↑

Properties

Label 608.bo
Modulus $608$
Conductor $304$
Order $36$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(608, base_ring=CyclotomicField(36)) M = H._module chi = DirichletCharacter(H, M([18,9,14])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(71,608)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(608\)
Conductor: \(304\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(36\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 304.bg
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: \(\Q(\zeta_{36})\)
Fixed field: 36.36.19036714782161565107424425435655777110146017378670996611401194085493506048.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(17\) \(21\) \(23\)
\(\chi_{608}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{608}(135,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{608}(167,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{608}(231,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{608}(279,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{608}(295,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{608}(375,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{608}(439,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{608}(471,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{608}(535,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{608}(583,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{608}(599,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{8}{9}\right)\)