Properties

Conductor 847
Order 33
Real no
Primitive no
Minimal yes
Parity even
Orbit label 2541.bo

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(2541)
 
sage: chi = H[67]
 
pari: [g,chi] = znchar(Mod(67,2541))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 847
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 33
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 = 2541.bo
Orbit index = 41

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 ]
 

\(\chi_{2541}(67,\cdot)\) \(\chi_{2541}(100,\cdot)\) \(\chi_{2541}(298,\cdot)\) \(\chi_{2541}(331,\cdot)\) \(\chi_{2541}(529,\cdot)\) \(\chi_{2541}(562,\cdot)\) \(\chi_{2541}(760,\cdot)\) \(\chi_{2541}(793,\cdot)\) \(\chi_{2541}(991,\cdot)\) \(\chi_{2541}(1024,\cdot)\) \(\chi_{2541}(1222,\cdot)\) \(\chi_{2541}(1255,\cdot)\) \(\chi_{2541}(1486,\cdot)\) \(\chi_{2541}(1684,\cdot)\) \(\chi_{2541}(1717,\cdot)\) \(\chi_{2541}(1915,\cdot)\) \(\chi_{2541}(1948,\cdot)\) \(\chi_{2541}(2146,\cdot)\) \(\chi_{2541}(2377,\cdot)\) \(\chi_{2541}(2410,\cdot)\)

Values on generators

\((848,1816,2059)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{10}{11}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{8}{33}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{20}{33}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{7}{33}\right)\)\(e\left(\frac{26}{33}\right)\)\(e\left(\frac{1}{11}\right)\)
value at  e.g. 2

Related number fields

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