Properties

Conductor 4033
Order 108
Real No
Primitive Yes
Parity Odd
Orbit Label 4033.ic

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[22]
 
pari: [g,chi] = znchar(Mod(22,4033))
 

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 = Odd
Orbit label = 4033.ic
Orbit index = 211

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 ]
 

\(\chi_{4033}(5,\cdot)\) \(\chi_{4033}(22,\cdot)\) \(\chi_{4033}(35,\cdot)\) \(\chi_{4033}(116,\cdot)\) \(\chi_{4033}(135,\cdot)\) \(\chi_{4033}(239,\cdot)\) \(\chi_{4033}(550,\cdot)\) \(\chi_{4033}(594,\cdot)\) \(\chi_{4033}(661,\cdot)\) \(\chi_{4033}(812,\cdot)\) \(\chi_{4033}(875,\cdot)\) \(\chi_{4033}(945,\cdot)\) \(\chi_{4033}(1078,\cdot)\) \(\chi_{4033}(1317,\cdot)\) \(\chi_{4033}(1495,\cdot)\) \(\chi_{4033}(1498,\cdot)\) \(\chi_{4033}(1623,\cdot)\) \(\chi_{4033}(1683,\cdot)\) \(\chi_{4033}(1715,\cdot)\) \(\chi_{4033}(1759,\cdot)\) \(\chi_{4033}(1942,\cdot)\) \(\chi_{4033}(2092,\cdot)\) \(\chi_{4033}(2420,\cdot)\) \(\chi_{4033}(2751,\cdot)\) \(\chi_{4033}(3125,\cdot)\) \(\chi_{4033}(3130,\cdot)\) \(\chi_{4033}(3132,\cdot)\) \(\chi_{4033}(3295,\cdot)\) \(\chi_{4033}(3460,\cdot)\) \(\chi_{4033}(3491,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{31}{36}\right),e\left(\frac{8}{27}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(-i\)\(e\left(\frac{43}{54}\right)\)\(-1\)\(e\left(\frac{35}{108}\right)\)\(e\left(\frac{59}{108}\right)\)\(e\left(\frac{11}{27}\right)\)\(i\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{23}{54}\right)\)
value at  e.g. 2

Related number fields

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