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Properties

Label 289.g
Modulus $289$
Conductor $289$
Order $34$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(34)) M = H._module chi = DirichletCharacter(H, M([27])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(16,289)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(289\)
Conductor: \(289\)
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: yes
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\) \(8\) \(9\) \(10\) \(11\)
\(\chi_{289}(16,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{9}{34}\right)\)
\(\chi_{289}(33,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{1}{34}\right)\)
\(\chi_{289}(50,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{27}{34}\right)\)
\(\chi_{289}(67,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{19}{34}\right)\)
\(\chi_{289}(84,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{11}{34}\right)\)
\(\chi_{289}(101,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{3}{34}\right)\)
\(\chi_{289}(118,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{29}{34}\right)\)
\(\chi_{289}(135,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{21}{34}\right)\)
\(\chi_{289}(152,\cdot)\) \(1\) \(1\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{34}\right)\)
\(\chi_{289}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{5}{34}\right)\)
\(\chi_{289}(186,\cdot)\) \(1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{13}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{31}{34}\right)\)
\(\chi_{289}(203,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{23}{34}\right)\)
\(\chi_{289}(220,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{15}{34}\right)\)
\(\chi_{289}(237,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{7}{34}\right)\)
\(\chi_{289}(254,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{33}{34}\right)\)
\(\chi_{289}(271,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{25}{34}\right)\)