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Properties

Label 12138.bg
Modulus $12138$
Conductor $289$
Order $17$
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(12138, base_ring=CyclotomicField(34)) M = H._module chi = DirichletCharacter(H, M([0,0,22])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(715,12138)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(12138\)
Conductor: \(289\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(17\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 289.f
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: \(\Q(\zeta_{17})\)
Fixed field: Number field defined by a degree 17 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{12138}(715,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{12138}(1429,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\)
\(\chi_{12138}(2143,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{17}\right)\)
\(\chi_{12138}(2857,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{17}\right)\)
\(\chi_{12138}(3571,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{12138}(4285,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\)
\(\chi_{12138}(4999,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{12138}(5713,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{12138}(6427,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{12138}(7141,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{17}\right)\)
\(\chi_{12138}(7855,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{2}{17}\right)\)
\(\chi_{12138}(8569,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\)
\(\chi_{12138}(9283,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\)
\(\chi_{12138}(9997,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{12138}(10711,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{12}{17}\right)\)
\(\chi_{12138}(11425,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{6}{17}\right)\)