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Properties

Label 12138.bn
Modulus $12138$
Conductor $6069$
Order $34$
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([17,17,20])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(545,12138)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(12138\)
Conductor: \(6069\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(34\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 6069.bp
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 34 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{12138}(545,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{10}{17}\right)\)
\(\chi_{12138}(1259,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{12138}(1973,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{17}\right)\)
\(\chi_{12138}(2687,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{12138}(3401,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{12138}(4115,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{12138}(4829,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{17}\right)\)
\(\chi_{12138}(5543,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{2}{17}\right)\)
\(\chi_{12138}(6257,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\)
\(\chi_{12138}(6971,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{17}\right)\)
\(\chi_{12138}(7685,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{12138}(8399,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{12}{17}\right)\)
\(\chi_{12138}(9113,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{6}{17}\right)\)
\(\chi_{12138}(10541,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{12138}(11255,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\)
\(\chi_{12138}(11969,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{16}{17}\right)\)