Properties

Conductor 4025
Order 660
Real No
Primitive Yes
Parity Odd
Orbit Label 4025.dp

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(4025)
 
sage: chi = H[17]
 
pari: [g,chi] = znchar(Mod(17,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 660
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 = 4025.dp
Orbit index = 94

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 ]
 

\(\chi_{4025}(17,\cdot)\) \(\chi_{4025}(33,\cdot)\) \(\chi_{4025}(38,\cdot)\) \(\chi_{4025}(103,\cdot)\) \(\chi_{4025}(122,\cdot)\) \(\chi_{4025}(152,\cdot)\) \(\chi_{4025}(178,\cdot)\) \(\chi_{4025}(222,\cdot)\) \(\chi_{4025}(227,\cdot)\) \(\chi_{4025}(283,\cdot)\) \(\chi_{4025}(297,\cdot)\) \(\chi_{4025}(313,\cdot)\) \(\chi_{4025}(327,\cdot)\) \(\chi_{4025}(362,\cdot)\) \(\chi_{4025}(383,\cdot)\) \(\chi_{4025}(388,\cdot)\) \(\chi_{4025}(402,\cdot)\) \(\chi_{4025}(458,\cdot)\) \(\chi_{4025}(467,\cdot)\) \(\chi_{4025}(488,\cdot)\) \(\chi_{4025}(502,\cdot)\) \(\chi_{4025}(523,\cdot)\) \(\chi_{4025}(563,\cdot)\) \(\chi_{4025}(572,\cdot)\) \(\chi_{4025}(612,\cdot)\) \(\chi_{4025}(628,\cdot)\) \(\chi_{4025}(642,\cdot)\) \(\chi_{4025}(663,\cdot)\) \(\chi_{4025}(677,\cdot)\) \(\chi_{4025}(733,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{13}{20}\right),e\left(\frac{1}{6}\right),e\left(\frac{7}{22}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{409}{660}\right)\)\(e\left(\frac{533}{660}\right)\)\(e\left(\frac{79}{330}\right)\)\(e\left(\frac{47}{110}\right)\)\(e\left(\frac{189}{220}\right)\)\(e\left(\frac{203}{330}\right)\)\(e\left(\frac{307}{330}\right)\)\(e\left(\frac{31}{660}\right)\)\(e\left(\frac{67}{220}\right)\)\(e\left(\frac{79}{165}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{660})\)