Properties

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

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[82]
 
pari: [g,chi] = znchar(Mod(82,4025))
 

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.db
Orbit index = 80

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 ]
 

\(\chi_{4025}(82,\cdot)\) \(\chi_{4025}(243,\cdot)\) \(\chi_{4025}(257,\cdot)\) \(\chi_{4025}(418,\cdot)\) \(\chi_{4025}(432,\cdot)\) \(\chi_{4025}(593,\cdot)\) \(\chi_{4025}(607,\cdot)\) \(\chi_{4025}(768,\cdot)\) \(\chi_{4025}(857,\cdot)\) \(\chi_{4025}(1018,\cdot)\) \(\chi_{4025}(1382,\cdot)\) \(\chi_{4025}(1543,\cdot)\) \(\chi_{4025}(1557,\cdot)\) \(\chi_{4025}(1718,\cdot)\) \(\chi_{4025}(2007,\cdot)\) \(\chi_{4025}(2082,\cdot)\) \(\chi_{4025}(2168,\cdot)\) \(\chi_{4025}(2243,\cdot)\) \(\chi_{4025}(2257,\cdot)\) \(\chi_{4025}(2418,\cdot)\) \(\chi_{4025}(2532,\cdot)\) \(\chi_{4025}(2607,\cdot)\) \(\chi_{4025}(2693,\cdot)\) \(\chi_{4025}(2707,\cdot)\) \(\chi_{4025}(2768,\cdot)\) \(\chi_{4025}(2868,\cdot)\) \(\chi_{4025}(2957,\cdot)\) \(\chi_{4025}(3118,\cdot)\) \(\chi_{4025}(3132,\cdot)\) \(\chi_{4025}(3232,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((i,e\left(\frac{5}{6}\right),e\left(\frac{7}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{25}{132}\right)\)\(e\left(\frac{101}{132}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{19}{132}\right)\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{25}{33}\right)\)
value at  e.g. 2

Related number fields

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