) \(\chi_{4033}(2211,\cdot)\) \(\chi_{4033}(2652,\cdot)\) \(\chi_{4033}(3508,\cdot)\) \(\chi_{4033}(3703,\cdot)\) \(\chi_{4033}(3767,\cdot)\) \(\chi_{4033}(3952,\cdot)\) \(\chi_{4033}(4024,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{13}{54}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{19}{54}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{5}{27}\right)\)\(1\)\(e\left(\frac{22}{27}\right)\)\(e\left(\frac{37}{54}\right)\)\(e\left(\frac{17}{54}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{27})\)