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Properties

Label 7728.ew
Modulus $7728$
Conductor $644$
Order $22$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7728, base_ring=CyclotomicField(22)) M = H._module chi = DirichletCharacter(H, M([11,0,0,11,8])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(223,7728)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(7728\)
Conductor: \(644\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(22\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 644.t
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{11})\)
Fixed field: Number field defined by a degree 22 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{7728}(223,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{7728}(1231,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{7728}(1567,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{7728}(2239,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{7728}(2911,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{7728}(3247,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{7728}(3583,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{7728}(3919,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{7728}(6607,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{7728}(7615,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\)