Properties

Conductor 805
Order 132
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4025.cy

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[107]
 
pari: [g,chi] = znchar(Mod(107,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 805
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 132
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4025.cy
Orbit index = 77

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 ]
 

\(\chi_{4025}(107,\cdot)\) \(\chi_{4025}(268,\cdot)\) \(\chi_{4025}(382,\cdot)\) \(\chi_{4025}(457,\cdot)\) \(\chi_{4025}(543,\cdot)\) \(\chi_{4025}(557,\cdot)\) \(\chi_{4025}(618,\cdot)\) \(\chi_{4025}(632,\cdot)\) \(\chi_{4025}(718,\cdot)\) \(\chi_{4025}(732,\cdot)\) \(\chi_{4025}(793,\cdot)\) \(\chi_{4025}(893,\cdot)\) \(\chi_{4025}(907,\cdot)\) \(\chi_{4025}(1068,\cdot)\) \(\chi_{4025}(1157,\cdot)\) \(\chi_{4025}(1257,\cdot)\) \(\chi_{4025}(1318,\cdot)\) \(\chi_{4025}(1332,\cdot)\) \(\chi_{4025}(1418,\cdot)\) \(\chi_{4025}(1493,\cdot)\) \(\chi_{4025}(1607,\cdot)\) \(\chi_{4025}(1768,\cdot)\) \(\chi_{4025}(1782,\cdot)\) \(\chi_{4025}(1857,\cdot)\) \(\chi_{4025}(1943,\cdot)\) \(\chi_{4025}(2018,\cdot)\) \(\chi_{4025}(2307,\cdot)\) \(\chi_{4025}(2468,\cdot)\) \(\chi_{4025}(2482,\cdot)\) \(\chi_{4025}(2643,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((i,e\left(\frac{1}{3}\right),e\left(\frac{17}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{61}{132}\right)\)\(e\left(\frac{59}{132}\right)\)\(e\left(\frac{61}{66}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{49}{132}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{28}{33}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)