Properties

Label 740.ca
Modulus $740$
Conductor $740$
Order $36$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(740, base_ring=CyclotomicField(36))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([18,18,35]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(19,740))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(740\)
Conductor: \(740\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(36\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{36})\)
Fixed field: 36.36.2021157996966699236888348986167488408933250634681517576814592000000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{740}(19,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{740}(39,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{740}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{740}(79,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{740}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{740}(279,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{740}(439,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{740}(459,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{740}(479,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{740}(499,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{740}(579,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{740}(679,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)