Properties

Conductor 805
Order 132
Real No
Primitive No
Parity Odd
Orbit Label 4025.cz

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[32]
 
pari: [g,chi] = znchar(Mod(32,4025))
 

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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4025.cz
Orbit index = 78

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 ]
 

\(\chi_{4025}(18,\cdot)\) \(\chi_{4025}(32,\cdot)\) \(\chi_{4025}(193,\cdot)\) \(\chi_{4025}(282,\cdot)\) \(\chi_{4025}(443,\cdot)\) \(\chi_{4025}(807,\cdot)\) \(\chi_{4025}(968,\cdot)\) \(\chi_{4025}(982,\cdot)\) \(\chi_{4025}(1143,\cdot)\) \(\chi_{4025}(1432,\cdot)\) \(\chi_{4025}(1507,\cdot)\) \(\chi_{4025}(1593,\cdot)\) \(\chi_{4025}(1668,\cdot)\) \(\chi_{4025}(1682,\cdot)\) \(\chi_{4025}(1843,\cdot)\) \(\chi_{4025}(1957,\cdot)\) \(\chi_{4025}(2032,\cdot)\) \(\chi_{4025}(2118,\cdot)\) \(\chi_{4025}(2132,\cdot)\) \(\chi_{4025}(2193,\cdot)\) \(\chi_{4025}(2293,\cdot)\) \(\chi_{4025}(2382,\cdot)\) \(\chi_{4025}(2543,\cdot)\) \(\chi_{4025}(2557,\cdot)\) \(\chi_{4025}(2657,\cdot)\) \(\chi_{4025}(2718,\cdot)\) \(\chi_{4025}(2732,\cdot)\) \(\chi_{4025}(2818,\cdot)\) \(\chi_{4025}(2832,\cdot)\) \(\chi_{4025}(2893,\cdot)\) ...

Inducing primitive character

\(\chi_{805}(32,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{5}{11}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{65}{132}\right)\)\(e\left(\frac{91}{132}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{25}{33}\right)\)\(e\left(\frac{89}{132}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{32}{33}\right)\)
value at  e.g. 2

Related number fields

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