Properties

Label 2601.o
Modulus $2601$
Conductor $51$
Order $16$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2601, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([8,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(224,2601))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2601\)
Conductor: \(51\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 51.i
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{16})\)
Fixed field: \(\Q(\zeta_{51})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{2601}(224,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{1}{16}\right)\) \(-1\)
\(\chi_{2601}(503,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{2601}(827,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(-1\)
\(\chi_{2601}(998,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(-1\)
\(\chi_{2601}(1025,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(-1\)
\(\chi_{2601}(1196,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{2601}(1520,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{2601}(1799,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(-1\)