Properties

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

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[30]
 
pari: [g,chi] = znchar(Mod(30,4033))
 

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.io
Orbit index = 223

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 ]
 

\(\chi_{4033}(30,\cdot)\) \(\chi_{4033}(67,\cdot)\) \(\chi_{4033}(262,\cdot)\) \(\chi_{4033}(321,\cdot)\) \(\chi_{4033}(696,\cdot)\) \(\chi_{4033}(733,\cdot)\) \(\chi_{4033}(854,\cdot)\) \(\chi_{4033}(987,\cdot)\) \(\chi_{4033}(1040,\cdot)\) \(\chi_{4033}(1175,\cdot)\) \(\chi_{4033}(1188,\cdot)\) \(\chi_{4033}(1261,\cdot)\) \(\chi_{4033}(1468,\cdot)\) \(\chi_{4033}(1730,\cdot)\) \(\chi_{4033}(1797,\cdot)\) \(\chi_{4033}(1801,\cdot)\) \(\chi_{4033}(1952,\cdot)\) \(\chi_{4033}(2167,\cdot)\) \(\chi_{4033}(2361,\cdot)\) \(\chi_{4033}(2409,\cdot)\) \(\chi_{4033}(2435,\cdot)\) \(\chi_{4033}(2445,\cdot)\) \(\chi_{4033}(2557,\cdot)\) \(\chi_{4033}(2685,\cdot)\) \(\chi_{4033}(2852,\cdot)\) \(\chi_{4033}(3062,\cdot)\) \(\chi_{4033}(3092,\cdot)\) \(\chi_{4033}(3284,\cdot)\) \(\chi_{4033}(3444,\cdot)\) \(\chi_{4033}(3540,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{77}{108}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{1}{36}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{23}{108}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{17}{108}\right)\)\(e\left(\frac{91}{108}\right)\)
value at  e.g. 2

Related number fields

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