Properties

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

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[15]
 
pari: [g,chi] = znchar(Mod(15,4033))
 

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.js
Orbit index = 253

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 ]
 

\(\chi_{4033}(15,\cdot)\) \(\chi_{4033}(187,\cdot)\) \(\chi_{4033}(198,\cdot)\) \(\chi_{4033}(315,\cdot)\) \(\chi_{4033}(348,\cdot)\) \(\chi_{4033}(405,\cdot)\) \(\chi_{4033}(439,\cdot)\) \(\chi_{4033}(461,\cdot)\) \(\chi_{4033}(836,\cdot)\) \(\chi_{4033}(1016,\cdot)\) \(\chi_{4033}(1112,\cdot)\) \(\chi_{4033}(1171,\cdot)\) \(\chi_{4033}(1313,\cdot)\) \(\chi_{4033}(1330,\cdot)\) \(\chi_{4033}(1356,\cdot)\) \(\chi_{4033}(1424,\cdot)\) \(\chi_{4033}(1615,\cdot)\) \(\chi_{4033}(1650,\cdot)\) \(\chi_{4033}(1793,\cdot)\) \(\chi_{4033}(1983,\cdot)\) \(\chi_{4033}(2151,\cdot)\) \(\chi_{4033}(2314,\cdot)\) \(\chi_{4033}(2386,\cdot)\) \(\chi_{4033}(2407,\cdot)\) \(\chi_{4033}(2625,\cdot)\) \(\chi_{4033}(2696,\cdot)\) \(\chi_{4033}(2869,\cdot)\) \(\chi_{4033}(3187,\cdot)\) \(\chi_{4033}(3234,\cdot)\) \(\chi_{4033}(3275,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{5}{27}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{54}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{41}{108}\right)\)\(e\left(\frac{101}{108}\right)\)\(e\left(\frac{26}{27}\right)\)\(-i\)\(e\left(\frac{1}{27}\right)\)\(e\left(\frac{8}{27}\right)\)\(e\left(\frac{11}{54}\right)\)
value at  e.g. 2

Related number fields

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