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Properties

Label 8216.fd
Modulus $8216$
Conductor $632$
Order $26$
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(8216, base_ring=CyclotomicField(26)) M = H._module chi = DirichletCharacter(H, M([13,13,0,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(27,8216)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8216\)
Conductor: \(632\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(26\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 632.w
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: \(\Q(\zeta_{13})\)
Fixed field: 26.26.151651640667491538463656289407733022385317053604971635802112.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{8216}(27,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(-1\)
\(\chi_{8216}(859,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(-1\)
\(\chi_{8216}(963,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(-1\)
\(\chi_{8216}(1483,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(-1\)
\(\chi_{8216}(1795,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(-1\)
\(\chi_{8216}(3043,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{26}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(-1\)
\(\chi_{8216}(3251,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(-1\)
\(\chi_{8216}(3667,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{7}{26}\right)\) \(-1\)
\(\chi_{8216}(3771,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{23}{26}\right)\) \(-1\)
\(\chi_{8216}(4811,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{21}{26}\right)\) \(-1\)
\(\chi_{8216}(4915,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{8}{13}\right)\) \(e\left(\frac{1}{26}\right)\) \(-1\)
\(\chi_{8216}(7203,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{26}\right)\) \(e\left(\frac{21}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{9}{26}\right)\) \(e\left(\frac{5}{13}\right)\) \(e\left(\frac{25}{26}\right)\) \(-1\)