Properties

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

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[10]
 
pari: [g,chi] = znchar(Mod(10,4033))
 

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.ir
Orbit index = 226

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 ]
 

\(\chi_{4033}(10,\cdot)\) \(\chi_{4033}(174,\cdot)\) \(\chi_{4033}(232,\cdot)\) \(\chi_{4033}(248,\cdot)\) \(\chi_{4033}(269,\cdot)\) \(\chi_{4033}(285,\cdot)\) \(\chi_{4033}(380,\cdot)\) \(\chi_{4033}(602,\cdot)\) \(\chi_{4033}(750,\cdot)\) \(\chi_{4033}(787,\cdot)\) \(\chi_{4033}(914,\cdot)\) \(\chi_{4033}(951,\cdot)\) \(\chi_{4033}(1025,\cdot)\) \(\chi_{4033}(1210,\cdot)\) \(\chi_{4033}(1268,\cdot)\) \(\chi_{4033}(1358,\cdot)\) \(\chi_{4033}(1617,\cdot)\) \(\chi_{4033}(1675,\cdot)\) \(\chi_{4033}(2024,\cdot)\) \(\chi_{4033}(2156,\cdot)\) \(\chi_{4033}(2193,\cdot)\) \(\chi_{4033}(2341,\cdot)\) \(\chi_{4033}(2468,\cdot)\) \(\chi_{4033}(2563,\cdot)\) \(\chi_{4033}(2579,\cdot)\) \(\chi_{4033}(2653,\cdot)\) \(\chi_{4033}(2674,\cdot)\) \(\chi_{4033}(2711,\cdot)\) \(\chi_{4033}(2764,\cdot)\) \(\chi_{4033}(2933,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{108}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{25}{108}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{85}{108}\right)\)\(e\left(\frac{23}{108}\right)\)
value at  e.g. 2

Related number fields

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