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Properties

Label 740.bw
Modulus $740$
Conductor $740$
Order $36$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) M = H._module chi = DirichletCharacter(H, M([18,27,19])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(183,740)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(740\)
Conductor: \(740\)
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: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.0.3947574212825584447047556613608375798697755145862339017216000000000000000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{740}(183,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{740}(187,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{740}(383,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{740}(427,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{740}(463,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{740}(503,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{740}(523,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{740}(587,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{740}(607,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{740}(647,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{740}(683,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{740}(727,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\)