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Properties

Label 8712.bx
Modulus $8712$
Conductor $99$
Order $15$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8712, base_ring=CyclotomicField(30)) M = H._module chi = DirichletCharacter(H, M([0,0,20,12])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(2689,8712)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8712\)
Conductor: \(99\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(15\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 99.m
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{15})\)
Fixed field: 15.15.10943023107606534329121.1

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{8712}(2689,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{8712}(4849,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{8712}(4921,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{8712}(5569,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{8712}(5593,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{8712}(7753,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{8712}(7825,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{8712}(8473,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{4}{5}\right)\)