Properties

Conductor 161
Order 66
Real No
Primitive No
Parity Odd
Orbit Label 4025.cp

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[26]
 
pari: [g,chi] = znchar(Mod(26,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 161
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 66
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.cp
Orbit index = 68

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 ]
 

\(\chi_{4025}(26,\cdot)\) \(\chi_{4025}(101,\cdot)\) \(\chi_{4025}(376,\cdot)\) \(\chi_{4025}(726,\cdot)\) \(\chi_{4025}(901,\cdot)\) \(\chi_{4025}(1076,\cdot)\) \(\chi_{4025}(1251,\cdot)\) \(\chi_{4025}(1501,\cdot)\) \(\chi_{4025}(2026,\cdot)\) \(\chi_{4025}(2201,\cdot)\) \(\chi_{4025}(2651,\cdot)\) \(\chi_{4025}(2726,\cdot)\) \(\chi_{4025}(2901,\cdot)\) \(\chi_{4025}(3176,\cdot)\) \(\chi_{4025}(3251,\cdot)\) \(\chi_{4025}(3351,\cdot)\) \(\chi_{4025}(3601,\cdot)\) \(\chi_{4025}(3776,\cdot)\) \(\chi_{4025}(3876,\cdot)\) \(\chi_{4025}(3951,\cdot)\)

Inducing primitive character

\(\chi_{161}(26,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{8}{11}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{8}{33}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{31}{33}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{47}{66}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{16}{33}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)